# Vibrational Coupling of Nearest Neighbors in 1-D Spin Crossover Polymers of Rigid Bridging Ligands. A Nuclear Inelastic Scattering and DFT Study

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{3}]

^{2+})

_{n}have been compared for the low-spin phase, for the mixed high-spin and low-spin phases, as well as for Zn(II) diluted samples. Within this series a change in the vibrational pattern in the 320–500 cm

^{−1}region is observed. Significant shifts and decreasing intensity of bands at ~320 cm

^{−1}and bands over 400 cm

^{−1}are observed as the molar fraction of the low-spin (LS) centers decrease. Density functional theory calculations using Gaussian09 (B3LYP/CEP-31G) for pentameric, heptameric, and nonameric model molecules yielded the normal modes of several spin isomers: these include the all high-spin (HS) and the all low-spin (LS) configuration but also mixtures of LS and HS centers, with a special focus on those with LS centers in a HS matrix and vice versa. The calculations reproduce the observed spectral changes and show that they are caused by strain extorted on a LS Fe(II) center by its HS neighbors due to the rigid character of the bridging aminotriazole ligand. Additionally, the normal mode analysis of several spin isomers points towards a coupling of the vibrations of the iron centers of the same spin: the metal-ligand stretching modes of the all LS and the all HS spin isomers reveal a collective character: all centers of the same spin are involved in characteristic normal modes. For the isomers containing both LS and HS centers, the vibrational behavior corresponds to two different subsets (sublattices) the vibrational modes of which are not coupled. Finally, the calculation of nuclear inelastic scattering data of spin isomers containing a ca. 1:1 mixture of HS and LS Fe(II) points towards the formation of blocks of the same spin during the spin transition, rather than to alternate structures with a HS-LS-HS-LS-HS motif.

## 1. Introduction

_{4})] complex [8,25] an interaction parameter Γ of more than 10

^{3}cm

^{−1}has been reported [26,27], which is one order of magnitude larger than Γ reported for molecular crystals of mononuclear Fe(II) SCO systems [24]. This indicates that, in 1-D polymers in which neighboring Fe(II) centers are linked by three rigid bridging ligands, the influence of the spin state of the neighbors on the spin transition energy of a given center is much higher than in molecular crystals of SCO complexes.

_{3}O

_{3}coordination. Therefore, the spin state of the terminal iron is always HS (cf. [1]). In order to simplify the DFT calculations all the models discussed here are centrosymmetric and contain an odd number of iron centers unless stated otherwise. It is worth to note that the calculated NIS spectra and the principal geometrical parameters do not differ significantly if calculated for a pentameric, or an even numbered hexameric, model molecule [29].

_{vib}for a transition e.g., in a pentameric chain from the HS-LS-LS-LS-HS to the HS-LS-HS-LS-HS state (furthermore denoted as: HLLLH → HLHLH) is about twice as large as for the HHLHH → HHHHH transition where the switching center has HS neighbors. We have interpreted this effect as the result of a softening of LS vibrational modes in the HS matrix and the corresponding hardening of the HS modes in the LS matrix. This effect is a result of the elongation with respect to shortening of the Fe-N bonds, as mentioned above [28].

^{57}Fe also called nuclear resonance vibrational spectroscopy (NRVS) is particularly well suited to study the vibrational properties of Fe(II) SCO systems [30,31]. This synchrotron-based technique uses the

^{57}Fe nucleus as a nuclear probe to detect vibrational modes, which include iron movement. NIS has no optical selection rules, the only requirement is that the vibrational mode involves the displacement of the

^{57}Fe site. The first results, including an initial modeling with a pentameric model, have been presented as a conference paper [32]. A previous NIS study of Fe(atrz)

_{3}

^{2+}complexes revealed that the HS and LS marker bands are clearly distinct and rich in spectral features, but their calculated frequencies are quite independent on the type of anion used in the trimeric and pentameric models [29]. Within the present work we extend the DFT calculations to heptameric and nonameric models, that allow to investigate more spin isomers than the pentameric ones and correspond better to the 1-D polymers of Fe(II) complexes. On the basis of DFT calculations we present calculated vibrational partial density of states (pDOS), which are compared to the experimentally obtained pDOS of three samples: (i) The methanosulphonate salt of Fe(atrz)

_{3}

^{2+}(atrz = 4-amino-1,2,4-triazole), denoted as (

**1**), which is completely LS at T = 80 K; (ii) the tosylate salt of Fe(atrz)

_{3}

^{2+}(

**2**) that reveals a hysteretic transition with T

_{c}between 273 and 288 K. For this sample we observe an approximate 1:1 mixture of LS and HS sites around 273 K; (iii) the same salt diluted to 10% in the matrix of a zinc analogue (

**3**). At 80 K this sample has LS centers which have predominantly Zn

^{2+}centers as neighbors to the iron centers. We have chosen Zn

^{2+}, because it is considered to be a structural analogue of HS Fe(II) [3].

## 2. Materials and Methods

**1**) and (

**2**) were prepared using standard methods as described in [29,33], respectively. (

**3**) was prepared analogously to (

**1**), using a 1:9 mixture of

^{57}Fe/Zn metanosulphonates. NIS was performed at the Nuclear Resonance Beamline ID 18 of the European Synchrotron Radiation Facility (ESRF) in Grenoble, France (see [32,33] for details) and at P01, PETRA III, DESY in Hamburg, Germany. The storage ring PETRA III was operated in 40 bunch mode with a bunch separation of 192 ns. DFT calculations were performed using the B3LYP* density functional [34,35] and the CEP-31G basis set [36,37,38] as described in [28] using Gaussian09 Rev. D.01 [39] with full-charge compensation. For the penta- and heptameric models, the terminal iron centers were modeled as HS ones, with three coordinated water molecules. In this study we will use the previously [28] introduced notation of spin isomers. For example (see Scheme 1) HLLLH denotes the pentameric model molecule (H

_{2}O)

_{3}Fe(atrz)

_{3}[Fe

_{3}(atrz)

_{6}] (atrz)

_{3}Fe(H

_{2}O)

_{3}, with the three inner Fe(II) in the LS state and the two terminal Fe(II) centers in the HS state. In the case of nonameric models HHHHHHHHH, HHHHLHHHH and HLLLLHHHH the terminal HS centers were modeled with Zn(II) ions. For each model molecule frequency calculations were performed using the DFT-optimized structure. Unless indicated otherwise the calculated model molecules have C

_{i}symmetry. In each case the tight option of the integration grid was used. The simulated NIS spectra and the partial density of vibrational states of

^{57}Fe were obtained by using the program nisspec2 [40].

## 3. Results and Discussion

**1**) revealed that all iron centers of this complex are in the LS state at 80 K. On the contrary, the tosylate salt (

**2**) showed 55% of LS and 45% of HS isomers at 273 K, while the zinc-diluted sample (

**3**) displays ca. 44% of LS and 56% of HS at 80 K. The data for (

**1**) and (

**2**) are line with the magnetic susceptibility data reported previously for methanosulphonate of Fe(II) aminotriazole systems. The former reveals a hysteretic transition with T

_{c}↓ of ~ 260 K and T

_{c}↑ of ~ 295 K [41]. Other authors [2] quote T

_{c}↓ ~ 273 K and T

_{c}↑ ~ 288 K. The tosylate salt reveals a hysteretic transition with T

_{c}↓ ~279 K and T

_{c}↑ ~ 296 K as detected by optical methods [42].

**1**), (

**2**) and (

**3**) obtained from the NIS experiments in the frequency region where iron ligand vibrations occur are shown in Figure 1a–c. Although (

**2**) and (

**3**) reveal both a ratio of HS to LS centers of ca. 1:1 under the experimental conditions applied here, the LS iron centers in (

**3**) are diluted to a molar ratio of 0.05 in a HS-like matrix of Zn

^{2+}centers. Thus, (

**3**) represents a sample which has LS iron centers as point “defects” in a HS matrix.

**1**) and (

**2**) occurs at about room temperature (with hysteresis), the pDOS shown in Figure 1a is characteristic for a [Fe(atrz)

_{3}]

^{2+}polymer with all iron sites being in the LS state and the pDOS shown in Figure 1b reflects a [Fe(atrz)

_{3}]

^{2+}polymer with ~50% HS iron sites and ~50% LS iron sites. The pDOS of (

**3**) shown in Figure 1c is also characteristic for a situation where ~50% of the NIS-visible

^{57}Fe sites are in the LS state and ~50% in the HS state, but these sites are separated from each other by the diamagnetic Zn(II) ions which act as NIS silent models of HS sites [3]. The inspection of Figure 1 shows that the band at ~320 cm

^{−1}is prominent in the pDOS of (

**1**) (Figure 1a) but it has less intensity in the pDOS of (

**2**) (Figure 1b) and in the Zn(II) diluted sample (

**3**) (Figure 1c). The same trend is observed for bands in the region between 420 and 500 cm

^{−1}, for (

**3**) these bands nearly vanish. These changes are concomitant with the decreasing probability that a LS center has LS neighbors within the 1-D polymer series (

**1**), (

**2**), and (

**3**). There is also a concomitant change of the spectral pattern in the 350–390 cm

^{−1}area—the relative broad band with at least two maxima at 358 and 386 cm

^{−1}in (

**1**) and (

**2**) is replaced by a more narrow band with a maximum at 379 cm

^{−1}in (

**3**).

_{i}symmetry were used. Calculations investigating the effect of the number of LS sites on the overall pDOS are shown in Figure 2b–d in comparison to the experimental pDOS (Figure 1a and Figure 2a). Surprisingly, the reproducibility of the experimental pDOS by all three structural models is quite reasonable. However, the vibrational signature of the central Fe(1) shows a very significant effect on the number of neighboring LS sites (Figure 2e–g). In fact, the calculations performed with the nonameric model show a pDOS of the central Fe(1) (Figure 2g) which very much resembles the shape of the pDOS of the whole nonameric model displayed in Figure 1d.

**1**) are shown in Table 1.

^{−1}for LS (

**1**) (see Figure 1a and Figure 2a). For the pentameric model two NIS active vibrations are predicted in this area: Fe–N stretching of Fe(1) (the central one) at 326 cm

^{−1}(movie ls_pent_326) and the corresponding vibration of centrosymmetrically located Fe(2) and Fe(2’) at 311 cm

^{−1}(movie ls_pent_311) (see Figure 2b). For the heptameric model the pDOS in this area is dominated by two vibrations occurring at 324 and 325 cm

^{−1}which involve primarily Fe–N stretching of Fe(1) (movie ls_hept_325) (see Figure 2c). The nonameric model reveals the significant stretching of Fe(1), Fe(2)/(2’) and Fe(3)/(3’) Fe–N at 327 cm

^{−1}(movie ls_non_327) (see Figure 2a). What happens when all the neighbors of the central LS Fe(1) turn to the HS state? With the heptameric model, two LS Fe–N stretching vibrations are now predicted at 301 and 305 cm

^{−1}(movie HHHLHHH_hept_305) (see Figure 3f), while the pentameric model yields two similar bands at 302 and 303 cm

^{−1}(movie HHLHH_pent_303) (see Figure 3e). For a nonameric model no band in the pDOS can be found that corresponds to a vibration involving the LS Fe(1) in the region below 350 cm

^{−1}(see Figure 3g). Accordingly, we explain the experimentally observed band shift of ca. 15 cm

^{−1}by the change of the bond lengths. Indeed, previously reported calculations reveal that the Fe(1)–N bond lengths for a pentameric HLLLH isomer (B3LYP*/CEP-31G) are ca. 0.024 Å shorter than for a HHLHH one, implying a possible shift of the stretching vibrations towards the lower frequencies for the latter.

**1**) to (

**3**) are those at 496 cm

^{−1}and 465 cm

^{−1}. The first one corresponds to the in-phase movement of all three LS Fe centers along the long axis of the molecule in the pentameric HLLLH model, predicted at 498 cm

^{−1}(movie ls_pent_498) (see Figure 2b). The analogous mode, involving the movement of all five LS Fe center is predicted to occur at 504 cm

^{−1}for the heptameric model, while the nonameric one predicts this mode at practically the same energy of 505 cm

^{−1}(movie ls_non_505) (see Figure 2c). Within the HS matrix, this LS vibration involves only the Fe(1) atom and does not involve the movement of the HS neighbors. It is predicted to occur at 461 cm

^{−1}for the pentameric HHLHH model and at 460 cm

^{−1}for the heptameric HHHLHHH (movie HHHLHHH_460) (see Figure 3e,f). In this case the observed shift of ~40 cm

^{−1}is, again, due to the differences in Fe-N bonds mentioned above. The pronounced change in the band intensity in the pDOS is related to a lower cumulative projection of the mean square displacement of the Fe atoms: the fewer iron atoms are involved in the stretching mode, the less displacement of the iron has been calculated.

^{−1}in (

**1**) is assigned to an out-of-phase Fe-N stretching, perpendicular to the long axis, involving movement of Fe(1) and Fe(2)/Fe(2’) within the pentameric model. This mode is calculated to occur at 467 cm

^{−1}for HLLLH (see Figure 2b). For the heptameric model the analogous vibration involves atoms Fe(3)/Fe(3’) and is predicted at 461 cm

^{−1}(see Figure 2c), while the nonameric model has it at 471 cm

^{−1}(see Figure 2d). Upon switching all Fe centers to the HS state except the Fe(1) centers, which stay LS, this vibration shifts to 445, 448 cm

^{−1}and 435 cm

^{−1}in the pentameric, heptameric, and nonameric models, respectively (see Figure 3e–g).

**2**). As shown previously, minor shifts (a few cm

^{−1}) of bands of the LS isomer above 400 cm

^{−1}are observed in comparison to the all LS (

**1**). These could be interpreted by using the pentameric HLLHH model [32]. Here we present the results of DFT calculations based on the heptameric and the nonameric models. These allow the comparison of three distribution patterns of the LS and HS centers by keeping an effective LS:HS ratio of one. We discuss first the situation where both spin isomers are present in one chain, distributed according to two different patterns: (a) the one with all centers having neighbors of different spin—this pattern we denote as the “chessboard” (alternate) one, for example in a HLHLHLH isomer; and (b) the one with two blocks of the same spin—this pattern we denote as the “block” one, for example HLLLHHH or HHHHLLH isomers. However, there is also a possibility that a sample with a LS:HS ratio of one consists of a mixture of all LS and all HS chains. The pDOS of such a system would then correspond to the sum of the pDOS calculated for all LS and all HS chains. This situation can be modeled by taking the sum of the pDOS calculated i.e., for a HLLLLLH and a HHHHHHH heptameric models (or corresponding nonameric ones). In Figure 4 the comparison of the experimentally-determined pDOS of (

**2**) with several models used for DFT calculations is shown.

**2**) at 273 K suggests that the block model fits better to the experimental results. The HS marker bands occurring at 180–290 cm

^{−1}are better reproduced by the block model, than by the chessboard one. For the block models they span the 210–290 cm

^{−1}range, while for the checkerboard they are calculated to occur in the 230–320 cm

^{−1}range. Additionally, the double peak character of this band cluster is better reproduced with the block model, particularly for the nonameric HLLLLHHHH model (see Figure 4f). On the other hand, the distribution of the bands of the LS center seems to be more evenly distributed for the block models compared to the checkerboard ones. Such an even distribution reflects better the character of the LS part of the experimentally determined pDOS of (

**2**) at 273 K displayed in Figure 4a.

**2**) obtained at a temperature close to T

_{c}implies that the 1:1 mixture of LS and HS centers reveals a spectral pattern that indicates the clustering of the centers of the same spin. It is not characteristic for an alternate or a random distribution of HS and LS centers along the chain.

^{−1}for the HHHHH model shifts only to 235 cm

^{−1}for HLHLH (see Figure 5, left) (compare the movies hs_pent_227 and HLHLH_pent_235). On the other hand the predicted mode at 160 cm

^{−1}in HLHLH resembles that predicted at 128 cm

^{−1}for HHHHH (cf. hs_pent_128 and HLHLH _pent_160). The mode predicted in the 181–187 cm

^{−1}range for heptameric HLLHLLH corresponds to the band obtained for HHHHHHH (see Figure 5, middle) as low as at 120 cm

^{−1}(cf. movies hs_hept_120 and HLLHLLH_hept_184). Yet the mode at 273 cm

^{−1}predicted for HHHHHHH that gives the most intensive NIS peak is comparable to both of those of HHHLHHH at 272 cm

^{−1}and and 291 cm

^{−1}) (cf. movies hs_hept_273, HLLHLLH _hept_272, and HLLHLLH _hept_291). Additionally, all three models predict a disappearance of the peak at 310–320 cm

^{−1}, which is present in the all HS molecule, upon spin switching of the neighbors of Fe(1). This less clear picture may be due to a higher elasticity of the HS Fe(II)-N

_{6}coordination core.

^{−1}(cf. movie non_chessb_411) involving only the LS centers and (ii) that at 318 cm

^{−1}(cf. movie non_chessb_318) involving only HS centers. A similar effect is observed for the block structure isomer HLLLHHL, for which the correlated stretching of the above type is predicted at 389 cm

^{−1}, involving the LS ensemble while the most similar modes for the HS one could be found at 256 and 267 cm

^{−1}(compare the movies hept_block_LLLHH_389/256/267). This effect suggests that in both alternate and in domain-like structures the two spin isomers form two independent subunits which can be regarded as “sublattices”. Taking into account that according to theoretical models the spin crossover in solids takes place via interactions communicated through low energy lattice vibrations the similar decoupling for the acoustic phonons may be of importance for the character of the transition [43,44].

_{4}] system diluted in Ni(pyrazine)[Pt(CN)

_{4}] and Co(pyrazine)[Pt(CN)

_{4}] matrices [45]. In this study it has been observed that low-frequency HS and LS Raman marker bands shift on increasing dilution of the spin crossover centers. The LS marker band at 120 cm

^{−1}shifted to lower frequencies with decreasing molar fraction of iron, while an upshift of the HS band at ca. 50 cm

^{−1}was observed.

_{vib}, is significantly higher for the first one. The entropy difference that we called S

_{coop}varies from ca. 20 J/K∙mol at 50 K to ca. 35 J/K∙mol at 400 K. Thus, the LS neighbors destabilize the LS center entropically, while the HS ones stabilize it. It is interesting to compare this outcome and the here presented results with the predictions of an Ising-like model by Bousseksou et al. [51]. These authors define the vibrational coupling parameter η as:

_{eq}= n

_{HS}/(1 − n

_{HS}) as follows:

_{HS/LS}the degeneracies of a given spin state. A positive value of η results in stabilization of the LS state below a critical temperature (n

_{HS}= ½) and its destabilization above it, i.e., corresponds to cooperative effect. We observe that (ω

_{LS})HS < (ω

_{LS})LS, while (ω

_{HS})HS ≅ (ω

_{HS})LS, hence η is negative for ([Fe(II)(4-amino-1,2,4-triazole)

_{3}]

^{2+}. This means that the vibrational coupling acts against a cooperative behavior, in line with the DFT predictions of [28], for which all normal vibrations were taken into account for the calculation of the vibrational entropy. In our opinion such a situation is more probable, at least at normal pressure.

## 4. Conclusions

_{c}imply the clustering of the centers of the same spin rather than an alternate structure. Another, complementary method that could be used to investigate the distribution of the spin centers in the spin isomers, containing both LS and HS centers, as well as subtle structural phenomena, is the X-ray powder diffraction technique (cf. refs. [52,53]). Our DFT modeling also suggests, that for spin isomers containing comparable amounts of both spin isomers, independently on the distribution patterns, the HS and LS centers form two sublattices showing independent vibrations. Finally, the simulations of the experimentally obtained 1:1 mixture of HS and LS centers may imply that the structure of 1-D chains at T

_{c}corresponds to a block (domain) pattern in one chain containing a 1:1 mixture of both spin isomers, rather than to corresponding alternate (chessboard) structures.

## Supplementary Materials

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

DFT | Density Functional Theory |

NIS | Nuclear Inelastic Scattering |

SCO | Spin Crossover |

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**Scheme 1.**Trimeric Fe

_{3}(atrz)

_{6}(H

_{2}O)

_{6}Cl

_{6}(

**a**); pentameric Fe

_{5}(atrz)

_{12}(H

_{2}O)

_{6}Cl

_{6}(

**b**); heptameric Fe

_{7}(atrz)

_{18}(H

_{2}O)

_{6}Cl

_{6}(

**c**); and nonameric Fe

_{9}(atrz)

_{24}(H

_{2}O)

_{6}Cl

_{6}(

**d**) model molecules used in calculations in [28] (trimeric and pentameric) and in this study (heptameric and nonameric). In each case, the two terminal iron centers, with three coordinated waters are assumed to be in the high-spin state. All other centers may be either low-spin (denoted as L) or high-spin (denoted as H). Thus, for example, for the pentameric model five spin isomers are possible, denoted as HHHHH, HLLLH, HHLHH, HLHLH and HHLLH (identical with HLLHH). The iron in the inversion center is denoted as Fe(1), the next centrosymmetrically related ones are denoted as Fe(2)/Fe(2’), Fe(3)/Fe(3’), etc.

**Figure 1.**(

**a**) Experimental pDOS of (

**1**) obtained at 80 K (

**a**); of (

**2**) at 273 K (

**b**); and of (

**3**) at 80 K (

**c**). Reprinted from [32].

**Figure 2.**Left: Experimental pDOS of (

**1**) (pure LS phase) (

**a**) and calculated pDOS involving modes of all LS centers for the pentameric (

**b**); heptameric (

**c**); and nonameric (

**d**) model molecules displayed in Scheme 1. Right: Simulated pDOS of only the central LS Fe(1) (red) calculated with the pentameric (

**e**); heptameric (

**f**) and nonameric (

**g**) model molecules. The bars denote the calculated vibrational modes scaled to 1/5 of their calculated intensity. The iron centers for which the pDOS has been calculated are marked in bold.

**Figure 3.**Left: Experimental pDOS of (

**3**) (ca. 1:1 mixture of LS and HS Fe(II) centers, diluted in Zn(II) matrix) (

**a**) and DFT simulations involving modes of all but the terminal centers for pentameric (

**b**); heptameric (

**c**); and nonameric (

**d**) model molecules with LS Fe(II) in center and all HS neighbors. Right: Simulated pDOS of only the central LS Fe(1) (red) calculated with the pentameric (

**e**); heptameric (

**f**); and nonameric (

**g**) model molecules. The centers taken for a given calculations of pDOS are marked in bold. The bars denote the calculated vibrational iron modes scaled to 1/5 of their calculated intensity. The most intensive iron vibration of the heptameric and nonameric model are truncated for clarity reasons. The calculations shown left involved all HS Fe(II) neighbors, although the spectrum was taken for the Zn(II) diluted sample; therefore, the intensity of the bands at 200–300 cm

^{−1}due to the HS vibrations is overestimated.

**Figure 4.**Comparison of the experimental pDOS of (

**2**) at 273 K (

**a**) with the calculated pDOS of the chessboard (

**b**,

**c**) and block models (

**d**–

**f**). The bars denote the calculated vibrational iron modes scaled to 1/5 of their calculated intensity. Note that the applied models have a LS:HS ratio of 3:2, 2:3, and 4:3, rather than an exact 1:1 ratio.

**Figure 5.**Calculated pDOS for HS Fe(1) (bold, highlighted blue) in HS (

**top**) and LS (

**bottom**) matrix for pentameric (

**left**), heptameric (

**middle**), and nonameric (

**right**) models. The bars denote the calculated vibrational iron modes scaled to 1/5 of their calculated intensity.

**Table 1.**Comparison of the energies (cm

^{−1}) of three experimentally-observed vibrational bands in the pDOS of (

**1**) and (

**3**) and of the corresponding modes calculated with DFT for the different indicated models displayed in Scheme 1b–d. The names of the corresponding movies showing a particular mode are given (cf. Supplementary Materials).

Experiment | Pentameric Model | Heptameric Model | Nonameric Model | ||||
---|---|---|---|---|---|---|---|

Sample Spin of neighbours | |||||||

LS (1) (1) | LS in Zn matrix (3) | LS | HS | LS | HS | LS | HS |

321 | 318 | 311 (ls_pent_311) 326 (ls_pent_326) | 302 303 (HHLHH_303) | 324 325 (ls_hept_325) | 301 305 (HHHLHHH_305) | 327 (ls_non_327) | Not observed |

465 | Weak peaks in 450–495 cm^{−1} region | 467 | 445 | 461 | 448 | 471 (ls_non_471) | 435 (HHHHLHHHH_non_435) |

496 | Weak peaks in 450–495 cm^{−1} region | 498 (ls_pent_498) | 461 | 504 | 460 (HHHLHHH_460) | 505 (ls_non_505) | 509 |

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**MDPI and ACS Style**

Wolny, J.A.; Faus, I.; Marx, J.; Rüffer, R.; Chumakov, A.I.; Schlage, K.; Wille, H.-C.; Schünemann, V.
Vibrational Coupling of Nearest Neighbors in 1-D Spin Crossover Polymers of Rigid Bridging Ligands. A Nuclear Inelastic Scattering and DFT Study. *Magnetochemistry* **2016**, *2*, 19.
https://doi.org/10.3390/magnetochemistry2020019

**AMA Style**

Wolny JA, Faus I, Marx J, Rüffer R, Chumakov AI, Schlage K, Wille H-C, Schünemann V.
Vibrational Coupling of Nearest Neighbors in 1-D Spin Crossover Polymers of Rigid Bridging Ligands. A Nuclear Inelastic Scattering and DFT Study. *Magnetochemistry*. 2016; 2(2):19.
https://doi.org/10.3390/magnetochemistry2020019

**Chicago/Turabian Style**

Wolny, Juliusz A., Isabelle Faus, Jennifer Marx, Rudolf Rüffer, Aleksandr I. Chumakov, Kai Schlage, Hans-Christian Wille, and Volker Schünemann.
2016. "Vibrational Coupling of Nearest Neighbors in 1-D Spin Crossover Polymers of Rigid Bridging Ligands. A Nuclear Inelastic Scattering and DFT Study" *Magnetochemistry* 2, no. 2: 19.
https://doi.org/10.3390/magnetochemistry2020019