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Computational Studies for Crystal Structures of Helicate Lanthanide Complexes Based on X-ray Analyses

2021, Vol.94, No.12

2973-2981

Computational Studies for Crystal Structures of Helicate Lanthanide Complexes Based on X-ray Analyses

Naofumi Nakayama ,^*¹Masahiro Hijikata ,²Hitomi Ohmagari ,²^,³Hideyuki Tanaka ,²Yudai Inazuka ,²Daisuke Saito ,⁴Shigeaki Obata ,¹Kazuo Ohta ,¹Masako Kato ,^*⁴^,⁵Hitoshi Goto ,^*⁶ and Miki Hasegawa ^*²^,³

¹CONFLEX Co., Shinagawa Center Bldg., 3-23-17 Takanawa, Minato-ku, Tokyo 108-0074, Japan
²Department of Chemistry and Biological Science, Aoyama Gakuin University, 5-10-1 Fuchinobe, Chuo-ku, Sagamihara, Kanagawa 252-5258, Japan
³Mirai Molecular Materials Design Institute, Aoyama Gakuin University, Sagamihara, Kanagawa 252-5258, Japan
⁴Department of Chemistry, Faculty of Science, Hokkaido University, North-10 West-8, Kita-ku, Sapporo, Hokkaido 060-0810, Japan
⁵Department of Applied Chemistry for Environment, School of Biological and Environmental Sciences, Kwansei Gakuin University, 2-1 Gakuen, Sanda, Hyogo 669-1337, Japan
⁶Toyohashi University of Technology, 1-1 Hibarigaoka, Tempaku-cho, Toyohashi, Aichi, 441-8580, Japan

https://doi.org/10.1246/bcsj.20210339

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Abstract

Section:

Computational approaches to elucidate the phase transitions in lanthanide complexes will support understanding their electronic structure changes by weak stimuli such as gas adsorptions. There are no examples as molecular models of Ln complexes for defining parameters, due to various molecular shapes with unexpected coordination numbers resulting in different packings with different Ln ions. Here, we succeeded in determining molecular force field parameters (van der Waals; vdW for Ln = Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er and Tm; and torsion parameters of the ligand) to apply the structural optimization of a series of Ln complexes taking uniform helicate for ten Ln ions with the same ligand, L, which reported previously as LnL. SmL, ErL, and TmL were newly synthesized for this calculation and the structure and luminescence properties experimentally determined. The coordination distances surrounding Ln are along the lanthanoid contraction. It is the first case to clarify the lanthanoid contraction in a 10-coordination system of a series of Ln ions. The applied optimized structures with these parameters for Eu well exhibit correspondence to observed results for four analogous of EuL. This work will strongly push development of luminescent Ln complexes with soft-crystalline behaviour.

In order to elucidate crystal phase transitions of lanthanide complexes by the computational chemistry, the van der Waals parameters were successfully determined using a series of helicate lanthanide complexes, which were experimentally identified molecular structures in uniform, and the parameter was proved to be suitable for the evaluation of structural optimization for four derivatives.

1. Introduction

Section:

Crystal structures of molecular systems and their phase transition systems accompanied with color-/luminescence-changing have recently attracted much attention in coordination compounds by weak stimuli.¹^–⁵ In recent decades, luminescent lanthanide (abbreviated to Ln) complexes have attracted much attention for both application and fundamental studies because of their highly pure luminescent colors derived from the ff-transition.⁶^–¹² The organic components in Ln complexes play important roles not only for variation of molecules, but also as photo-antennas,¹³^,¹⁴ for electroluminescence devices¹⁵ and skeletons for coordination polymers.¹⁶^,¹⁷ Energy donor levels of the ligand with high absorption coefficient enhance the ff emission of Ln ion through intramolecular energy transfer. There are few reports showing vapochromic luminescence of Ln complexes,¹⁸^–²⁹ for example, a system consisting of porous coordination polymers of Ln ions linked by ruthenium complexes which exhibits dual luminescence of the ³MLCT and ff transitions under different gas adsorption conditions.²⁷^–²⁹

Recently, a vapochromic luminescent terbium (Tb) complex with helicate molecular structure with hexadentate bipyridine derivative, LH, not taking the coordination polymer structure was discovered. This Tb complex depicted drastic luminescence intensity changes by phase transitions depending on the existence of solvent molecules or mechanical stimuli.³⁰ There is insufficient discussion of such un-polymerized Ln complexes to show luminescence under stimuli. Computational approaches of optimized molecular packing surely contribute to elucidate the phase transition mechanism between several polymorphisms. However, among the parameters required for crystallography, there is insufficient information on Ln elements and their quantitative trends.

Advantages of using computational approaches to metal complexes have been surely recognized.²²^,³¹^,³² For instance, Hatanaka expected an azomethine bond in TbL (Scheme 1) with low luminescence compound prohibit forwarded energy transfer, because the active potential between the triplet level of L and accepter level of Tb ion is larger than that in an expected molecule with the azomethine-reduction, TbLH, before the synthesis.²²

Scheme 1. Molecular structure of the helicate complex, LnL.

The coordination sphere of Ln ion is not easy to envision without experimental results, due to their coordination numbers being widely variable from six to twelve. Additionally, it is also known that molecular packings of 1,10-phenanthroline complexes with Eu, Tb, Tm and Gd are changed by deuteriation of the ligand.³³^,³⁴ Thus, the optimization of crystalline phases of Ln compounds have yet to be confirmed by using such Ln complexes as components.

In the present study, a series of Ln complexes, (abbreviated to LnL: Ln = Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er and Tm) with uniform molecular structures was used as a model system for the determination of vdW parameters. The framework of classical force field including Ln changes depended on whether the model Ln is bound to other atoms (Ln-X, X = N or O)³⁵^–⁴⁰ or is regarded as trivalent ion.⁴¹^–⁵⁶ The development of potentials for isolated Ln^III are further divided into two categories; additive⁴¹^–⁴⁸ and polarizable.⁴⁹^–⁵⁶ In this work, Ln is regarded as isolated ion and the parameters for nonbonded interactions are developed and introduced in MMFF94s⁵⁷^–⁶³ which is an additive molecular force field. These parameters are applied to the molecular crystal structure optimization of LnL by CONFLEX 8.C,⁶⁴ and their optimized structures are compared with those observed ones. The parameters of Eu are also applied to the optimization of EuL derivatives for evaluation.

The Sm, Tm and Er complexes with L were newly synthesized for this calculation and their crystal structures were determined by single crystal X-ray structural analyses as well as other complexes already reported.⁶⁵^,⁶⁶ Luminescence spectra of these new complexes were also examined.

2. Calculations and Experiments

Section:

Calculation Methods.

Definition of Crystal Energy for Optimization:

The structure of a molecular crystal is defined by molecular geometry, orientation and spatial position in an asymmetric unit (AU), lattice constants of a unit cell and space group symmetry. The structure optimization for the molecular crystal is performed by minimizing crystal energy with respect to these structural parameters under the space group symmetry. In the CONFLEX program,⁶⁴ the crystal energy (E_crystal) is defined as⁶⁷^–⁷⁰

\begin{equation} E_{\text{crystal}} = E_{\text{intra}} + E_{\text{lattice}} \end{equation}

(1)

\begin{equation} E_{\text{lattice}} = E_{\textit{inter}} + \frac{1}{2}\sum_{i}^{N}\sum_{S}^{M}\sum_{J}^{N}E_{\text{inter}}(i;S,J) \end{equation}

(2)

where \(E_{\text{intra}}\) is the total intramolecular energies of molecules in AU, and \(E_{\text{lattice}}\) is the sum of the total intermolecular interaction energies in AU (\(E_{inter}\)) and the total interatomic interaction energies between atom i in AU (original molecules in Figure 1) and atom J in a symmetry-related unit S (\(E_{\text{inter}}( i;S,J )\)), which is generated by applying a symmetry operation to AU (replica molecules in Figure 1). N is the number of atoms in AU, and M is the total number of symmetry-related units within a cut-off radius (R_crystal in Figure 1) from AU; that is, only the molecules for which the closest interatomic distance from the molecule in AU is less than or equal to R_crystal are included in the interatomic energy calculations. In this work, R_crystal was set to 20 Å.

Figure 1. Molecular crystal calculation model by CONFLEX. R_crystal is cut-off radius for \(E_{\text{inter}}( i;S,J )\).

Energy Expression of MMFF94s:

MMFF94s includes terms which are bond stretching, angle bending, stretch-bend interactions, out-of-plane bending, torsion interactions, vdW interactions, and electrostatic interactions as below⁵⁷^–⁶³

\begin{align} E &= \sum EB_{ij} + \sum EA_{ijk} + \sum EBA_{ijk} + \sum EOOP_{ijk; l}\\ &\quad + \sum ET_{ijkl} + \sum EvdW_{ij} + \sum EQ_{ij} \end{align}

(3)

All these terms are employed in the calculation of \(E_{\text{intra}}\), and the nonbonded interactions including vdW and electrostatic terms are applied to \(E_{\text{inter}}\) and \(E_{\text{inter}}( i;S,J )\). In this study, newly assigned and modified force field parameters for some species which consist of LnL crystals are also included in all calculations and summarized in Table S2–S4.

The vdW interactions in MMFF94s employ “Buffered 14-7” (Buf-14-7) form⁵⁸^,⁷¹ as

\begin{equation} EvdW_{ij} = \varepsilon_{IJ}\left(\frac{1.07R_{IJ}^{*}}{R_{ij} + 0.07R_{IJ}^{*}} \right)^{7}\left(\frac{1.12R_{IJ}^{*7}}{R_{ij}^{7} + 0.12R_{IJ}^{*7}} - 2 \right) \end{equation}

(4)

where i and j designate the specific atoms in crystal, and \(R_{ij}\) is the interatomic distance between them. I and J designate the atom types for atoms i and j, and \(R_{IJ}^{*}\) is defined as

\begin{equation} R_{IJ}^{*} = 0.5(R_{II}^{*} + R_{JJ}^{*})(1 + 0.2(1 - \exp(- 12\gamma_{IJ}^{2}))) \end{equation}

(5)

\begin{equation} \gamma_{IJ} = (R_{II}^{*} - R_{JJ}^{*})/(R_{II}^{*} + R_{JJ}^{*}) \end{equation}

(6)

The expression of \(R_{II}^{*}\) is given in the section “Results and Discussion”. \(\varepsilon_{IJ}\) is well depth and is expressed as

\begin{equation} \varepsilon_{IJ} = \frac{181.16G_{I}G_{J}\alpha_{I}\alpha_{J}}{(\alpha_{I}/N_{I})^{1/2} + (\alpha_{J}/N_{J})^{1/2}}\frac{1}{R_{IJ}^{* 6}} \end{equation}

(7)

where N_I and N_J are the Slater-Kirkwood effective numbers of valence electrons, and G_I and G_J are scale factors. These are set to 1.404 and 6.95 for all Ln, which are the same values as those for iodine. The α values of Ln are also shown in the section “Results and Discussion”.

Crystallization and Structural Analyses.

Synthesis of LnL (Ln = Sm, Er and Tm):

The Sm, Er and Tm complexes with L were newly synthesized by the previously reported method with corresponding metal nitrate as sources.⁶⁵^,⁶⁶ These single crystals were obtained from a mixed solution of acetonitrile and diethylether.

Apparatus:

Structural analyses of LnLs were performed with a RIGAKU Synergy S for ErL and TmL, and a Bruker APEX II CCD for SmL at 77 K. The crystal information of SmL, ErL and TmL are available in the CIF files 1948108, 1948109 and 1948107, respectively, deposited at the CCDC database. Electronic absorption and luminescence spectra were recorded on Shimadzu UV3600S and Horiba Jovin Ybon Fluorolog 3-22 instruments, respectively.

3. Results and Discussion

Section:

Experimental Determination of Structures of SmL, ErL and TmL and the Luminescence Spectra.

Structural uniqueness is a characteristic property of Ln ions, and the six to twelve coordination forms have been reported as mentioned above. This is dependent on the electronic state of the Ln ion, and it is known that monodentate, bidentate, or tridentate ligands take a variety of molecular structures. Therefore, we focused on a series of complexes using the hexadentate ligand L, which can adopt the same structure. So far, we have newly prepared and crystalized SmL, ErL and TmL to experimentally determine the molecular and packing structures for the calculation.

The molecular structures of SmL, ErL and TmL are shown in Figure 2. These three complexes with helicate have isostructure in molecules, however the packing structures exhibit differences (Table 1). For instance, the space group of SmL was P-1(1), and those of ErL and TmL were P-1(2) (Figure S1). Actually, a unit cell of SmL has a pair of acetonitrile molecules for two SmL, while that of ErL or TmL has two pairs of solvent molecules. Interestingly, these structural behaviors can be classified to the complexes with L in light and heavy rare earths.

Figure 2. Observed ORTEP drawings (top) and their packing structures (bottom) of SmL (a, d), ErL (b, e) and TmL (c, f). Gray, blue, red, pink, violet and pale blue are carbon, nitrogen, oxygen, Sm, Er and Tm, respectively. Hydrogen atoms, acetonitrile and PF₆⁻ are omitted for clarity. Gold and silver are left- and right-handed form, respectively.

Table 1. Crystallographic data of SmL, ErL and TmL.

	SmL	ErL	TmL
Formula	C₂₆H₂₃F₆N₉O₆PSm	C₂₈H₂₆ErF₆N₁₀O₆P	C₂₈H₂₆F₆N₁₀O₆PTm
Formula weight	852.85	910.82	912.49
Crystal size (mm)	0.350 × 0.300 × 0.180	0.125 × 0.073 × 0.037	0.2 × 0.092 × 0.042
Crystal system	Triclinic	Triclinic	Triclinic
Space group	P1	\(P\bar{1}\)	\(P\bar{1}\)
a (Å)	8.9750(4)	9.9747(3)	9.9555(2)
b (Å)	12.2147(5)	13.4483(3)	13.5086(4)
c (Å)	16.2631(9)	13.6827(4)	13.6834(7)
α (°)	112.05	68.524(3)	68.416(4)
β (°)	104.2450(10)	86.050(2)	85.876(3)
γ (°)	92.11	87.435(2)	87.311(2)
V (Å³)	1584.98(13)	1703.57(9)	1706.33(12)
Z value	2	2	2
D_calcd (Mg m⁻³)	1.787	1.776	1.776
(mm⁻¹)	1.994 (Mo Kα)	5.83 (Cu Kα)	6.125 (Cu Kα)
F (000)	842	898	900
(Å)	0.71073 (Mo Kα)	1.54184 (Cu Kα)	1.54184 (Cu Kα)
Temperature (K)	90	90	90
R₁^a (I > 2.00σ(I))	0.0292	0.0415	0.0449
wR₂^b (I > 2.00σ(I))	0.0742	0.1085	0.1187
Goodness of fit	1.091	1.056	1.042
Largest peak and hole (e Å⁻³)	2.367, −1.336	2.400, −1.651	1.527, −1.433

^aR₁ = Σ||F_o| − |F_c||/Σ|F_o|. ^bwR₂ = {Σ[w(F_o² − F_c²)²]/Σ[w(F_o²)²]}^1/2.

Intramolecular interatomic distances (r_Ln-N) between Ln and nitrogen atoms of L of these three complexes and others already published are summarized in Figure 3. The r_Ln-N decreased with increasing in the atomic numbers, while the dihedral angels in them increased as the atomic numbers increased. Thus, notably it shows the first case to clarify the Ln contraction in a 10-coordination system of a series of Ln ions.

Figure 3. Coordination distances of r_Ln-N compared to the ionic radii¹⁴ along lanthanoid contraction. Ln-N_py and Ln-N_en are the averaged distance from Ln to nitrogen atoms of pyridine moieties and of ethylenediamine ones, respectively.

Newly synthesized complexes, SmL, ErL and TmL, have the possibility of luminescence originating from each center Ln ion. Luminescence spectra of these complexes were observed in the solid state (Figure 4 and S2).

Figure 4. Luminescence spectra of SmL (a) and TmL (b) in the solid state at rt (λ_ex = 315 nm). *: due to Eu^III as impurity.

Luminescence bands of each Ln ion were sensitized by ligand excitation at 315 nm. It is already known that the excited triplet state of L showing a phosphorescence band around 500 nm acts as an energy donor to enhance ff emission of a series of Ln ions.³⁵^–³⁷^,⁶⁵^,⁶⁶^,⁷²

SmL shows a luminescence band at 563, 599, 647 and 705 nm assigned to the ⁴G_2/5→⁶F_J (J = 5/2, 7/2, 9/2 and 11/2, respectively), and at 892, 935, 956, 1026, 1193 and 1288 nm assigned to the ⁴G_2/5→⁶H_J (J = 1/2, 3/2, 5/2, 7/2, 9/2 and 11/2) transitions of Sm^III. Tm ion in TmL also depicted weak luminescence bands at 477, 650, 790 and 1171 nm assigned to the ¹G₄→³H₆, ¹G₄→³F₄, ³H₄→³H₆ and ³H₄→³H₅ transition, respectively. Luminescence intensities of SmL and TmL are strengthened under 77 K (Figure S2). The luminescence bands of ErL are negligibly weak to detection, but the electronic absorption band of ErL corresponds to those of SmL and TmL even in solutions (Figure S3). It suggests that these complexes also keep their helicity through coordination to Ln ion even in solutions as well as other Ln systems with L.

Determination of van der Waals Parameters for Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er and Tm.

The nonbonded terms in MMFF94s consist of the Coulombic electrostatic and Buf-14-7 vdW potentials.⁵⁸^,⁷¹ The expressions of Buf-14-7 are indicated in the section “Calculation methods”. The structural parameters around Ln^III of computationally optimized geometries are strongly affected by the vdW radii of Ln^III and the atoms in ligand. The vdW radius corresponds to half of the minimum-energy separation between same atom type I (\(\boldsymbol{{R}}_{\boldsymbol{{II}}}^{\boldsymbol{{*}}}\)) derived as

\begin{equation} R_{II}^{*} = A_{I}\alpha_{I}^{1/4} \end{equation}

(8)

where α_I is atomic polarizability and A_I is a scale factor that is taken to be invariant across a row of the periodic table.⁷¹ In this study, A is set to 3.08 which is same value as that for iodine,⁵⁸ since it was the largest element for which MMFF94s parameters were available. We determined the α values of Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er and Tm as 2.05, 2.00, 1.85, 1.80, 1.75, 1.65, 1.35 1.20, 1.15 and 1.10, respectively, to reproduce the molecular structures of LnL in a series of observed results. It is worthy to note that the magnitude of these α values is ordered along the lanthanide contraction. The α value is largest in Pr, and slightly decreases with increasing of atomic numbers. Finally, the value in Tm takes mostly half in Pr. It is suitable to evaluate the effect of lanthanide contraction.

Table 2 shows coordination bond distances between Ln and nitrogen atoms of L for both observed and optimized crystal structures and the averages of their differences (|Diff.|_ave). The |Diff.|_ave value of each complex is quite small, since they are calculated with the corresponding α value. If the superimposed molecules of experimental and optimized structure were rotated, it was found that they roughly overlapped as shown in the supplemental movie for EuL in ESI. Optimized molecular structures of other LnLs are also shown with the overlap of experimental results in Figure S4.

Table 2. Coordination bond distances of Ln-N observed and optimized structures (Å) for LnL. |Diff.|_ave is the average value of their differences (Å).

	PrL		NdL		SmL		EuL		GdL
	Obs.	Calcd.	Obs.	Calcd.	Obs.	Calcd.	Obs.	Calcd.	Obs.	Calcd.
Ln-N1	2.652	2.658	2.643	2.644	2.622	2.641	2.621	2.627	2.616	2.624
Ln-N2	2.655	2.663	2.645	2.659	2.620	2.645	2.591	2.608	2.588	2.602
Ln-N3	2.584	2.495	2.572	2.489	2.542	2.471	2.533	2.470	2.525	2.463
Ln-N4	2.587	2.499	2.570	2.493	2.543	2.477	2.531	2.465	2.518	2.458
Ln-N5	2.641	2.634	2.629	2.631	2.602	2.611	2.607	2.640	2.602	2.635
Ln-N6	2.657	2.642	2.651	2.641	2.629	2.626	2.616	2.629	2.610	2.626
\|Diff.\|_ave	0.035		0.031		0.032		0.033		0.032
	TbL		DyL		HoL		ErL		TmL
	Obs.	Calcd.	Obs.	Calcd.	Obs.	Calcd.	Obs.	Calcd.	Obs.	Calcd.
Ln-N1	2.596	2.621	2.596	2.589	2.576	2.635	2.567	2.634	2.553	2.626
Ln-N2	2.586	2.625	2.555	2.552	2.538	2.565	2.536	2.559	2.517	2.554
Ln-N3	2.505	2.446	2.494	2.411	2.487	2.379	2.460	2.364	2.459	2.358
Ln-N4	2.510	2.453	2.496	2.405	2.490	2.400	2.474	2.389	2.458	2.379
Ln-N5	2.569	2.588	2.576	2.604	2.542	2.587	2.535	2.587	2.525	2.581
Ln-N6	2.601	2.613	2.586	2.608	2.615	2.644	2.597	2.640	2.601	2.640
\|Diff.\|_ave	0.035		0.039		0.060		0.061		0.064

Figure 5 and Table 3 show the comparison of experimental and optimized structures and lattice parameters. The optimized crystal structures in unit cells well demonstrated agreement with those observed results for LnL. Furthermore, the optimized molecular structure closely corresponds to the observed structure. The structural differences (abbreviated to RMSD₂₀⁷³^,⁷⁴) for them are also summarized in Table 3. RMSD₂₀ is the root mean square deviation of the corresponding atoms in the molecular cluster composed of a central molecule and the nearest 19 molecules between observed and optimized structures.⁷³^,⁷⁴ Thus, it indicates that the parameters and calculation conditions may be applied to other series of similar Ln complexes.

Figure 5. Superimposed representation of observed (green) and optimized structures (yellow) of a series of Ln complexes with the helicate ligand L.

Table 3. Observed and calculated lattice constants with RMSD₂₀ (Å) of LnL.

	PrL		NdL		SmL		EuL		GdL
	Obs.	Calcd.	Obs.	Calcd.	Obs.	Calcd.	Obs.	Calcd.	Obs.	Calcd.
a (Å)	8.937	9.243	8.949	9.344	8.975	9.269	9.000	9.346	9.015	9.350
b (Å)	12.244	12.271	12.231	12.222	12.215	12.251	12.253	12.224	12.214	12.222
c (Å)	16.343	16.571	16.394	16.922	16.263	16.924	16.253	16.840	16.184	16.813
α (°)	110.2	108.4	112.2	112.3	112.1	112.2	112.3	112.3	112.0	112.3
β (°)	105.6	104.6	104.1	103.4	104.2	104.2	104.4	103.5	104.3	103.4
γ (°)	92.6	93.9	92.4	94.3	92.1	93.6	91.8	93.9	91.8	93.9
RMSD₂₀	0.32		0.35		0.34		0.36		0.36

	TbL		DyL		HoL		ErL		TmL
	Obs.	Calcd.	Obs.	Calcd.	Obs.	Calcd.	Obs.	Calcd.	Obs.	Calcd.
a (Å)	9.017	9.319	9.056	9.322	9.961	10.464	9.975	10.314	9.956	10.306
b (Å)	12.239	12.236	12.222	12.240	13.593	13.585	13.448	13.925	13.509	13.943
c (Å)	16.133	16.810	16.139	16.636	13.751	13.576	13.683	13.922	13.683	13.919
α (°)	112.1	112.3	112.1	112.3	68.3	67.5	68.5	65.7	68.4	65.7
β (°)	104.3	103.7	104.5	103.7	86.0	87.3	86.1	86.1	85.9	86.0
γ (°)	91.6	93.4	91.5	93.0	87.4	90.5	87.4	89.4	87.3	89.3
RMSD₂₀	0.36		0.31		0.46		0.41		0.43

The Structure Optimization of LnL Derivatives.

The validity of the vdW parameter α was verified using several helical Eu complexes with modified L (Scheme 2) because crystallographic data were experimentally decided. These molecular structures and packings have already been reported.⁶⁵^,⁷⁵ Each Eu complex forms ten coordination with hexadentate aromatic chromophore and two nitrate ions. Azomethine sites of EuL are reduced to compose EuLH. Two bipyridine moieties in EuL^pr, EuL^dmpr and EuL^me are bridged with a propylenediamine, dimethylpropylenediamine and methylethylenediamine, respectively. These four complexes also form helicate structure. Table 4 shows coordination distances between Eu and nitrogen atoms and |Diff.|_ave of observed and optimized structure of Eu complexes. The |Diff.|_ave values were 0.02 to 0.04 Å for each complex, with a maximum of 0.041 Å for EuL^pr.

Scheme 2. Molecular structures of various derivatives of EuL.

Table 4. The observed and optimized atomic distances (Å) between Eu and nitrogen atoms of EuL^pr, EuL^dmpr, EuL^me and EuLH by using α = 1.80. |Diff.|_ave is average value of their differences for each complex. EuLH exists as a dimer with slightly different formation.

For comparison, superposition and crystal parameters of observed and optimized structures of EuL derivative are shown in Figure 6 and Table 5, respectively. The molecular (Figure S5) and packing structures of these Eu complexes with α = 1.80 show good correspondence to the experimental results. The errors of the lattice constants a, b and c were in the range from 0.008 to 1.897 Å, and of their angles were in the range 0.4°–2.0°. These results support that obtained force field parameter of Eu gives positive aspects for the application to other crystalline systems of Eu complexes.

Figure 6. Superposition of observed (green) and optimized structures (yellow) by using α = 1.80 of (a) EuL^pr, (b) EuL^dmpr, (c) EuL^me and (d) EuLH.

Table 5. Observed and calculated lattice constants with RMSD₂₀ (Å) of four Eu complexes. α = 1.80 was used for the optimization.

	EuL^pr		EuL^dmpr		EuL^me		EuLH
	Obs.	Calcd.	Obs.	Calcd.	Obs.	Calcd.	Obs.	Calcd.
a (Å)	13.265	13.232	16.752	18.649	24.708	24.047	11.306	12.242
b (Å)	11.747	12.697	14.542	14.276	12.120	12.486	15.635	15.848
c (Å)	20.565	20.573	25.718	25.590	24.378	25.601	19.340	19.600
α (°)	90.0	90.0	90.0	90.0	90.0	90.0	106.1	106.6
β (°)	96.9	97.7	90.0	90.0	119.7	117.7	91.4	92.4
γ (°)	90.0	90.0	90.0	90.0	90.0	90.0	105.7	106.1
RMSD₂₀	0.43		0.61		0.40		0.47

4. Conclusion

Section:

We successfully determined the van der Waals parameter α for a series of Ln ions (Ln = Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er and Tm) defined from the observed structural analyses of corresponding Ln complexes with hexadentate ligand. SmL, ErL, and TmL were newly prepared for this determination and single crystals X-ray structure analyses successfully completed. These complexes take uniform helicate on the equatorial site with two nitrate ions on both apical sites, and their observed interatomic distances of Ln-N between Ln and coordinating nitrogen of L exhibit an order along the lanthanide contraction clearly. It is the first case to demonstrate the Ln contraction in a 10-coordination system of a series of Ln ions. SmL and TmL also luminesced in the solid state originating from ff transition through the antenna effect. It was confirmed that molecular force field parameters, vdW for Ln (Ln = Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er and Tm) and torsion parameters localized on the ligand were newly determined based on the above structures. The applied optimized structures with obtained vdW parameter for Eu exhibit good correspondence to observed results for EuL^pr, EuL^dmpr, EuL^me and EuLH. Therefore, defined α values will be useful for the optimization of molecular and packing structure of Ln complexes. In the near future, unknown structures of Ln complexes exhibiting soft crystalline phenomena, which may be difficult cases for observation, will be resolved together with structural search programs.

M. Hasegawa, H. Goto and N. Nakayama conceived and designed the study with S. Obata and K. Ohta. M. Hijikata precisely performed the calculations with Y. Inazuka, and H. Tanaka prepared and crystallized the complexes. H. Ohmagari evaluated these experimental results with spectral measurement. M. Kato and D. Saito experimentally determined crystal structures.

Authors thank Dr. Kenta Goto of Institute for Materials Chemistry and Engineering, Kyushu University for the measurement of elemental analyses. This work was supported by JSPS KAKENHI “Soft Crystals (Area Number 2903)”, Grant Numbers 17H06367 (MK), 17H06373 (HG), 17H06374 (MH) and 21K05105 (NN), and Grant-in-Aid for Early-Career Scientists JP20K15041 (HO) and the Sasakawa Scientific Research Grant from The Japan Science Society (HO; 2020-3017).

Supporting Information

Observed structure information, additional electronic spectra, determination of field force parameters and optimized molecular structures of each complex are described and shown in the Supporting Information. This material is available on https://doi.org/10.1246/bcsj.20210339.

Naofumi Nakayama

He received his PhD in 2001 from University of Tsukuba under the supervisions of Prof. Osamu Kikuchi. In 2001, he worked at Best Systems Inc. In 2003, he worked as a postdoc in the laboratory of Prof. Hitoshi Goto at Toyohashi University of Technology. He has worked at CONFLEX Corporation since 2008, and as Senior Researcher since 2019. His research interests are in quantum and computational chemistry for organic and organometallic compounds.

Masako Kato

She received her Ph.D. degree in 1986 from Nagoya University. After she worked at Institute for Molecular Science and Kyoto University, she joined the Department of Chemistry at Nara Women’s University as an Assistant Professor in 1989 and was promoted to an Associate Professor in 1996. During 1998–2001, she was also engaged in PRESTO research. She was a Professor of Chemistry at Faculty of Science, Hokkaido University during 2006–2020, and currently a Professor at Kwansei Gakuin University. Her research interests are luminescence properties, photofunctionalities, and the structural chemistry of metal complexes.

Hitoshi Goto

He received his PhD in 1993 from Hokkaido University under the supervisions of Prof. Eiji Ōsawa and Prof. Haruhisa Shirahama. In 1996, he worked as a research associate in the laboratory of Prof. Nobuyuki Harada at Tohoku University. In 1998, he independently started his own research group at Toyohashi University of Technology as an associate professor. He has held a concurrent post at TUT as full professor and special advisor to the president since 2020. His research interests are in computational chemistry and chemoinformatics for organic compounds and materials.

Miki Hasegawa

She received her PhD in 1998 from Aoyama Gakuin University under the supervision of Prof. Toshihiko Hoshi, and worked as a research professor in the laboratory for four years. In 2002, she independently started her own research group at AGU as a lecturer, and was promoted to full professor in 2011. She has held a concurrent post at AGU as Director of MMMDI (Mirai/Future Moleular Materials Design Institute) since 2018. Her research interests are in photochemistry of coordination compounds and molecular assembly systems.

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2021, Vol.94, No.12

Computational Studies for Crystal Structures of Helicate Lanthanide Complexes Based on X-ray Analyses

Abstract

Calculation Methods.

Crystallization and Structural Analyses.

Experimental Determination of Structures of SmL, ErL and TmL and the Luminescence Spectra.

Determination of van der Waals Parameters for Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er and Tm.

The Structure Optimization of LnL Derivatives.

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