Revisiting the Role of Hydrogen Bonding in the Strong Dimer Superexchange of a 2D Copper(II) Halide Honeycomb-Like Lattice: Structural and Magnetic Study

Structural and Magnetic Study

Article

Revisiting the Role of Hydrogen Bonding in the Strong Dimer

Superexchange of a 2D Copper(II) Halide Honeycomb-Like Lattice:

Je ﬀ rey C. Monroe,* M. Angels Carvajal, Merce

and Mark M. Turnbull*

Deumal,* Christopher P. Landee, Melanie Rademeyer,

Cite This: https://dx.doi.org/10.1021/acs.inorgchem.0c00433

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sı Supporting Information

ABSTRACT: The title compound H L(CuCl H O)Cl (H L = 1-(4′-pyridinium)pyridin-4-ol-ium), 1) was synthesized and

investigated structurally and magnetically as well as via a ﬁrst-principles, bottom-up theoretical analysis of the potential magnetic

superexchange pathways. Compound 1 can be described structurally as a well-isolated, distorted 2D-honeycomb lattice with two

potential exchange pathways: a dimeric interaction via hydrogen-bonded pairs of (CuCl H O) ions and a chain structure via

bridging chloride ions. Surprisingly, the experimental magnetic data are best ﬁtted using both a simple dimer model with a Curie−

Weiss correction for interdimer exchange (J = −107.4(1) K, θ = −1.22(4) K) and a strong-rung ladder model (J = −105.8(7)

dimer

rung

K, J_r_a_i_l= 2(7) K). Theoretical analysis at the UB3LYP/6-31+G(d) level supports the strong exchange observed through the

−

−1

[

CuCl (H O)] dimer moiety superexchange pathway (−102 K = −71 cm ). However, the apparent vanishingly small exchange

−1

through the single halide bridge is merely a brute average of competing ferromagnetic (FM) (+24.8 K = +17.0 cm ) and

−

antiferromagnetic (AFM) (−21.0 K = −14.6 cm ) exchange interactions. Our computational study shows that these ﬁtting

parameters carry no physical meaning since a honeycomb plaquette must be taken as magnetic building block for 1. The competition

between FM and AFM pair interactions leads to geometrical frustration in 1 and could induce interesting magnetic response at low

temperatures, if the magnetic exchange is adequately tuned by modifying substituents in ligands and, in turn, interactions within the

crystal packing.

INTRODUCTION

instance, has a mixed ground state and achieves long-range

■

order at a temperature proportional to J′/J, where J′ is the

Renewed interest in the magnetic properties of low-dimen-

sional transition metal lattices followed the discovery of low-

dimensional superexchange (2D) in high-temperature copper

interlayer exchange and J is the intralayer exchange. For J′ = 0,

the 2D-QHAF model orders at T = 0 K, while at ﬁnite

−4

temperatures thermal ﬂuctuations hinder ordering. One robust

oxide superconductors.

Thus, over the course of three

9−15

approach

toward achieving such 2D lattices is to synthesize

decades, the synthesis of low-dimensional copper(II) lattices

has been a major focus of attempts to understand the eﬀects of

structure on the magnitude and sign of the superexchange and

to study the ground state behavior and long-range order

salts of the type (HL) CuX where HL is a protonated organic

Received: February 11, 2020

(

LRO) in these quantum dominated systems. It has been

subsequently found that interesting quantum eﬀects are

observed depending on the interaction topology in the ground

−7

state of such low-dimensional systems.

The 2D-quantum

Heisenberg antiferromagnetic (2D-QHAF) square lattice, for

XXXX American Chemical Society

Inorg. Chem. XXXX, XXX, XXX−XXX

Inorganic Chemistry

under study (Figure 1 ). Neutral ligand L is ambidentate and

Article

base, such as a substituted pyridine-based cation, and X is

chloride or bromide. In these complexes, the HL ions pack

were used as received. Elemental analysis was performed at the

Marine Science Institute, University of California Santa

Barbara, CA. The infrared spectrum was collected using a

PerkinElmer FT-IR 100 spectrometer on a powdered sample.

1-(4′-Pyridyl)pyridin-4-one Dihydrate. The ligand 1-(4′-

pyridyl)pyridin-4-one dihydrate was synthesized in a manner

such that CuX layers may be well-isolated, giving the desired

D superexchange which may be comprised of two-halide

8,11

exchange pathways.

Investigation of many such lattices

allows the construction of magnetostructural correlations

toward understanding the nature of superexchange and

ordering phenomena. For instance, the magnitude and sign

similar to the literature procedure. A neat mixture of acetic

anhydride (124 mmol, 12.63 g) with 4-hydroxypyridine (53

11,16

of J through a two-halide pathway

has been qualitatively

mmol, 5.03 g) was reﬂuxed while stirring under N atmosphere

related to the distance X···X and the torsion angle Cu−X···X−

for 5 h. The resulting brown reaction mixture was allowed to

cool while stirring and eventually solidiﬁed. The solid was

triturated with diethyl ether and then ﬁltered giving the brown

crude product. The crude product was recrystallized from

Cu where short X···X distances and torsion angles near 0 and

80° give strong superexchange. While much work in this ﬁeld

exists, there is a strong push toward synthesizing more diverse

structures which may contain unique or interesting super-

exchange pathways and topologies. For instance, the diﬃcult-

toluene giving yellowish needles (1.83 g, 33% yield). NMR H

(solvent: D O) (ppm) 8.72 (doublet J = 1.46 Hz), 8.2

to-synthesize honeycomb lattice is well-studied theoretically

(doublet J = 2.2 Hz), 7.65 (doublet J = 1.62 Hz), 6.35

−

because a number of quantum eﬀects may dominate the

ground state depending on slight deviations from an isotropic

Heisenberg system, including the sought after quantum spin

(doublet J = 2 Hz). IR ν (cm ): 3232 (br, db), 3037 (w,

mult), 1633 (s), 1588 (sh), 1568 (s, db), 1496 (s), 1410 (m),

1355 (m), 1331 (w), 1288 (s), 1223 (m), 1198 (s), 1070 (w),

1028 (m), 996 (w), 844 (sh, m), 829 (s), 717 (m) (s = strong,

m = medium, w = weak, db = double, mult = multiple, br =

,17−21

liquid phase.

In an attempt to provide a structurally diverse family of

copper(II) lattices, compounds with L, HL , and H L are

broad, sh = shoulder, v = very). The H NMR spectrum is

shown in Supporting Information section 1.

-(4′-Pyridinium)pyridin-4-ol-ium) Aquatrichlorocopper-

(

II) Chloride (1). 1-(4′-Pyridyl)pyridin-4-one dihydrate (419

mg, 2.00 mmol) was dissolved in HCl (6 M, 10 mL) giving a

yellow solution. CuCl ·2H O (175 mg, 1 mmol) was dissolved

in H O (5 mL) giving a blue solution which was added to the

acid solution, turning it green. This solution was ﬁltered and

left to slowly evaporate at room temperature; it became yellow

as it concentrated. After 4 days, green hexagonal crystals of 1

were picked from solution with a spatula and dried

mechanically (0.264 g, 65%). Attempts to wash the crystals

with a variety of solvents caused degradation. Calcd CHN: C

(

30.21%) H (3.04%) N (7.05%). Found CHN: C (30.59%) H

2.99%) N (7.07%). IR ν (cm ): 3326 (db, br), 3019 (br,

−

mult), 2652(w), 2502 (w), 2431 (br), 1607 (s), 1524 (m),

483 (s), 1392 (w), 1359 (m), 1347 (m), 1280 (m), 1239.52

m), 1201 (s), 1095 (w) 1035 (w, mult), 866 (m), 802 (vs),

62 (m, mult) (s = strong, m = medium, w = weak, db =

(

double, mult = multiple, br = broad, sh = shoulder, v = very).

Figure 1. Forms of the molecule L (1-(4′-pyridyl)-4-pyridone) from

X-ray Crystallography. Data collections of 1 (H L)[Cu-

H O)Cl ]Cl were carried out on a Bruker D8 Venture

2 3

treatment with protic acid.

(

diﬀractometer ﬁtted with a Photon 100 CMOS detector

employing graphite-monochromated Mo Kα radiation, using φ

and ω scans. Using the SAINT+ software, the data were

may coordinate a transition metal via the pyridone oxygen

22−26

atom or the pyridine nitrogen atom,

specie HL may behave in similar fashion, although

and monoprotonated

reduced, and absorption corrections were made using

coordination of the protonated oxygen atom is less likely.

SADABS. The structure solution was carried out using

The doubly protonated molecule, H L , may provide charge

SHELXS-97, while reﬁnements were performed using

balance for a CuX₄⁻moiety and control the lattice formation

through hydrogen bonding. However, it is no longer a good

candidate as a ligand as there are no available coordination

sites. Our group has proposed that use of this versatile trio of

compounds may give structurally diverse complexes because of

the unusual charge balance motif and the potential to evaluate

existing magneto-structural correlations via investigation of the

likely large family of such. Here we report the results of our

SHELXL-2016. Non-hydrogen atoms were reﬁned using

anisotropic thermal parameters. Hydrogen atoms were located

in the lattice and reﬁned isotropically. Hydrogen atoms

attached to N21, O14, and O1 were reﬁned using an

antibumping restraint (0.88 Å). Table 1 summarizes the

crystallographic information for 1. The data were deposited

with the CCDC as deposition number 1983353 .

Magnetism. The magnetization of 1 was measured using a

Quantum Design MPMS-XL SQUID magnetometer on

powdered single-crystals (93.4 mg). Magnetization as a

function of applied magnetic ﬁeld from 0 to 50 kOe was

recorded at 1.8 K. The moment was measured at several points

while decreasing the magnetic ﬁeld back to zero to check for

the presence of hysteresis; none was observed. Temperature-

initial investigation in applications of H L , the synthesis,

structure, magnetic and theoretical characterization of H L-

[

CuCl (H O)]Cl (1).

3 2

Experimental Section. Materials and Methods. 4-

Hydroxypyridine was purchased from Alfa Aesar, and CuCl₂·

H O was purchased from Allied Chemical Corporation. Both

Inorg. Chem. XXXX, XXX, XXX−XXX

Inorganic Chemistry

Article

Table 1. Crystallographic Data for 1

dependent data for 1 were measured in a 1 kOe applied ﬁeld

from 1.8 to 310 K. The data were corrected for the

temperature-independent paramagnetic contribution of Cu(II)

formula

C H N O Cl Cu

10 12 2 2 4

molecular weight

crystal system

space group

a (Å)

b (Å)

c (Å)

α (deg)

β (deg)

γ (deg)

V (Å³)

397.57

orthorhombic

Pbca

6.8757(3)

16.2729(5)

25.0962(10)

and the diamagnetic contributions of the constituent atoms

(

estimated from Pascal’s constants ). Powder X-ray diﬀraction

data were used to verify that the sample used for magnetic data

collection was the same phase as the single-crystal structure

(

see Supporting Information section 2).

Computational Studies. The magnetic susceptibility data of

have been calculated using a ﬁrst-principles, bottom-up

(

FPBU) working strategy. In brief, the FPBU procedure has

been used to (i) identify all A···B radical pair candidates that

might be magnetically important (threshold Cu···Cu distance

2807.95(19)

150(2)

1.881

2.303

0.71073

.0 Å), (ii) compute the magnetic exchange interaction J_A_B

T (K)

between those selected pairs of radicals, (iii) deﬁne the

ρ_c_a_l_c(g cm⁻¹)

μ (mm⁻¹)

λ (Å)

^m^a^gⁿ^e^tⁱ^c^t^o^p^o^l^o^g^y^o^f^t^h^e^c^r^y^s^t^a^lⁱⁿ^t^e^r^m^s^o^f^a^l^l^sⁱ^gⁿⁱ^ﬁ^c^aⁿ^t^JAB

interactions, and (iv) calculate the magnetic susceptibility χ(T)

by means of statistical mechanics and compare it to the

experimental data.

−

10 ≤ h ≤ 10

−23 ≤ k ≤ 23

36 ≤ l ≤ 36

index ranges

For the evaluation of the J_A_Bmagnetic interaction between

radicals, the most appropriate cluster model has to be selected

to account for not only the spin carriers but also the radical

environment. Therefore, two diﬀerent types of models have

been used. The ﬁrst level of modeling accounts for just the

−

obs. reﬂections

indep. reﬂections [I > 2σ(I)]

parameters

goodness of ﬁt

R₁[I > 2σ(I)]

R_w[I > 2σ(I)]

R1 (all reﬂections)

^Rw (all reﬂections)

111015

4278

220

1.103

0.0202

0.0505

0.0243

0.0520

−

[

CuCl (H O)] radicals’ bare skeleton, either as a dimer,

4 2

trimer, or tetramer. The second level of modeling expands

these bare skeleton simple models by taking into account not

only the nearest-neighbor (nn) H₂L²⁺counterions but also the

closest isolated chloride anions when necessary. All J_A_B

Figure 2. (a) Thermal ellipsoid plot (50% probability) of the molecular unit of 1. Hydrogen atoms are shown as spheres of arbitrary size and only

N−H and O−H hydrogen atoms are labeled for clarity (symm. op. A: −1/2 + x, 1/2 − y, 1 − z). (b) Axial−equatorial bridging between copper(II)

ions via Cl3 (Cl3A symm op A: −1/2 + x, 1/2 − y, 1 − z; symm. op. B: x − 1, y, z). (c) Hydrogen bonding observed in 1. Equivalent species are

related by inversion (symm. op. A: −x, −y, 1 − z).

Inorg. Chem. XXXX, XXX, XXX−XXX

Inorganic Chemistry

Article

exchange interactions have been calculated in terms of energy

Table 2. Selected Bond Lengths and Angles of the Cu(II)

Coordination Sphere

diﬀerences at the DFT/UB3LYP level using the broken

symmetry approach when appropriate. Since the radicals are

anions, a series of basis sets were tested in order to

discriminate whether diﬀuse and/or polarization functions

bond lengths (Å)

bond angles (deg)

Cu1−Cl2

2.2543(3)

2.7094(3)

2.2795(3)

1.9983(9)

2.2757(3)

O1−Cu1−Cl2

86.23(3)

87.79(3)

174.20(3)

88.27(3)

102.289(11)

91.725(11)

161.234(14)

97.952(8)

102.28(3)

Cu1−Cl3

Cu−Cl4

Cu−O1

O1−Cu1−Cl3

O1−Cu1−Cl3A

O1−Cu1−Cl4

Cl2−Cu1−Cl3

Cl2−Cu1−Cl3A

Cl2−Cu1−Cl4

Cl3−Cu1−Cl3A

Cl3−Cu1−Cl4

were required to correctly describe the magnetic interactions.

Diﬀuse functions are concluded to be important since the spin-

carriers are anions. Therefore, all subsequent calculations were

performed at all-electron 6-31+G(d) level. In addition,

comparison of J_A_Bresults using 6-31+G(d) and 6-31G (as a

reference) basis sets shows that the use of 6-31G systematically

calculates values too small for the magnetic interactions

between radicals, reinforcing the importance of diﬀuse basis set

functions. The energies for radical dimer pairs and tetrameric

Cu−Cl3A

Symm. op. A: −1/2 + x, 1/2 − y, 1 − z.

structures were calculated using Gaussian 09 (revision D01).

Finally, prior to calculating the magnetic properties of

interest, one needs to choose a minimal set of radicals such

that its repetition along crystallographic a-, b-, and c-axes

reproduces the magnetic topology of 1. It thus follows that the

most adequate magnetic model will include all signiﬁcant J_A_B

exchange couplings in a ratio as close as possible to that found

in the inﬁnite crystal. On the basis of a regionally reduced

rings of the H L²⁺ions are twisted relative to one another at an

23−26,43

angle of 39.7° as observed previously.

Charge balance is

attained via noncoordinated lattice chloride ions which

stabilize the structure through hydrogen bonds to the

pyridinium NH groups and both water and phenolic OH

groups (Table 3), contributing signiﬁcantly to the 3D structure

of 1. Table 3 details some of the important hydrogen bonding

interactions present in 1, speciﬁcally those which provide

information regarding the superexchange discussion (vide

infra).

density matrix approach, the matrix representation of the

Heisenberg Hamiltonian is built and fully diagonalized by

using the space of spin functions of the selected minimal

magnetic model as a basis set. The resulting energy and spin

multiplicity of all possible magnetic states are then used in the

Magnetization. The M(H) plot (Figure 4) shows a linear

relationship from 0 to ∼6 kOe and then approaches saturation

as the ﬁeld reaches 50 kOe where the moment reaches 65.6

appropriate statistical mechanics expression to obtain the

macroscopic magnetic susceptibility χ(T) of 1.

Results. Synthesis. Reaction of acetic anhydride and 4-

pyridone gave 1-(4′-pyridyl)pyridin-4-one dihydrate (L) in

varying yield depending on the duration of the reﬂux. Reaction

emu/mol, a small fraction (∼1%) of the expected M (∼5700

sat

emu/mol for g = 2.00) for a mole of noninteracting copper(II)

ions which is in good agreement with the ﬁtted value of the

paramagnetic impurity (∼1.1%, Table 4, vide infra). The

magnetization observed clearly corresponds to that of a trace

paramagnetic impurity and indicates the presence of signiﬁcant

antiferromagnetic interactions and a singlet ground state in the

sample.

in air rather than N did not aﬀect the yield appreciably.

Reaction of CuCl ·2H O and L in HCl gave 1 in good yield

(

65%) as large bright green hexagonal blocks. Compound 1

was produced through the traditional slow evaporation

technique even at diﬀerent stoichiometries (1L/1CuCl₂·

H O to 2L/1CuCl ·2H O). Aqueous washes were avoided

Magnetic Susceptibility. The magnetic susceptibility as a

function of temperature from 1.8 to 310 K in 1 kOe ﬁeld is

shown in Figure 5. The susceptibility increases as temperature

decreases down to 67 K at which point it reaches a broad

as 1 may decompose. The purity and reproducibility of 1 were

conﬁrmed using combustion analysis, IR spectroscopy, and

powder X-ray diﬀraction.

−

Crystal Structure of 1. The molecular unit of 1 is shown in

Figure 2a. The Cu(II) distorted square pyramidal coordination

maximum at 3.4 × 10 emu/mol Oe and then decreases as the

temperature is decreased further down to 14 K (5.45 × 10⁻

emu/mol Oe) indicating strong antiferromagnetic interactions.

The sharp increase in the susceptibility observed as the

temperature is decreased further below 14 K is indicative of a

slight paramagnetic impurity. Thus, the magnetic susceptibility

suggests a singlet ground state in the bulk sample.

sphere (τ_A_d_d_i_s_o_n= 0.216) is completed by the Cl3 ion which

bridges neighboring Cu(II) units forming an axial−equatorial,

zigzag chain parallel to the a-axis, as shown in Figure 2b. The

Cu1−Cl3A−Cu1A angle is 127.825(13)°. The equatorial Cu1

plane is parallel to the 012 crystallographic plane and is

occupied by the H O molecule and three symmetry-unique

chloride ions coordinating in a distorted square planar fashion

Although a uniform S = 1/2 chain model does not generate

a singlet ground state, based on the crystal structure (see

Figure 2b), attempts to ﬁt the data to a uniform chain model

were made with little success. We are unaware of an analytical

model for a 2D honeycomb lattice (see Figure 3a). Therefore,

the data were ﬁt to the strong-rung ladder model using an

isotropic J Hamiltonian (see eq 1 and Supporting Information

section 3) where a negative value of J indicates antiferro-

(

mean deviation from the plane including Cl2, Cl3A, Cl4, and

O1 = 0.1258 Å) with Cu1 located 0.2321 Å above the plane.

Angles between adjacent ligands are close to 90° (see Table 2).

The axial bridging chloride ion Cl3 is coordinated to Cu1 via a

Jahn−Teller lengthened bond (2.7094(3) Å) as expected for a

40−42

distorted square pyramidal Cu(II) ion.

Chloride-bridged copper(II) chains are connected via pairs

of hydrogen bonds (Cl4A···H2−O1) to inversion related

neighboring chains in the b direction, as shown in Figure 2c.

This results in honeycomb-like layers (Figure 3a) which are

well-isolated from the neighboring layer (d_C_u_·_·_·_C_u₌11.2801(7)

Å) as a result of the bulky H₂L²ions which stack in a V-

shaped pattern between the layers (Figure 3b). The pyridine

magnetic interactions. In this regime the axial−equatorial

chloride-bridged chain is easily interpreted as the ladder rail

(Jrail ≈ −1 K, vide infra), while the hydrogen bonded dimer

motif is interpreted as the ladder rung (Jrung ≈ −106 K, vide

infra).

z z

= −J ∑ [S S + S S + S S ]

(1)

Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Figure 3. (a) Hydrogen-bonded, chloride-bridged chains form a honeycomb-like layer parallel to the ab plane (viewed parallel to the c-axis). Only

the copper coordination sphere is shown for clarity. (b) Separation between layers of hydrogen bonded copper(II) chains by the bulky cation

H₂L²⁺is shown. The two-headed arrows indicate the Cu···Cu separation.

Table 3. Hydrogen Bonding Parameters

donor−acceptor pair

D−H (Å)

H−A (Å)

D···A (Å)

D−H−A (Å)

O1−H1···Cl1A

O1−H2···Cl4A

O14−H14···Cl1

N21−H21···Cl2B

N21−H21···Cl3C

0.849(15)

0.826(15)

0.856(15)

0.852(15)

2.307(15)

2.309(15)

2.060(15)

2.628(18)

2.423(16)

3.1383(9)

3.1094(9)

2.9126(10)

3.2648(12)

3.1742(11)

167(2)

163(2)

174(2)

132.5(17)

147.4(18)

Symm. op. A: x , y , z + 1; B: x , y + 1, z + 1; C: −1/2 + x , 1/2 − y, 1 − z.

ladder and honeycomb models; both models have three

nearest neighbors (nn) which may be of two diﬀerent types.

The strong-rung ladder model parameters are summarized in

Table 4. Addition of a Curie−Weiss correction parameter θ to

account for interactions between motifs did not improve the

quality of the ﬁt. Attempts to employ the strong rail ladder

model gave unphysical results, conﬁrming the idea that the

strong exchange occurs through the H-bonded dimers.

The Heisenberg dimer model with a Curie−Weiss

correction for interdimer interactions also gave a satisfactory

ﬁt as shown in Figure 5 and Table 4 (see eq 2:

i CC y

i4CC y

χ = 0.01Xj

z + (1 − 0.01X)j

kT − θ {

k 3T {

J/T −1

(

1 + 0.3333 e

)

(2)

where X is the percent paramagnetic impurity, CC = Curie

constant, θ is the Weiss constant, and J is the exchange

strength (K)). This model suggests the axial−equatorial

chloride bridged chains propagate weak exchange (θ ≈ −1

K), while the hydrogen-bonded dimer interacts strongly (J ≅

−106 K). The ﬁts to both models are acceptable; however the

Figure 4. Magnetization as a function of ﬁeld for 1 measure at 1.8 K.

This approach has precedence in our group and has been

justiﬁed on the basis of topological similarity between the

spin-ladder model is a slightly better ﬁt to χT(T) (R χ(dimer)

Table 4. Fitting Parameters for the Dimer and Strong Rung Ladder Models with the Standard Error in Parentheses

model

CC (emu K/mol Oe)

J₍_r_u_n_g₎(K)

J₍_r_a_i_l₎(K)

θ (K)

X (%)

R²

strong-rung ladder

dimer

0.448(12) [0.4607(8)]

0.4498(7) [0.4441(5)]

−105.8(7) [−106.96(16)]

−107.4(1) [−105.5(1)]

2(7) [0.6(8)]

1.12(4) [1.42(3)]

1.61(1) [1.27(5)]

0.98866 [0.99997]

0.99968 [0.99989]

−1.22(3) []

Fits to χT(T) are shown in brackets and do not include the Curie−Weiss correction θ.

Inorg. Chem. XXXX, XXX, XXX−XXX

10 K. Right axis: χ T vs T (□). The models include the presence of a trace paramagnetic impurity [1.12% in (a) and 1.6% in (b)].

Article

Figure 5. Susceptibility data for 1, (a) ﬁt to the dimer model, (b) ﬁt to the strong-rung ladder model (solid lines). Left axis: χ vs T (ο) from 1.8 to

2−

Figure 6. Schematic view along a-, b-, and c-crystallographic axes of the crystal packing of the ﬁve pairs of [CuCl (H O)] radicals (namely, d₄₄in

blue, d₆₁in red, d₆₈in black, d₈₆in purple, and d₈₉in green).

0.99968, R χT(dimer) = 0.99989, R χ(SP ladder) =

From direct observation of the selected pairs of radicals within

the crystal packing, one can immediately realize that the

selected d_x_ypairs will deﬁne (at most) a two-dimensional

magnetic topology since radicals are connected along the ab-

axes but not along the c-axis (see Figure 6). Once selected,

bare spin-containing units are ﬁrst considered for evaluation,

either as a dimer, trimer, or tetramer model. For instance, the

through-bond J magnetic exchange interaction between

.98866, and R χT(SP ladder) = 0.99997) (see Table 4).

Evaluation of Magnetic Exchange Couplings and

Calculation of Magnetic Susceptibility Data. Analyzing the

crystal packing (see Figure 6), we found ﬁve diﬀerent pairs of

−

[

CuCl (H O)] radicals that might be magnetically signiﬁ-

4 2

cant (with Cu···Cu units within a 9.0 Å cutoﬀ), and whose J_A_B

exchange interaction should be evaluated. The pairs of radicals

are referred to as d , where xy stands for the Cu···Cu span.

−

[CuCl (H O)] radicals, which are 4.481 Å apart, has been

4 2

Speciﬁcally, the Cu-based dimers are 4.481 (d ), 6.181 (d ),

evaluated using two, three and four radical models (see Figure

7).

.876 (d ), 8.687 (d ), 8.948 (d₈₉₅), and 8.993 Å (d₈₉₉) apart.

68 86

Inorg. Chem. XXXX, XXX, XXX−XXX

models and a full discussion on J _A _B evaluation).

Article

All J_A_Bexchange interactions have been calculated in terms

35,36

of energy diﬀerences at DFT/UB3LYP level (see Table 5).

It is concluded that all calculated J_A_Bvalues using bare radical

models are underestimated at both 6-31G and 6-31+G(d)

level, irrespective of using a dimer, trimer, or tetramer cluster

models. This means that the environment (namely, H₂L₋

nearest-neighbor (nn) counterions and isolated chloride (Cl )

anions) must be explicitly accounted for in the cluster model

employed to evaluate J_A_Bmagnetic interactions.

The value of J is clearly improved when the environment is

considered. Speciﬁcally, the inclusion of 2nn in the dimer

model or 4nn in the tetramer model enhances the

ferromagnetic (FM) character of the J interaction (from

−

−1

7.2 to 54.2 cm for dimer and 14.0 to 30.6 cm for

Figure 7. Dimer, trimer and tetramer bare radical skeleton models

designed to evaluate J , J −J , and J −J −J magnetic

tetramer, see Table 5). Indeed, the use of counterions in a

dimer model to evaluate J₆₁also enhances its FM character

(see Table 5). Therefore, J₆₁is smaller in absolute value than

using a bare dimer model, i.e., J₆₁becomes less antiferro-

interactions, respectively.

−

magnetic (AFM) (from −91.8 to −77.8 cm with 2nn to

−

−1

−

68.4 cm with 4nn to −34.8 cm with 4nn and 2Cl ). This

From the ab-view in Figure 6, one also realizes that the

crystal packing of H₂L²counterions suggests that they might

aﬀect the magnetic interaction between most d_x_ypairs of

radicals alike. On the contrary, the J exchange interaction for

is exceedingly important in the tetramer model for which J

−1

varies from −102.0 to −75.4 cm taking into account four

H L (4nn) counterions. Addition of 2 Cl anions does not

imply signiﬁcant changes in the value of J₆₁(−71.0 cm ).

Nevertheless, when two chloride ions are added to the 4nn

−

−1

d₆₁would be the most aﬀected by the crystal arrangement of

the isolated chloride anions, while J₄₄and J₆₈would be hardly

aﬀected. Clearly, the bare-radical simple models must also be

^e^x^t^eⁿ^d^e^d^,^t^a^kⁱⁿ^gⁱⁿ^t^o^a^c^c^o^uⁿ^tⁿ^o^t^oⁿ^l^yⁿ^e^a^r^e^s^t^-ⁿ^eⁱ^g^h^b^o^r^H2^L

counterions but also the closest isolated chloride anions when

necessary.

tetramer model to better describe J , one realizes that the only

presence of H

character of the J₄₄interaction (from 30.6 to 17.0 cm in

nn counterions overestimates the FM

−1

Table 5). This is surprising since from direct crystal

observation we had envisaged that J₄would not be much

We note that the trimer model in addition to J also

−

aﬀected by the presence of isolated Cl anions. However, it is

evaluates the through-two-bonds intrachain next-nearest-

neighbor J₆₈magnetic interaction. In order to study the eﬀect

of the environment in the J₄₄magnetic interaction evaluation,

the dimer and trimer models have been extended including the

two and four closest H₂L²counterions (nn), respectively

clear that the strength of the hydrogen bonds between N

^a^t^o^m^sⁱⁿ^H2^Land nearby radicals is overenhanced in a

tetramer with 4nn model and, thus, a more complete model

−

with 2 Cl is required.

The trimer model is the best model to evaluate J magnetic

(

Figure 8a,b). Finally, a tetramer model with four counterions

was evaluated together with and without two chloride anions

see Figure 8c). Besides J , all remaining magnetic interactions

interactions (see trimer 4nn vs dimer 4nn in Table 5). In fact,

using a dimer model J68 becomes a FM interaction instead of

AFM. This result is not surprising since in the dimer models

(

were evaluated using bare and extended models (see

Supporting Information section 4 for a complete account of

the through-to-two-bonds J interaction is considered as if it

was through-space. All remaining J ’s are apparently

Figure 8. (a) Dimer model used to calculate J₄₄(in blue), which includes two H L counterions. (b) Trimer model including four H₂L²⁺

counterions. (c) Tetramer model including four H₂L²⁺counterions with and without two isolated chloride anions shown in purple (J₄₄in blue, J₆₁

in red, and J₈₆in purple).

Inorg. Chem. XXXX, XXX, XXX−XXX

Inorganic Chemistry

model (highlighted in purple) used to reproduce the entire magnetic topology of 1 .

Article

−

Table 5. Calculated J_A_BExchange Interactions (cm ) Using a Variety of Diﬀerent Dimer/Trimer/Tetramer Models between

Cu-Radicals at 6-31+G(d) Level

dimer

trimer

tetramer

4nn

skeleton

2nn

4nn

4nn2Cl

6nn

0.0

6nnlCl

skeleton

17.2

4nn

skeleton

4nn2Cl

J₄₄

J₆₁

J₆₈

17.2

−91.8

0.8

54.2

−77.8

36.6

14.0

−102.0

30.6

−75.4

17.0

−71.0

−68.4

4.0

0.0

−34.8

−1.2

−14.6

J₈₆

0.0

0.2

0.0

J₈₉₅

J₈₉₉

0.0

−0.4

0.4

30.2

−

“

skeleton” stands for bare radical models, without counterions (nn) and chloride Cl anions. “Xnn” stands for models with X number of nearest-

−

neighbor H ₂ L counterions (nn). “X nn Y Cl ” stands for models with X number of nn counterions and Y number of chloride Cl anions.

Figure 9. (a) Magnetic topology using J_A_Bcalculated with dimer/trimer and tetramer/trimer models, where FM J (solid blue line), AFM J₆₈(solid

2−

black line), and AFM J₆₁(solid red line) are displayed. All [(CuCl H O)Cl] radicals have been replaced by Cu point sites (blue). (b) Six-radical

honeycomb magnetic building block motif (6s) and possible extended chain and 2D magnetic models. (c) 2D cyclic 16-radical minimal magnetic

−

−1

Figure 10. Magnetic susceptibility data using J values obtained from tetramer/trimer models (J₄₄= 17.0 cm , J = −71.0 cm , J = −14.6

−

cm ). Color code: experimental data in black, 16-radical 2D cyclic model in purple.

suﬃciently small to be neglected (namely, J , J₈₉₅, and J₈₉₉),

irrespective of the model used.

strong-rung spin-ladder were good ﬁtting models to

reproduce the experimental data, in spite of their good

regression coeﬃcients (Table 4).

The calculated J ’s deﬁne a 2D honeycomb-like magnetic

topology (see Table 5 and Figure 9a for the ab-view). For

either the dimer/trimer or tetramer/trimer models, there are

three driving magnetic interactions: FM J₄₄and AFM J₆₈

compete as a chain motif along the a-axis, and chain motifs

are then connected by AFM J (see Figure 9a). Therefore, the

The magnetic models, which are all multiples of the 6-radical

honeycomb magnetic building block motif, used to calculate

the χ(T) magnetic susceptibility data include open and cyclic

models to explore the cooperativity between magnetic

exchange along the a - and b -crystallographic axes (see Figure

9b and Supporting Information section 5 for a detailed

discussion). Calculated χ(T) magnetic susceptibility data agree

magnetic topology that results from the FPBU study is a very

useful tool to understand why neither a simple dimer nor a

Inorg. Chem. XXXX, XXX, XXX−XXX

and AFM J ₆ ₈ = −14.6 cm . Geometric frustration is shown inset as green ⌀ symbols in (a) and purple ⌀ symbols in (b).

Article

Figure 11. Spin alignment represented schematically according to (a) AFM J = −71.0 cm and FM J₄₄= +17.0 cm ; (b) AFM J = −71.0 cm⁻¹

−

−1

−

Figure 12. (a) Relationship between the honeycomb (J_s_o_l_i_d, J_d_a_s_h_e_d), dimer (J, θ), and ladder (J_r_u_n_g, J ) models shown diagrammatically. Note that

rail

−

comparison should be established between J_s_o_l_i_d, J, J_r_u_n_gand J_d_a_s_h_e_d, θ, J . (b) Potential superexchange pathways present in the [CuCl (H O)]

rail

dimer moiety, indicated by dashed lines, including the hydrogen bond pathway (Cu1−O1−H2···Cl4A−Cu1A, in black) and the two-halide

pathway (Cu1−Cl4···Cl4A−Cu1A, in blue).

with experiment and indicate that the 16-radical 2D cyclic

geometrical frustration in 1 is an advantage to further pursue

investigation in this family of compounds.

model using J from tetramer/trimer (J , namely, J = 17.0

−

−1

cm , J = −71.0 cm , and J = −14.6 cm ) models has to

be used to simulate the magnetic susceptibility of 1 (see Figure

Magneto-Structural Discussion. The investigation of this

lattice relies heavily on existing magneto-structural correla-

tions. The relationship between the dimer, ladder, and

honeycomb models are shown in Figure 12. The strong-rung

ladder and dimer models give a strong J coupling of ca. −106 K

c for model and purple circles in Figure 10 for χ(T) data).

The experimental magnetic susceptibility data as a function

of temperature for 1 shows an increase in susceptibility to a

maximum of 0.00337 emu/mol Oe at 65.5 K with no observed

increase in χT(T), which is indicative of dominant AFM

interactions. At lower temperatures, χ(T) decreases rapidly

toward 0, supporting the presence of AFM interactions, as well

as indicating a singlet ground state. The calculated χ(T) data

increase to a maximum of 0.00308 emu/mol Oe at 59.0 K in

good agreement with the experimental data. Competing FM J₄₄

and AFM J , J interactions are thus found to be crucial to

−1

(

−74 cm ) in the dimer moiety, which is unusual for the

potential pathways present in 1, namely, the two-halide

pathway or the hydrogen bonded O−H···Cl pathway (see

Figure 12b). Furthermore, while the strong-rung ladder model

ﬁts the data with J_r_u_n_gand J_r_a_i_lvalues similar to the dimer ﬁt

values for J and θ, respectively, it is only topologically related

to the honeycomb lattice and has a larger residual standard

deviation in the ﬁtted parameters which suggests that the

ladder model may not be appropriate for the honeycomb

tune the resulting macroscopic magnetic response.

In fact, the competition between FM and AFM pair

interactions leads to geometrical frustration in 1 (see Figure

lattice under study in spite of prior successful use.

It has been found that the axial−equatorial halide bridged

chain should propagate very weak interactions in square

1). Bearing in mind that the strong AFM J has to be always

pyramidal copper(II) complexes. The Curie−Weiss correc-

satisﬁed, there are two possible limiting spin arrangements

depending on whether FM J (Figure 11a) or AFM J (Figure

tion to the dimer ﬁt and the ladder J_r_a_i_lis an indication of the

AFM exchange strength through the monohalide bridge (θ =

1b) is satisﬁed, since the disposition of the AFM J₆₁coupled

−1

−1.15K = −0.8 cm ), J

≈ −1 K = −0.7 cm ) coupling

rail

radicals is not compatible with the two remaining exchange

ⁱⁿ^t^e^r^a^c^tⁱ^oⁿ^s^.^I^tⁱ^s^c^l^e^a^r^t^h^a^t^f^u^l^ﬁ^l^l^m^eⁿ^t^o^f^F^M^J⁴4 interactions

introduces a higher degree of geometrical frustration (compare

Figures 11a,b). Therefore, it is more likely that compound 1

satisﬁes both AFM J₆₁and J₆₈to the detriment of FM J₄₄_.In

any case, the possibility of exploitation of the intrinsic

dimers in the layer, which agrees qualitatively with existing

46−48

trends.

[Due to diﬀerences in the Hamiltonian employed

(number of nearest neighbors) and the Curie−Weiss Law, only

the magnitudes of θ and J should be compared.] The sign of

rail

the monohalide bridged superexchange has been related to the

angle ϕ(Cu1−X−Cu1A) where a large ϕ tends to give

Inorg. Chem. XXXX, XXX, XXX−XXX

Inorganic Chemistry

Article

−

Table 6. Details of the Potential Superexchange Pathways within the [CuCl (H O)] Dimer Moiety

pathway

∠t (°)

∠Cu1−Cl4···H2A (°)

∠Cu1A−O1A−H2 (°)

∠Cl4···H2A−O1A (°)

dCl4···H2A (Å)

Cu1−Cl4···H2A−O1A−Cu1A

168.4(3); 175.99(7)

136.1(3)

118.8(8)

163.1(10)

2.19(5)

∠

t°

∠Cu1−Cl4···Cl4A (°)

dCl4···Cl4A (Å)

3.9501(12)

Cu1−Cl4···Cl4A−Cu1A

180

92.84(6)

∠

t is the torsion angle.

increasingly antiferromagnetic exchange while small ϕ gives

the 2-halide pathway. These results are in complete agreement

with the results of the FPBU study which support the strong

ferromagnetic exchange. However, there exists a complex

Cu(μ-Cl)(caﬀeine)H O]Cl) with weak ferromagnetic inter-

−

(

exchange observed through the [CuCl (H O)] dimer moiety

−

−1

actions (+0.5 cm ) through the same chloride-bridged ϕ

angle (128°) as 1, and thus this relationship is tentative. Other

attempts have been made to correlate structural aspects with

the observed superexchange with only moderate success, e.g.,

ϕ/R where R = long Cu−Cl bond length and ϕ = Cl−Cu−L

superexchange pathway (J₆₁= −71 cm , see J

in Figure

solid

12a). However, the apparent vanishingly small exchange

through the single halide bridge is merely a brute average of

−

the competing nn (FM, J = 17 cm , see J in Figure 12a)

dashed

−

and nnn (AFM, J₆₈= −15 cm , not shown in Figure 12a)

angle where L = ligand trans to the bridging Cl. In general,

exchange interactions.

however these observations agree well with the orbital overlap

Computational results show that the magnetic topology of

picture between the radical containing x −y orbital and ﬁlled

compound 1 is a honeycomb, but no full analytical ﬁtting of

orbital as is expected for a square pyramidal geometry

a honeycomb model exists. Instead dimer, with an interdimer

exchange parameter, and strong-rung ladder ﬁtting models

were used. Upon the basis of experimental data alone, there

appear to be only a large −106 K exchange and a small/

negligible −1 K exchange. Yet again, we are ﬁtting a distorted

honeycomb system with at least three ﬁtting parameters, based

upon calculations, to models with only two ﬁtting parameters:

the dimer and strong-rung ladder models. Thus, the apparently

negligible second exchange parameter results from the

accidental near cancellation of the nearest-neighbor and next-

nearest-neighbor exchange interactions. In the absence of a

valid analytical model for the honeycomb lattice, the models

employed are the most reasonable available but are used being

fully aware that the obtained ﬁtting parameters are estimates of

the real ones.

involved in an axial−equatorial interaction. Distortion

toward trigonal bipyramidal mixes the ground state bearing

the unpaired electron and thus the interaction may become

stronger.

The often observed two-halide pathway is present in dimer

d₆₁of 1, and the parameters for both potential pathways

(

namely, two-halide and hydrogen bonded) are shown in

Table 6 and Figure 12b. The curiously strong ﬁtting parameter

−

(

J, J_r_u_n_g−106 K = −74 cm ) is uncommon for either of these

pathways. For instance, for the Cu−Br···Br−Cu two-bromide

pathway J is typically in the range of 0−20 K depending on the

distance between bromide ions and the angles containing the

−1

interaction. However, J = −234 K (163 cm ) has been

observed in (2,5-dimethylpyrazine)copper(II)dibromide.

Additionally, moving from the bromide to the chloride

pathway in an isostructural pair typically results in much

weaker exchange strengths due to the relative size of the

CONCLUSIONS

The ﬁrst-principles, bottom-up study of 1 demonstrates that

the environment of [(CuCl H O)Cl] radical/spin-contain-

ing units is crucial to evaluate the strength of a given radical···

radical magnetic interaction. It has been disclosed that

■

−

bromide and chloride ions. In fact, Butcher et al. suggest

through density functional theory calculations that the

isostructural dichloride compound with 2,5-dimethylpyrazine

with a Cl···Cl distance of 3.633 Å should have J = −72 K (−50

hydrogen bonding between radicals and environment (H L

−

cm ). Comparison of this value to the ﬁtting J, J

counterions and Cl ) enhances the FM character of pair

exchange interactions in 1.

rung

parameters of 1, which relates to a Cl···Cl distance of

.9501(12) Å, makes us realize that a much stronger exchange

The magnetic topology of 1 has been found to be two-

dimensional (crystallographic ab-direction). According to the

tetramer cluster model, there are two predominant competing

−

(J = −106 K = −74 cm ) is achieved using H L as

counterion.

Thus, based on existing magneto-structural correlations, the

two-chloride pathway in 1 should propagate weak exchange.

On the contrary, the hydrogen bonded superexchange

pathway, speciﬁcally the Cu−OH···O−Cu pathway, has been

recognized to have exchange strengths that typically vary

J_A_Binteractions along the a-axis, namely, FM J (+24.8 K =

−

−1

+17.0 cm ) and AFM J (−21.0 K = −14.6 cm ), which

deﬁne a chain motif. These chain motifs are then connected

along the b-axis through strong AFM J (−102 K = −71

−

cm ), resulting in a 2D honeycomb-like magnetic topology. It

must be stressed that although strong-rung ladder and a dimer

models can ﬁt the experimental χ(T) data our computational

study shows that these ﬁtting parameters carry no physical

meaning since a honeycomb plaquette must be taken as

magnetic building block for 1, as was foreseen from crystal

inspection. A cyclic 16-radical minimal magnetic model thus

based on this honeycomb plaquette perfectly reproduces the

χ(T) behavior for all range of temperatures.

−

greatly from very weak to strong (−94 cm ) and depend

qualitatively on the degree of x −y orbital overlap given by

parameters such as the O···O distance and the vertical distance

between copper coordination planes. For 1 the relevant O···

Cl distance is 3.1093(9) Å and the equatorial planes of Cu1

and Cu1A (as shown in Figure 12b and Table 6) are

−

coincident. Given the larger size of Cl relative to O (∼2.5×),

this contact is expected to confer strong exchange since the

O···X distance/sum of radii here is only 20% larger than that

Finally, it is worth mentioning that the competition between

FM J₄₄and AFM J₆₈could induce interesting magnetic

response at low temperatures if the magnetic exchange is

adequately tuned by modifying substituents in ligands and, in

found for the O···O case (2.32 Å). It is therefore reasonable

to infer that the strong exchange is propagated via the

hydrogen bonded pathway with a smaller contribution from

Inorg. Chem. XXXX, XXX, XXX−XXX

Inorganic Chemistry

Article

turn, interactions within the crystal packing. Besides, geo-

metrical frustration could also be manipulated to proﬁt from

certain superexchange pathways and thus enhance the FM

interactions within this family of compounds.

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ASSOCIATED CONTENT

sı Supporting Information

https://pubs.acs.org/doi/10.1021/acs.inorgchem.0c00433.

■

(

¹H and ¹³C NMR spectra of the ligand, powder X-ray

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AUTHOR INFORMATION

Corresponding Authors

Jeﬀrey C. Monroe − Carlson School of Chemistry and

Biochemistry, Clark University, Worcester, Massachusetts

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(

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1610, United States; Email: jmonroe@clarku.edu

Merce Deumal − Department Ciencia de Materials i Quimica

Fisica & IQCTUB, Universitat de Barcelona, Barcelona E-

8028, Spain; orcid.org/0000-0002-6385-8149;

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Email: mangelscarvajal@gmail.com

Mark M. Turnbull − Carlson School of Chemistry and

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Complete contact information is available at:

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