Theoretical investigation of magnetic properties of a dinuclear copper complex [Cu2(μ-OAc)4(MeNHpy)2]

Journal of Molecular Structure: THEOCHEM 775 (2006) 19–27 www.elsevier.com/locate/theochem

Theoretical investigation of magnetic properties of a dinuclear copper complex [Cu2(l-OAc)4(MeNHpy)2] Md. Ehesan Ali, Sambhu N. Datta

*

Department of Chemistry, Indian Institute of Technology – Bombay, Powai, Mumbai 400076, India Received 19 April 2006; received in revised form 26 June 2006; accepted 29 June 2006 Available online 20 July 2006

Abstract We have investigated the magnetic properties of a recently synthesized dinuclear complex, [Cu2(l-OAc)4(MeNHpy)2], by broken-symmetry (BS) density functional (DFT) methodology. The complex has several pairs of magnetic orbitals. Therefore, we have explicitly calculated the overlap integral Sab between the two natural magnetic orbitals, and found a value of 0.8589. Deviating from the common practice of approximating Sab by 1 for the strongly delocalized systems, the computed value has been used in calculating the magnetic exchange coupling constant (J) from the two electron-two orbital BS model. The calculated J is 290 cm1, in excellent agreement with the observed value of 285 cm1. The contribution of the overlap between the orbitals of the two copper atoms to Sab is negligibly small. Also, the calculated J value is a weakly varying function of the Cu–Cu distance. The last two observations confirm that the throughligand superexchange phenomenon is responsible for the high magnetic exchange interaction in the Cu2(l-OAc)4 complex(es). Furthermore, we have shown that the onset of intramolecular hydrogen bonding reduces the spin density on the bridging atoms and consequently the magnitude of J. This explains why the complex under investigation has a J value smaller than that of [Cu2(l-OAc)4(H2O)2] (299 cm1). While establishing this trend, we predict that the complex [Cu2(l-OAc)4(py)2] would have a higher J value, about 300 cm1.  2006 Elsevier B.V. All rights reserved. Keywords: Natural magnetic orbital; Broken-symmetry

1. Introduction The study of intramolecular magnetic coupling between two magnetic centers within a molecule is a fascinating subject [1]. Intramolecular and intermolecular magnetic interactions play the major role in controlling the magnetic properties of molecular crystals. The intramolecular magnetic coupling in dinuclear transition metal complexes is controlled by the number of bridging ligands, the angle M(metal)–L(bridging-ligand)–M(Metal), the M–M distance, and the nature of bridging ligands and other ligands. A large body of theoretical and experimental work has been performed to explain the magnetic properties [2].

*

Corresponding author. E-mail address: [email protected] (S.N. Datta).

0166-1280/$ - see front matter  2006 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2006.06.043

A number of compounds with the same basic structure Cu2(l-OAc)4 have been synthesized and the cooperative magnetic interactions in these have been investigated, thereby establishing that the through-ligand superexchange leads to the rather strong intramolecular interaction in these complexes [3–6]. Recently, Barquı´n et al. [7] have synthesized a similar compound by introducing 2-methyl imino pyridine in the axial position as shown in Fig. 1. This has the important characteristic of having two intramolecular hydrogen bonds as shown by the dotted lines, while the corresponding analogs with H2O and NH3 molecules as axial ligands do not have intramolecular hydrogen bonds. Complexes with the Cu2(l-OAc)4 basic structure have quite high intramolecular magnetic exchange coupling constants [8]. The coupling constant J is 299 cm1 for [Cu2(l-OAc)4(H2O)2] and 285 cm1 for [Cu2(l-OAc)4

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Fig. 1. The dinuclear copper complex [Cu2(l-OAc)4(MeNHpy)2].

(NH3)2]. The strong antiferromagnetic interaction in these compounds was initially thought to be explained by the doverlap of dx2 y 2 orbital of each copper atom, which contains the unpaired electron [9]. It is now theoretically accepted that the through-space interaction has much less contribution to the overall J in comparison to the through-bridge exchange contribution [10]. Ruiz et al. have extensively carried out theoretical calculations by varying the substituents of the bridging carbon atoms [10]. These substitutents have been found to play a very important role in controlling the value of J. As the electronegativity of the atom or the group attached to the bridging carbon atoms increases, the J value generally decreases. In the case of very strongly electronegative groups like –CF3 and –CCl3, however, the opposite effect is observed. Ruiz et al. [10] have also noticed that the changes in axial ligands introduce only a little variation of J. The qualitative model of Hay–Thibeut–Hoffmann (HTH) [11] cannot explain the observed variation of J in acetate-bridged compounds. This model is mainly based on the energy differences between the singly occupied molecular orbitals (SOMOs). The participation of the axial ligands in the SOMOs is forbidden by symmetry. It is also

generally known that the coupling constant depends on the number of bridging ligands n and can be expressed as J = JF + nJAF where JF and JAF are respectively the ferromagnetic and antiferromagnetic contributions. In addition to these controlling factors, the spin density of the bridging atoms must be ultimately responsible for the J value. Any physical phenomenon that can affect the spin density on the bridging atoms can control the intramolecular coupling constant. The main objective of this work is to carry out a theoretical investigation and evaluate the magnetic exchange coupling constant by broken-symmetry approach while avoiding any approximation to the overlap integral between the magnetically active orbitals. We have calculated the intramolecular magnetic exchange coupling constant for the complex synthesized by Barquı´n et al. [7]. The second aim of this paper is to reinvestigate the mechanism of the magnetic exchange interaction of the same complex. This has been done in two ways. First, we have shown that the contribution of the overlap between the orbitals of the two copper atoms to the overlap of the two magnetic orbitals is truly small. Second, we have performed computations on structures with varying Cu–Cu distance while the rest of the structure is kept intact, and analyzed the spin distribution in each case. The third goal here is to demonstrate that the J value undergoes reduction with the onset of intramolecular hydrogen bonding. This has been investigated by comparing the spin density distribution in three systems, namely, the original complex, a complex with pyridine substitution in the axial position (a possible new compound) and a complex with the axial ligands in a different conformation. The latter structures are shown in Fig. 2. 2. Theoretical background The magnetic exchange interaction between two magnetic sites 1 and 2 is normally expressed by the Heisenberg spin Hamiltonian ^ ¼ J S^1  S^2 H

ð1Þ

where Sˆ1 and Sˆ2 are the respective spin angular momentum operators. A positive sign of J indicates a ferromagnetic interaction, whereas the negative sign indicates an

Fig. 2. Structure of (a) the pyridine substituted complex, and (b) a conformer with the MeNHpy ligands in the axial positions rotated through 45.

M.E. Ali, S.N. Datta / Journal of Molecular Structure: THEOCHEM 775 (2006) 19–27

antiferromagnetic interaction. The eigenfunctions of the Heisenberg Hamiltonian are eigenfunctions of S2 and Sz where S is the total spin angular momentum. The coupling constant J can be directly related to the energy difference between the eigenstates. For a diradical, EðS ¼ 1Þ  EðS ¼ 0Þ ¼ J :

ð2Þ

The Heisenberg description of magnetic interaction can be correlated with the electronic structure of a given system [12,13]. Recently a large number ab initio calculations have been performed to evaluate J [14]. A proper mapping between the Heisenberg spin eigenstates and suitable ab initio electronic states is necessitated for the above procedure, which is computationally very expensive and not practical for a large system. An alternative approach has been proposed by Ginsberg, Noodleman, Yamaguchi, and others so as to reliably compute the magnetic exchange coupling constant with less computational effort [15–17]. The spin polarized, unrestricted formalism and a broken-symmetry (BS) solution is needed for the lowest spin-state in this method. The BS ˆ . It is an equal mixture of a state is not an eigenstate of H singlet and a triplet states. The coupling constant can be written as J ð1Þ

2ðEBS  ET0 Þ ¼ 1 þ S2ab

UHF is not fully justified. They have recommended the use of the strongly localized limit for the general cases. In the strongly delocalized limit, however, the BS state becomes accidentally degenerate with the singlet state, and J ¼ EBS  ET :

where Sab is the overlap integral between the two magnetic orbitals a and b in the broken-symmetry solution. The quantity EBS is the energy of the broken-symmetry solution and ET0 is the energy of the triplet state in the unrestricted formalism using the unchanged BS orbitals. In a singledeterminant approach, ET0 can be approximated by the energy of the true triplet state (ET0  ET ) because of the very less spin contamination in the high spin state. Eq. (3) is valid when there are only two singly occupied magnetic orbitals, and the rest of the spatial orbitals are either doubly occupied or unoccupied. If the above assumption fulfills then ÆS2æBS equals 1  S2ab . It is observed in literature that Eq. (3) is used in the strongly localized or orthogonal limit where Sab fi 0 as well as the strongly delocalized limit where Sab fi 1. The current literature is full of controversy regarding the choice of limit. Generally, in DFT based calculations on transition metal complexes, the magnetic orbitals turn out to be more delocalized than those obtained from the UHF calculations, and some of the authors have suggested the use of the strongly delocalized limit [18]. However, Bencini et al. have invoked the strongly localized limit [19], which truly holds for organic diradicals with extensive p-conjugation. It has also been concluded that the limit should be chosen on the basis of the proximity of calculated and experimental values, rather than a consideration of rigorous theoretical complications [20]. Illas et al. [21] have shown that the most often quoted trend concerning the much larger degree of delocalization of magnetic orbitals obtained from DFT as opposed to

ð4Þ

Despite these problems and several other deficiencies in DFT as recently mentioned by several authors, Eq. (4) produced very impressive numerical results by using B3LYP exchange correlation functional [22]. A large volume of literature is found on this issue [10,18,23]. In our recent work [24], we have neither resorted to any arbitrary assumption about the value of Sab, nor we have relied on an empirical ground of comparing theoretical and experimental values. The magnetic exchange coupling constants have been calculated by using the explicitly computed overlap integral in Eq. (3) in each case. The same approach is adopted here, though the choice of magnetic orbitals is somewhat more involved in the present case. Finally, the magnetic exchange coupling constants (J) are also calculated using Ginsberg, Noodleman, Davidson (GND) Bencini, and Ruiz’s spin projection formula for the strong overlap cases J ð2Þ ¼

ð3Þ

21

2ðDFT EBS  DFT ET Þ : S max ðS max þ 1Þ

ð5Þ

3. Computational method The molecular geometry of the complex is obtained from the crystal structure reported by Barquı´n et al. in ref. [7]. The geometry was not theoretically optimized, as we want to keep up the effects of the surrounding molecules on the geometry of the selected molecule in the real crystal. To obtain the broken-symmetry states, all the single-point UB3LYP calculations have been performed with the accurate guess values of molecular orbitals, which are in turn retrieved from the proper ROHF calculations. In all the calculations, 6-311G(d,p) basis sets are used for the lighter atoms. For the copper atoms, we have used 6-311G(d,p) [without any pseudopotential], LANL2DZ and CEP-121G basis sets. The single-point computations have been performed with Gaussian 03 quantum chemical package [25]. The Z-matrix editor in Molden [26] software has been used to vary the Cu–Cu distance. The Hyperchem PR 7.0 software [27] has been used to obtain the molecular geometry with axial ligands in a rotated conformation. The visualization software Molekel [28] has generated the view of the molecular orbitals from the outputs of the Gaussian 03 calculations. We have ourselves written a program to compute the overlap integral Sab between the two magnetic orbitals, and to evaluate the contribution of the overlap between the orbitals of the two copper atoms to Sab. This program uses the basis set information and molecular orbital coefficients from the log files of Gaussian 03 software.

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computed overlap integral between the selected magnetic orbitals is 0.8589(49).

4. Choice of magnetic orbitals The interaction between two magnetic centres A and B is similar to the existence of a very weak chemical bond between them. In the present case, both the singlet and triplet states are very close to each other in energy, and both can be thermally populated. When the interaction vanishes, the dynamics of the two active electrons (one from A and another from B) become uncorrelated. The Heitler–London approach in this case results in two semilocalized orbitals a and b which can be identified as the magnetic orbitals. Orthogonalized magnetic orbitals and natural magnetic orbitals are oft-quoted types of magnetic orbitals [1,29]. The results from the BS calculations here necessitate the choice of the natural magnetic orbitals. The overlap integrals between the spatial parts of the occupied a and b orbitals in the BS states are given in Table 1. There are several pairs of magnetic orbital in this complex, but the HOMO and HOMO-1 pairs are certainly not among them. The calculated overlap integrals in Table 1 indicate that the net overlap between the spatial parts of the product of a orbitals and that of b orbitals is quite small. Therefore, the calculated ÆS2æBS should be a little less than 1. Indeed, the computed ÆS2æBS values vary from 0.98 to 0.99. As such, an application of the two-orbital model would fail in the present case. One must resort to the consideration of natural magnetic orbitals to calculate an effective value of Sab for possible use in Eq. (3). To obtain the natural magnetic orbital a for the present complex [Cu(7)(l-OAc)4Cu(13)(MeNHpy)2], single-point calculations have been performed by treating Cu(13) as dummy to prevent any orbital interaction between Cu(13) and the rest of the molecule. The resulting singly occupied HOMO is chosen as orbital a. Similarly, the magnetic orbital b has been obtained by treating atom Cu(7) as dummy. These calculations have been carried out at the UB3LYP/ 6-311G(d,p) level using charge 0 and multiplicity 2. The

Table 1 The computed overlap integral between the spatial parts of alpha and beta occupied orbitals in the BS state of the dinuclear copper complex HOMO

HOMO HOMO-1 HOMO-2 HOMO-3 HOMO-4 HOMO-5 HOMO-6 HOMO-7 HOMO-8 HOMO-9 HOMO-10

Orbital energy (a.u.)

Sab

a

b

0.20278 0.20294 0.23769 0.24290 0.25369 0.26021 0.26385 0.26912 0.27105 0.27914 0.28208

0.20273 0.20299 0.23753 0.24310 0.25370 0.26016 0.26384 0.26914 0.27098 0.27915 0.28206

0.9997 0.9997 0.2876 0.4977 0.7405 0.7478 0.9913 0.8126 0.7020 0.9844 0.9554

5. Results and discussion The intramolecular magnetic coupling constants are calculated using Eq. (3). The computed value of the overlap integral Sab for the natural magnetic orbitals remains more or less unchanged through three digits for the different basis sets and the varying Cu–Cu distance investigated here. Therefore, Sab = 0.859 has been used throughout in these calculations to generate a three digit accuracy for the calculated J. The calculated J values are given in Table 2. The metal atoms are known to control the magnetic properties of transition metal complexes, and it is necessary to treat these atoms with effective core potentials. In fact, when we use the 6-311G(d,p) basis set for the valence orbitals of copper atoms, we obtain a J value of 272 cm1 from Eq. (3), whereas both CEP-121G and LANL2DZ bases give a coupling constant of 290 cm1. The latter J values excellently match the observed value 285 cm1 that was reported by Barquı´n et al. [7] and corresponds to Eq. (1). The overlap of the d-orbitals of the two copper atoms (mainly dx2 y 2 in the magnetic orbitals is indicative of dbonding between the two Cu atoms, that is, the strength of the through-space interaction. The computed value of this overlap integral is around 0.000011 in absolute magnitude. This is not surprising as the two copper atoms are considerably away from each other, but it confirms that the direct exchange would be negligibly small. In each complex with one dummy copper atom, the gross d-orbital population and the total electronic population are 8.75 and 27.32 respectively for the copper atom that is involved in the calculation. To test the absence of direct exchange further, the distance between the two copper atoms is varied from 2.62 ˚ with an interval of 0.05 A ˚ . The rest of the structo 2.87 A ture is kept intact at the crystallographic geometry. The observed Cu–Cu distance in the crystallized complex is ˚ . Table 3 shows a very systematic variation of the 2.72 A single-point total energy with the Cu–Cu distance. Fig. 3 illustrates this trend. The CEP-121G basis set consistently Table 2 Single-point calculations in UB3LYP method using 6-311G(d,p) basis sets for atoms other than the Cu atoms Cu basis set

6-311G(d,p) Lanl2dz CEP-121G a

Energy (a.u.) ÆS2æ BS

T

4881.0236208 0.987599 4881.0934244 0.983606 4881.1188212 0.987053

4881.0225427 2.002953 4881.0922747 2.003598 4881.1176725 2.003776

Using Sab = 0.859 in Eq. (3).

J (2) (cm1)

J (1)a (cm1)

237

272

252

290

252

290

M.E. Ali, S.N. Datta / Journal of Molecular Structure: THEOCHEM 775 (2006) 19–27

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Table 3 Single-point calculations by UB3LYP method using 6-311G(d,p) basis sets for atoms other than the Cu atoms with varying Cu–Cu distance ˚) J (2) Cu basis set Cu–Cu distance (A Energy (a.u.) 2 (cm1) ÆS æ

2.62 2.67 Lanl2dz

2.72 2.77 2.82 2.87 2.62 2.67

CEP-121G

2.72 2.77 2.82 2.87

a

BS

T

4881.061151 0.981953 4881.083968 0.983567 4881.0934244 0.983606 4881.0927969 0.982964 4881.0844034 0.982456 4881.065495 0.983909

4881.0601861 2.003702 4881.0828751 2.003693 4881.0922747 2.003598 4881.0916344 2.003604 4881.083226 2.00372 4881.0643415 2.003576

4881.0870304 0.987054 4881.1097856 0.987016 4881.1188212 0.987053 4881.1198784 0.986935 4881.1114843 0.98607 4881.0924631 0.987672

4881.0859311 2.003776 4881.1086601 2.003789 4881.1176725 2.003776 4881.1187121 2.003775 4881.110294 2.003824 4881.0913333 2.003771

J (1)a (cm1)

212

244

240

276

252

290

255

294

258

297

253

291

241

278

247

284

252

290

256

295

261

301

248

285

Using Sab = 0.859 in Eq. (3).

˚ . These values are in good agreement with the 2.75 A ˚ in crystal. We notice observed Cu–Cu distance of 2.72 A from Table 3 that the calculated J value is only weakly dependent on the Cu–Cu distance. The absolute magnitude of the calculated coupling constant increases as the dis˚ and then it decreases tance increases up to about 2.82 A (Fig. 4). This is only possible if there is no d-bonding. The through-space interaction contributes very little to the J value, and the through-bridge exchange is the dominant contribution. The slight variation of the J value arises from the change in the overlap and bonding with the atoms

Energy (a.u.)

-4881.06

-4881.12

-220 2.600

2.925

Fig. 3. The plot of the calculated total energy against the Cu–Cu distance. The total energy was calculated by UB3LYP method with 6-311G(d,p) basis sets for atoms other than the Cu atoms. The dotted lines are for the triplet states and bold lines are for the broken-symmetry states. The upper set of curves is for the lanl2dz basis set used for the copper atoms and the lower one is for the CEP-121G basis set.

J (cm -1)

Cu-Cu distance in Angstrom

-320

yields a lower energy for each state. Both the bases yield a BS state more stable than the T state. In the case of the LANL2DZ basis set, the minimum of the energy curve is ˚ . For CEP-121G basis set it is at about around 2.74 A

2.6

2.7

2.8

2.9

Cu-Cu distance in Angstrom Fig. 4. Variation of the calculated J values with the Cu–Cu distance for the lanl2dz (dotted line) and CEP-121G (bold line) copper basis sets.

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of the bridging ligands. The DFT treatment can produce incorrect results, especially when the interaction is weak. The magnetic interaction is fairly strong in the present system. Still, the use of diffuse functions along with 6-311G** is expected to improve the calculated J value. The reason for the absence of direct exchange can be understood from Fig. 5. The dx2 y 2 orbitals of the copper atoms as shown in Fig. 5b form the singly occupied HOMO’s whereas the dz2 orbitals in Fig. 5e are fully occupied. As the dx2 y 2 point towards the bridging ligands while the dz2 orbitals are along the Cu–Cu axis, the throughbridge interaction determines the magnetic properties. The overlap between the dz2 orbitals is negligibly small. The average squared spin populations of the Cu atoms are correlated with the computed J values in Table 4. The spin densities are obtained from the calculation at UB3LYP/6-311G(d,p)/CEP-121G level. The nature of the plot of DP2(Cu) [defined as DP2(Cu) = P2 (Cu)HS  P2 (Cu)BS] against the Cu–Cu distance is in general agreement with the nature of the plot of the calculated J versus the

Cu–Cu distance (Table 3). But for the O atoms, it is observed that only the triplet spin population matches with the nature of variation of J. These plots are given in the supporting information. The intramolecular hydrogen bonding has a minor influence on the magnetic exchange coupling constant. Table 5 shows that the absolute magnitude of J increases by about 10 cm1 for the pyridine substituted species and for the 45-rotated conformation. To find a reason for this behavior, we have investigated the spin density on the bridging oxygen atoms. The Mulliken spin density distribution is shown in Table 6. The spin density changes progressively along each Cu–O–C–O–Cu chain, manifesting an antiferromagnetic trend. The spin densities on the hydrogenbonded O(22) and O(34) atoms in the original complex are lower than those on the non-hydrogen-bonded oxygen atoms, and also much reduced compared to the spin densities in the pyridine substituted complex and the 45-rotated conformer. The spin densities on all other oxygen atoms remain almost unchanged in the latter two

Fig. 5. View of molecular orbitals: (a) LUMO, (b) HOMO, (c) HOMO-1, (d) HOMO-2, and (e) HOMO-5. The electronic population of HOMO and HOMO-1 is 1.0. The MOs are obtained from the ROHF/6-311G(d,p)/Lanl2dz calculation for the triplet.

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Table 4 The variation of average spin density square and the difference of average spin density square between the broken-symmetry (BS) and Triple (HS) state for Cu(7) and Cu(13) ˚) Cu–Cu distance (A 2.62 2.67 2.72 2.77 2.82 2.87 P 2HS ðCuÞ P 2BS ðCuÞ DP2(Cu) J (cm1)

0.4533 0.4497 0.0037 278

0.4568 0.4526 0.0043 284

0.4585 0.4536 0.0049 290

0.4637 0.4566 0.0071 295

0.4643 0.4577 0.0066 301

0.4703 0.4641 0.0063 285

Table 5 Single-point calculations by UB3LYP method using 6-311G(d,p) basis sets for the atoms other than Cu atoms by replacing the axial ligands with pyridine and by rotating the axial ligands through 45 Cu basis set

Condition

Original Lanl2dz

Pyridine subst. 45 rotation Original

Cep-121G

Pyridine subst. 45 rotation

a

Energy (a.u.) ÆS2æ BS

T

4881.0934244 0.983606 4691.7378766 0.982556 4881.0903817 0.985857

4881.0922747 2.003598 4691.7366646 2.003666 4881.0891793 2.003708

4881.1188212 0.987053 4691.7654575 0.986742 4881.1147885 0.986682

4881.1176725 2.003776 4691.764268 2.003831 4881.1136113 2.00381

J(2) (cm1)

J(1)a (cm1)

252

290

266

306

264

303

252

290

261

300

258

297

Using Sab = 0.859 in Eq. (3).

Table 6 The Mulliken spin densities on different atoms from the UB3LYP calculations on the broken-symmetry state Original Pyridine 45 rotated

Cu(7) 0.6766 0.6691 0.6736

O(8) 0.0795 0.0778 0.0765

C(9) 0.0004 0.0001 0.0003

O(31) 0.0797 0.0787 0.0766

Cu(13) 0.6705 0.6685 0.6687

Original Pyridine 45 rotated

Cu(7) 0.6766 0.6691 0.6736

O(30) 0.0785 0.0785 0.0758

C(20) 0.0002 0.0001 0.0002

O(28) 0.0805 0.0779 0.0775

Cu(13) 0.6705 0.6685 0.6687

Original Pyridine 45 rotated

Cu(7) 0.6766 0.6691 0.6736

O(34)a 0.0650 0.0721 0.0707

C(26) 0.0660 0.0011 0.0010

O(25) 0.0804 0.0802 0.0829

Cu(13) 0.6705 0.6685 0.6687

Original Pyridine 45 rotated

Cu(7) 0.6765 0.6691 0.6736

O(24) 0.0791 0.0803 0.0823

C(23) 0.0018 0.0011 0.0014

O(22)a 0.0660 0.0719 0.0718

Cu(13) 0.6705 0.6685 0.6687

For Cu atoms, the CEP-121G basis set was used. For all other atoms, the 6-311G(d,p) basis set was adopted. a Hydrogen bonded oxygen atoms in original compound.

species. Thus the intramolecular hydrogen bonding reduces the spin density on the hydrogen bonded oxygen atoms. This reduction leads to a diminished extent of the through-bridge magnetic interaction, thereby lowering the absolute magnitude of the J value. The complex [Cu2(l-OAc)4(py)2] is seen to have a J value of about 300 cm1 (Table 5) that is as much as that for the water-substituted complex.

In molecular magnetism, the influence of hydrogen bonding on the spin–spin interaction and spin migration is a very common phenomenon [30]. Recently, Desplanches et al. [31] have reported a computational study on dinuclear Cu(II) complexes with two monomeric units linked by O–H  O to form a dimer. These authors noted that the hydrogen-bonded H atom does not have a major contribution to the SOMOs but it takes part in spin density delocal-

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ization between the two Cu atoms. This leads to an intramolecular magnetic coupling. In the present case, we notice the opposite phenomenon, that is, the spin density delocalization in the superexchange pathway is reduced by the formation of a hydrogen bond. The difference is that the monomeric units are directly linked here and hydrogen bonding reduces the spin distribution in this linkage.

[2]

6. Conclusions The magnetic exchange coupling constant of the recently synthesized dinuclear copper complex [Cu2(l-OAc)4(MeNHpy)2] has been calculated by using broken-symmetry density functional methodology, and in doing so we have explicitly computed the overlap integral between the two magnetic orbitals. The complex has several pairs of magnetic orbitals although HOMO and HOMO-1 pairs are not magnetic orbitals. Overlap integrals are computed by using the concept of natural magnetic orbitals. The calculated magnetic coupling constant 290 cm1 is in good agreement with the observed value of 285 cm1. This result is better than that of obtained by Eq. (5). The direct exchange between the two copper atoms is negligibly small, and the superexchange interaction is predominant. This conclusion is made after determining the contribution of the overlap between the orbitals of the two copper atoms to Sab, and also by studying the spin density distribution while the Cu–Cu distance is varied. There is a lack of d-bonding between the dx2 y 2 orbitals that carry the unpaired electrons. Intramolecular hydrogen bonding reduces the spin density of the oxygen atoms, and leads to a lower absolute magnitude of J as compared to the complex that contains H2O instead of MeNHpy. The magnitude of the J value for [Cu2(l-OAc)4(py)2] is predicted to be as high as that for the complex with water as axial ligands, nearly 300 cm1. 7. Supporting information available

[3] [4] [5] [6]

[7] [8]

[9]

[10]

[11] [12]

[13] [14]

The coordinates of the pyridine substituted complex and 45 axial ligands rotated complex, tables and plots of spin density distribution for all the bridging atoms against Cu– Cu distance. This material is available free of charge via the Internet. Acknowledgement

[15] [16]

Financial support from the Department of Science and Technology is gratefully acknowledged. References [1] O. Kahn, Molecular Magnetism, VCH, New York, 1993; J.B. Goodenough, Magnetism and the Chemical Bond, Interscience, New York, 1963; E. Coronado, P. Delhae`, D. Gatteschi, J.S. Miller (Eds.), Molecular Magnetism: From Molecular Assemblies to the Devices, vol. 321

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