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Journal of Molecular Structure 890 (2008) 18–23

DFT modelling of the [M–Pd–M]6+ metal atom chains (M = Ni, Pd):Structural, electronic and magnetic issues

Xavier Lopez a,*, Marie-Madeleine Rohmer b, Marc Benard b

a Departament de Quımica Fısica i Inorganica, Universitat Rovira i Virgili, Campus Sescelades, c/Marcel�lı Domingo s/n, 43007 Tarragona, Catalonia, Spainb Laboratoire de Chimie Quantique, Institut de Chimie, UMR 7177, CNRS-ULP, 67100 Strasbourg, France

Received 10 October 2007; received in revised form 10 December 2007; accepted 10 December 2007Available online 22 January 2008

Dedicated to the memory of F.A. Cotton.

Abstract

Following the recent findings on heterometallic string complexes, we extend the recently published work on NiPdNi(dpa)4Cl2 todiscuss the Ni–Pd–Ni and Pd3 chains with equatorial ligands (L) being dipyridylamide (dpa), 2,6-bis(phenylamido)pyridine (BPAP)and N,N0-bis-(p-toluenesulfonyl)-pyridyldiamide (Lpts), using the DFT formalism. The analysis of such a hypothetical series of lineartrimetallics anticipates that, for NiPdNi(dpa)4Cl2, the extended valence shell of palladium strengthens the antiferromagnetic couplingbetween high-spin terminal nickel atoms. For L = BPAP the system, as expected, becomes diamagnetic, and antiferromagnetism reap-pears for L = Lpts. The theoretical modelling of the coupling following the Heisenberg Hamiltonian applied to two magnetic centresð bH ¼ �2J AB

bSA � bSBÞ gives �2J = 320 and 497 cm�1 for L = dpa and Lpts, respectively. Pd3 chains display an enhanced tendency to bediamagnetic with various ligands. More specifically with dpa, Pd3(dpa)4Cl2—should it be synthesized—could be magnetically inactivesince the strongly antiferromagnetic state generated by the coupling of two terminal, high-spin Pd atoms (�2J = 1393 cm�1) is com-puted to be in close competition with the diamagnetic, closed-shell state. For L = Lpts as for BPAP, the hypothetic [Pd3]6+ chain ispredicted to be diamagnetic, resulting from the high energy of the antibonding d(Pd)–p(N) orbital. The shift toward diamagnetisminduced by the replacement of Ni by Pd in terminal position is therefore assigned to a stronger N ? M donation interaction withM = Pd.� 2007 Elsevier B.V. All rights reserved.

Keywords: Density functional theory; Molecular wires; Electronic structure; Magnetic properties

1. Introduction

Efforts focused on the development of Extended MetalAtom Chains (EMACs) are being rewarded with a flowof diverse and unexpected achievements since the first sys-tematic studies [1] reported in the mid 1990s, especiallyconcerning the molecular structure and physicochemicalproperties [2–4]. From the very pioneering works devotedto multinuclear string complexes—where only a few homo-trimetallic molecules dominated the scene [5]—we presentlyenvision a chemical richness that dramatically enlarges the

0022-2860/$ - see front matter � 2007 Elsevier B.V. All rights reserved.

doi:10.1016/j.molstruc.2007.12.007

* Corresponding author. Tel.: +34 977 55 82 83; fax: +34 977 55 95 63.E-mail address: javier.lopez@urv.cat (X. Lopez).

potentialities of these organometallic compounds. In recentyears, the knowledge gained in the synthesis and in thecontrol of new p-dentate ligands belonging to the familyof n-pyridylamides, [C5H4N–(N–C5H3N)n–N–C5

H4N](n+1)� (p = 2n + 3) [6] has produced major successesalong two main lines: (i) the lengthening of the metal chain,going from three atoms to almost any number up to nineatoms [7–9], and (ii) the synthesis of heterometallic frame-works, either symmetric such as CoPdCo, CuMCu(M = Pd, Pt), or non-symmetric like Cr–Cr� � �Fe orRu–Ru–M (M = Cu, Ni) derivatives [10]. n-Pyridylamideligands are characterized by an alternation of amido andpyridylic coordination sites. Controlling this alternationleads to a possible tuning of the most important character-

R

R

R

R

RR

RR

(A) M3(dpa)4Cl2 (B) M3(L)4

Fig. 1. Ball-and-stick representation of the trimetallic (A) M3(dpa)4Cl2 and (B) models of the M3(L)4 (L = BPAP, Lpts) species, where R = H or SO2H.Color code: black—transition metal; dark gray—nitrogen; light gray—chlorine; white—carbon. Hydrogen atoms belonging to the equatorial ligands havebeen omitted for clarity.

X. Lopez et al. / Journal of Molecular Structure 890 (2008) 18–23 19

istics of EMACs, especially the properties related to electricconductivity [4] and magnetism. A recently documentedexample concerns the different structural and magneticbehaviour of trinuclear compounds coordinated to fourequatorial ligands (L) exhibiting different amido/pyridylicalternation such as the monoanionic dpa on the one hand(Fig. 1A); the dianionic BPAP [11] or Lpts [12] on the otherhand (Fig. 1B). It has been shown that the switch of theamido and pyridyl positions characteristic of these twotypes of ligands influences the electronic state—high-spinor low-spin—of Ni(II) atoms in terminal position of themetal framework, and their ability to accommodate axialligands [11–14].

The effect of metal substitution is being investigated inparallel by Peng et al. and by our group. Recent experimen-tal and theoretical data have shown that the replacement ofeither all metal atoms [15], or of the central one only by alarger, second-row element, entails important changes inthe electronic structure [10a,16]. Starting from Ni3(d-pa)4Cl2, we have already considered the still hypotheticalsubstitution of the central Ni atom by Pd, predicting thatthe antiferromagnetic coupling between the high-spin ter-minal nickels is enhanced by a factor of �3–4 [16]. We havealso analyzed from DFT calculations the effect of replacingdpa by BPAP or Lpts in trinickel complexes. In that workwe showed that the electron-withdrawing character of thep-toluenesulfonyl groups in the Lpts ligand has a dramaticeffect on the electronic structure of the [Ni3]6+ framework[14]. In order now to explore the intricacy of metal andligand influences on the magnetic properties of trinuclear

Chart 1

complexes involving d8 metal atoms, we herein present acomputational study carried out on a set of yet unknownMPdM(L)4 or MPdM(L)4Cl2trimetallic compounds, withM = Ni or Pd, and L = dpa, BPAP and Lpts.

2. Computational details

In the present calculations we use the model ligandsshown in Chart 1, where hydrogen atoms replace phenyland tolyl groups in BPAP2� and Lpts2�, respectively. Thisstrategy was successfully adopted and justified in our previ-ous study on Ni3(L)4 chain complexes to reduce the com-putational demands [14]. Note however, that the presenceof bulky substituents, combined with the enhanced basicityof the dianionic BPAP and Lpts ligands, might influencethe issue of axial coordination, which appears critical asfar as the electronic and magnetic properties are concerned.

All calculations herein discussed have been carried outusing the density functional theory (DFT) formalismimplemented in the Gaussian’03 [17] software and theB3LYP exchange-correlation functional. Double-f valencebasis sets have been used for all atoms, either including allelectrons in the basis set for the first-row atoms (D95Vbases) or describing the core of Cl and metal atoms withLos Alamos electron core potentials (LanL2DZ basis). Fulldouble-f (D95) basis were employed and supplementedwith one and two d-type polarization functions for Nand S, respectively. The polarization functions on S, withexponents 1.064 and 0.266, were found necessary to accu-rately reproduce the experimental S–N bond length [18].

.

Fig. 2. Sequence and qualitative molecular orbital energy diagram forNiPdNi(dpa)4Cl2, Pd3(dpa)4Cl2 and Pd3(L)4 (L = BPAP, Lpts) trimetalliccomplexes.

20 X. Lopez et al. / Journal of Molecular Structure 890 (2008) 18–23

The valence basis sets of Ni and Pd metal atoms have beencompleted with f-type polarization functions (exponents3.130 and 1.472), respectively.

All open-shell states have been characterized by meansof the unrestricted formalism. The antiferromagnetic low-spin states have been obtained and their geometries opti-mized using the Broken Symmetry (BS) approach proposedby Ginsberg [19] and developed by Noodleman [20]. Theexchange parameter 2JAB between two magnetic centresA and B with spin momenta SA and SB is defined as followsby the Heisenberg–Dirac–van Vleck (HDVV) Hamiltonian[21]:

bHHDVV ¼ �2J ABbS A � bSB ð1Þ

Within the framework of the DFT, the treatment ofsome open-shell states is not straightforward. Notably,the energy BSE arises from a single-determinant calculationaveraging the weights of the pure spin multiplets involvedin such a state. The correction, by means of approximateprojection methods, of the spin contamination arising fromthis procedure is still controversial, as far as DFT is con-cerned [22]. In the present work as in our previous studies,we have been using the projection method proposed byYamaguchi et al. [23], which relies on the dependence ofJAB upon the spin contamination of the BS solution:

2J AB ¼ 2ðBSE � HSEÞ

ðHShS2i � BShS2iÞð2Þ

where HShS2i and BShS2i denote the total spin angularmomentum calculated in the high-spin and in the brokensymmetry solutions, respectively. All geometry optimiza-tions have been carried out assuming the symmetry con-straints of the D4, or, for the broken symmetrycalculations, of the C4 symmetry point groups.

3. Results and discussion

The study of the electronic and magnetic properties oftrimetallic chains is subject to the comprehension of thesequence of molecular orbitals (MOs) with predominantmetal character. The deprotonated BPAP and Lpts ligandsare dianionic and it is clear that the distribution of theadditional charge density contributes to prevent the metalchain from accepting axial coordination. It seems howeverthat a key point to be considered for explaining the unwill-ingness of Lpts and especially BPAP complexes to axiallycoordinate lies in the switch of the amido and pyridyl posi-tions with respect to dpa. The more basic amido ends arenow facing the outermost metal atoms. An enhanced basi-city corresponds to a stronger donation, hence to a desta-bilization of the antibonding d(Mterminal)–p(N) orbitals.With BPAP, these d* metal MOs are rejected at higherenergies than their homolog centred on the inner metalatom, thus making them unavailable to electrons of a metalatom in a high-spin d8configuration (Fig. 2). In such a case,a square planar environment favouring a low-spin configu-

ration is preferred to the square pyramid implied by axialcoordination. With Lpts, the presence of an electron-attracting tosylate substituent weakens the basicity ofthe amido ends and reduces the destabilization of thed(Mterminal)–p(N) orbitals (Fig. 2). The structural behav-iour of trinuclear complexes incorporating Lpts orLms (N,N0-bis[4-methylsulfonyl]-pyridyldiamide) thereforeappears unpredictable, sometimes exhibiting weaklybound, neutral axial ligands, and sometimes not [12,18].

The presence or the lack of axial ligands has directimplications on the magnetic properties of the complex.It has been reminded above that a square planar coordina-tion of d8 metals favors a low-spin, diamagnetic configura-tion, whereas a square pyramidal arrangement induces ahigh-spin atomic configuration, then giving rise to mag-netic coupling. In the language of molecular orbitals, axialligands produce antibonding interactions with all r-typemetal MOs, and more specifically with rnb and r*. Axialcoordination raises these orbitals toward the energy rangeof the d* MOs, thus generating a set of singly occupiedfrontier orbitals. Conversely, the removal of axial ligandsstabilizes the metal r MOs and creates an energy gap favor-ing diamagnetism (Fig. 2).

3.1. [NiPdNi(dpa)4Cl2] and [NiPdNi(BPAP,Lpts)4]2�

Table 1 shows selected structural, electronic and mag-netic parameters computed for NiPdNi(dpa)4Cl2 (1),NiPdNiðBPAPÞ2�4 (2) and NiPdNiðLptsÞ2�4 (3). The inter-atomic distances for 1–3 qualitatively follow the patternsencountered in previous works. In general, the Pd–N(c)distances are somewhat longer than the typical Ni–N ana-logues, a consequence of the expansion of the ligand coat-ing due to the larger palladium ionic radius. However, forcompound 1, Ni–N(t) are longer than Pd–N(c) by 0.12 A inthe high-spin (HS) and antiferromagnetic (AF) cases,where two S = 1 Ni atoms are present. This results frompopulating the d(Ni)–p(N) antibonding orbitals in high-

Table 1Selected interatomic distances (in A), relative energies (DE, kcal mol�1) and magnetic properties computed for the closed-shell (CS), high-spin (HS) andantiferromagnetic (AF) singlet ground states of NiPdNi(dpa)4Cl2 and NiPdNiðLÞ2�4 (L = BPAP, Lpts)

NiPdNi(dpa)4Cl2 (1)a NiPdNiðBPAPÞ2�4 (2) NiPdNiðLptsÞ2�4 (3)

CS HS AF CS HS CS HS AF

Distances

Ni–Cl 2.912 2.392 2.398Ni–Pd 2.473 2.526 2.513 2.477 2.498 2.460 2.492 2.470Ni–N(t) 2.013 2.166 2.162 1.954 2.074 2.017 2.120 2.117Pd–N(c) 2.022 2.040 2.040 2.040 2.095 2.033 2.067 2.066

Spin distribution (electrons)

Ni 1.63 ±1.62 1.26 1.68 ±1.64Pd 0.053 0.00 0.07 0.06 0.00Cl 0.10 ±0.094N(t) 0.06 ±0.06 0.12 0.06 ±0.06N(c) 0.01 0.00 0.00 0.01 0.00hS2i 6.010 1.977 6.093 6.008 1.963DE +52.6 +1.80 0.00 0.00 +25.1 +19.6 +2.88 0.00�2J (cm�1) 320 497

a Ref. [16].

X. Lopez et al. / Journal of Molecular Structure 890 (2008) 18–23 21

spin states. Conversely, for compounds 2 and 3, in which aclosed-shell configuration is assumed for all metal atoms,Ni–N distances are shorter than Pd–N ones by 0.09 and�0.02 A, respectively (Table 1). And, as listed in the table,averaged Ni–N distances are �0.05 A longer with L = Lptsthan with BPAP. This effect can be attributed to the pres-ence of the sulfonyl groups in 3, which tend to make theterminal nitrogen atoms less basic, thus leading to weakerNi–N bonds, as already computed in Ni3ðLptsÞ2�4 andNi4(Tsdpda)4 (Tsdpda2� = N-[p-toluenesulfonyl]dipyridyl-diamido) [14,18]. The shortening of the Ni–Pd distance in2 and 3 is a consequence of the removal of the axial ligands,thus cancelling the associated trans effect. Back to theclosed-shell state of 1, let us stress the extremely long dis-tances computed for Ni–Cl (2.912 A), which are indicativeof a dissociative trend. This trend, already stemming froma calculation on Ni3(dpa)4Cl2 [13] clearly illustrates theeffect of a double occupancy of the antibonding Ni–Clr* orbital. Later in this article, we will show that a similareffect occurs in Pd3(dpa)4Cl2.

A comparative analysis of the spin populations calcu-lated for the high-spin and broken symmetry solutions alsoprovide information of interest (Table 1). The distributionof the spin density is rather similar in the open-shell statesof 1 and 3, and is limited to the nickel atoms (>1.6 e) and totheir coordination environment. Conversely, the spin pop-ulation on Ni in 2 decreases to 1.26 e. Part of the spin pop-ulation is transferred to the four equatorial N atoms,whose spin population increases from 0.24 e to 0.48 e, butas much as 0.44 e becomes delocalized over the rest ofthe BPAP ligands. This metal-to-ligand transfer of spindensity arises through the antibonding d(Mterminal)–p(N)d* MOs and therefore illustrates the strength of the dona-tion interactions arising from the amido ends of BPAP tothe Ni atoms. This increase of the Ni–N bond strength withrespect to NiPdNi(dpa)4Cl2 is corroborated by the contrac-tion of the Ni(t)–N bonds from 2.166 A in the high-spin

state of 1 to 2.074 A in the same state of 2. In complex 3,the strength of the donation from the amido ligands tonickel is reduced by the electron-withdrawing effect of thesulfonyl substituent, which entails in the high-spin state(i) an increase of the calculated Ni–N(t) bond lengths from2.074 to 2.120 A, and (ii) a concentration of the spin den-sity on the Ni atoms, as in NiPdNi(dpa)4Cl2.

3.2. [Pd3(dpa)4Cl2] and [Pd3(BPAP,Lpts)4]2�

The structural parameters and relative energies com-puted for Pd3(dpa)4Cl2 (4), Pd3ðBPAPÞ2�4 (5) andPd3ðLptsÞ2�4 (6) are listed in Table 2. Most trends in thisseries are similar to those obtained for NiPdNi when goingfrom closed-shell to high-spin states. As for NiP-dNi(dpa)4Cl2, the Pd–Cl distance of 2.950 A calculatedfor the closed-shell configuration is indicative of a tendencyto dissociate. In the high-spin and BS states of 4, a Pd–Clbond arises from the partial depopulation of the r* orbital,with a distance of �2.55 A. The trends concerning thePd(t)–N bond lengths are in keeping with those calculatedwith the Ni–Pd–Ni frameworks, accounting for the largerionic radius of palladium.

DFT calculations suggest that the ground state of com-pound 4 (L = dpa) might be diamagnetic rather than anti-ferromagnetic, at variance with its homologues obtainedwith a Ni3 framework, or computed with a heteronuclearmetal chain. A delicate energetic balance indeed occursbetween these two states, separated by no more than0.90 kcal mol�1 (Table 2). Moreover, the energy differencebetween the high-spin state and the broken symmetry solu-tion is unusually large (8.69 kcal mol�1), leading to a hugevalue of 1393 cm�1 for the magnetic coupling constant�2J, compared to calculated values of 110 cm�1 for Ni3(d-pa)4Cl2 [13] (observed: 216 cm�1 [24]), and 320 cm�1 forNiPdNi(dpa)4Cl2 (Table 1). For all three complexes with24 metal electrons, this AF coupling involves four electrons

Table 2Selected interatomic distances (in A), relative energies (DE, kcal mol�1) and magnetic properties for the closed-shell (CS), high-spin (HS) andantiferromagnetic (AF) singlet ground states of Pd3(dpa)4Cl2 and Pd3ðLÞ2�4 (L = BPAP, Lpts)

Pd3(dpa)4Cl2 (4) Pd3ðBPAPÞ2�4 (5) Pd3ðLptsÞ2�4 (6)

CS HS AF CS HS CS HS

Distances

Pd–Cl 2.950 2.545 2.564Pd–Pd 2.560 2.590 2.544 2.585 2.575 2.552 2.534Pd–N(t) 2.114 2.277 2.258 2.062 2.191 2.124 2.250Pd–N(c) 2.054 2.065 2.062 2.078 2.127 2.067 2.104

Spin distribution (electrons)

Pd(t) 1.24 ±1.13 0.96 1.03Pd(c) 0.18 0.00 0.39 0.32Cl 0.21 ±0.16N(t) 0.11 ±0.10 0.14 0.12N(c) 0.017 0.00 0.013 0.018hS2i 6.011 1.647 6.029 6.024DE +0.90 +8.69 0.00 0.00 +65.7 0.00 +36.9�2J (cm�1) 1393

22 X. Lopez et al. / Journal of Molecular Structure 890 (2008) 18–23

arising from the terminal metals in high-spin configuration.It may be viewed as the addition of two contributions: (i) ad-like contribution, which couples the two electronsoccupying antibonding d(Pd)–p(N) MOs via a superex-change mechanism [10], and (ii) a r-like contribution,involving a direct coupling through the central Pd atomby means of delocalized combinations of the d(z2)-typeorbitals. The small spin population assigned to the terminalPd atoms (1.13 e, Table 2) and the distribution of the miss-ing spin density over all surrounding atoms, including cen-tral palladium, suggest that both contributions areenhanced as a consequence of the diffuseness of the palla-dium d orbitals. A similar trend was recently reported forDFT-computed [Cu3]7+/[Ag3]7+ chains [15], although thatsituation is slightly different because terminal metals con-tain one unpaired electron only.

It should eventually be noticed that both electronic con-figurations competing for the ground state of Pd3(dpa)4Cl2suffer from specific drawbacks. On the one hand, the verystrong coupling constant calculated for the AF singlet stateis indicative of a tendency toward covalent bonding thatcannot be expressed by means of a superexchange mecha-nism. On the other hand, the diamagnetic state corre-sponds to all metal orbitals doubly occupied, exceptthose with antibonding character with respect to the equa-torial ligands. Such a status of no bond between electron-rich metal atoms constrained to remain at bonding distanceby the ligand bite is acceptable between two Ni atoms,and—possibly—between Ni and Pd, the r and the p over-laps remaining relatively small. It should however generatea strong Pauli repulsion between adjacent palladiumatoms. Recent attempts to synthesize compound 4

remained unsuccessful until now, possibly for this reason.The electronic state of lowest energy for compounds 5

and 6 is computed to be clearly diamagnetic. In complex5, as in the [Ni3(BPAP)4]2� and [NiPdNi(BPAP)4]2�, theinversion of amido and pyridyl positions goes against thetendency of terminal metal atoms to display high-spin con-

figurations, a trend already attenuated by the diffuseness ofpalladium d orbitals. For this reason, and at variance withthe case of the heterometallic backbone, the decrease of thebasicity of the amido ligand induced by the sulfonyl substi-tuent in Lpts is not sufficient to reverse the relative energiesof the two configurations of [Pd3(Lpts)4]2�. The closed-shell state of 6 therefore remains advantaged over thehigh-spin state by 36.9 kcal mol�1 (Table 2). As for com-pound 4, however, the Pauli repulsion in the closed-shellground state of the hypothetic compounds 5 and 6 couldbe sufficiently destabilizing to make the synthesis of[Pd3]6+ chain complexes difficult. A protocol to overcomethis difficulty could be the direct synthesis of an oxidizedspecies, displaying some delocalized r-bonding character.

4. Conclusion

Replacing nickel by bulkier palladium in trimetallicchain complexes, either at the central position only, or inthe whole metal framework entails the expected expansionof the organic coating. Concerning the electronic structureof the ground state, the trends previously observed andcomputed for the [Ni3]6+ framework are computationallyreproduced with NiPdNi chain complexes, which featureopen-shell, antiferromagnetic singlet ground states withdpa� and Lpts2� equatorial ligands, and a diamagneticground state with BPAP2�. This shift to diamagnetism incomplexes containing BPAP is assigned to the conse-quences of the interchange, with respect to dpa, betweenthe pyridyl and the more basic amido ends of the ligand.The complexes of Lpts, a ligand exhibiting the sameexchange between coordinative tips, however remain anti-ferromagnetic due to the counteracting influence of the tos-ylate substituent. The magnitude of the antiferromagneticcoupling expected to occur in appropriate NiPdNi chaincomplexes is enhanced by a factor of �3–5 with respectto that computed for Ni3(dpa)4Cl2. The replacement ofall nickel atoms by palladium yields hypothetic [Pd3]6+

X. Lopez et al. / Journal of Molecular Structure 890 (2008) 18–23 23

chain complexes whose stability in the ground state isthreatened by a conflict between the marked tendency ofsecond-row transition metals to link covalently at short dis-tance and the d8 population of PdII prohibiting such cova-lent bonding along the metal framework.

Acknowledgement

The calculations were performed in the facilities of theDepartament de Quımica Fısica i Inorganica (URV,Tarragona).

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