Article pubs.acs.org/JPCC
Unexpected High Spin Polarization in Cr4 Cluster Omar López-Estrada,† Sarai López-Olay,† Andrea Aburto,‡ and Emilio Orgaz*,† †
Departamento de Física y Química Teórica, Facultad de Química, and ‡Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México, Cd. Universitaria, CP 04510, México, D.F. México S Supporting Information *
ABSTRACT: Recent X-ray magnetic circular dichroism (XMCD) spectroscopy has demonstrated a total high spin ground state of S = 11/2 in the Cr2+ cluster. The accuracy of these experiments opens the possibility to observe small magnetic particles with greater detail than those obtained in Stern−Gerlach setups. Particularly the chromium clusters, where a high total magnetization can be observed due to their localized d-electrons, are an excellent candidate to be detected in this sophisticated experiments. In this work, the small-sized chromium tetramer has been investigated in detail by means of zero and finite temperature ab initio methods. The dimer and trimer chromium clusters are reported as a benchmark in order to establish a reliable approach. We found the existence of a spin competition between a lower S = 1 and a higher S = 6 spin state in the Cr4 cluster; both spin states are close in geometry, allowing a spin-flip due to an spin−orbit coupling mechanism.
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INTRODUCTION For several years, the well-known antiferromagnetism of chromium1 films have been used to coating tips in scanning tunneling microscopy.2−4 By contrast, in a smaller system scale, the antiferromagnetic character does not remain, leading to a ferromagnetic high spin polarization.5,6 Recently, manipulations of metallic clusters in helium nanodroplets, opened the possibility to produce small size-selected clusters, particularly chromium clusters7,8 which can lead to new technological developments. The cold and confined environment allows one to grow pure clusters or aggregate dopants into them.8 Indeed, new precise experiments allow to improve the understanding of such complex systems. X-ray-absorption spectra of 3d transition-metal cations have been resolved in photoion-yield detection in their electronic ground states.9 In the same way, recent X-ray magnetic circular dichroism spectroscopy (XMCD) setups have been the main tool to investigate the electronic ground states of smallsized transition metal clusters.5,10,11 As a result, high spin states have been reported in half d-occupied chromium5 and manganese10 dimer cations in a ferromagnetic coupling. The necessity of accurate predictions is a challenge for standard electronic structure methods. Particularly the highly correlated small-sized chromium clusters exhibit a complex electronic structure. The multiconfigurational character plays the central role, and many-electron wave functions expanded in terms of Slater determinants to include electron correlation are available only for selected small Cr clusters.6,12−14 For a system of two chromium atoms, it can reach up to 2.8 billion configuration state functions.12 For larger systems (Crn, n ≥ 3 atoms), these calculations are quite demanding since strenuous to almost impossible to carry out.12,15 Thus, the computational difficults are the essential © XXXX American Chemical Society
reason that the Kohn−Sham density functional approach is the method of choice for large systems, even knowing that the highly correlated systems could be poorly described.16−19 In this sense, the present investigation about the electronic, geometrical, and magnetic structure of chromium clusters has been carried out through a variety of methodological approaches. The ambition is to encompass as much as possible the different local minimum geometries along the enables spin multiplicities. The multirreferential character of these systems will continue as an open question, and the challenge for the more precise description of the chromium clusters will invoke the most elaborated techniques. In spite of this, the inquiry with the density functional theory (DFT) approach is pertinent since nowadays it is the only technique that allows the investigation of large systems. A parallel interest is then to test the reliability of these methods to describe, within a certain confidence, these highly correlated compounds.
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METHODOLOGY The geometry optimization, not considering symmetry restrictions, of chromium neutral and cationic clusters up to 4 atoms have been performed employing DFT as coded within the GAUSSIAN 09 suite.20 A large all-electron basis sets have been tested at different multiplicities for each starting configuration. The DFT functionals employed were the GGA PBE,21 and the meta-GGA TPSS.22 Four different quality Gaussian basis sets have been employed; Def2TZVPP23,24 and the augmented correlation consistent aug-cc-pVxZ (x = D,T).25 The local Received: August 24, 2016 Revised: September 28, 2016
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DOI: 10.1021/acs.jpcc.6b08575 J. Phys. Chem. C XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry C
meta-GGA results reported the total high magnetization in agreement with the XMCD conclusions in a ferromagnetic state μ = 11μB37 with a long BL (2.96,37 2.86 Å19) and small De (1.5437 and 1.57−3.36 eV19). In the ferromagnetic coupling the normal frequency is found between 138 and 635 cm−1.19 A more elaborated computations (CCSD/aug-cc-pVQZ) found the ferromagnetic coupling 12Σ+u GS a De of 1.50 eV, BL of 2.906 Å and normal frequency of ν = 150 cm−1.6,15 In this investigation the vertical ionization energy (VIE) to the 2 Σg state was found higher for the GGA functionals (6.927− 6.996 eV) than for the meta-GGA functionals (6.737−6.794 eV, see Tables S5−S9). Our results can be compared with the experimental photoionization spectroscopy and XMCD experiments5 which set the VIE to 6.99879 ± 0.00099 eV35 and 6.9988 eV5 with a small relaxation of −0.22 eV to the high spin 12Σu state.5 The computed stability of the 12Σu Cr+2 is summarized in Tables S6−S10. Surprisingly, the GGA functionals are unable to correctly predict the cation ground state regardless the employed basis set as previously reported.19,37 However, meta-GGA’s functionals perform pretty well exhibiting stabilizing energies respect to the relaxed (unrelaxed) 2Σg cation of −0.385 (−0.062) eV. Although we found systematically VIE close to the experimental data, only the TPSS results found the right cationic ground state in agreement with previous reports.5,6,15,19,37 This results allow us to assert that meta-GGA functionals as TPSS are well suited for this kind of studies. For the chromium trimer, it has been reported in a D3h symmetry or a Jahn−Teller distorted C2v geometry.32,41 The resonance Raman spectroscopy of mass selected chromium trimers in argon matrix exhibited three lines; one at ν = 432.2 cm−1 corresponding to the symmetric frequency and 302.0 cm−1 corresponding to a degenerate bending frequency, consistent with a D3h symmetry.42 Cr3 supported in Au(111) surfaces exhibit a spin frustration revealed by a decrease of the Kondo temperature respect to symmetrical geometry.43 The Kondo temperature could be suppressed by a transition from an equilateral to an isosceles shape.44 DFT results are in well agreement with the C2v symmetry.16,19,33 A lower total magnetization has been reported (1.5μB16 and 2μB18) compared with the experimental results.41 Moreover, a nonsymmetrical structure (Cs) has been found as ground state with two different BLs.18 In fact, herein the Cr3 possesses a third atom appart from the dimer structure conserving a six unpaired electrons33 in a C2v structure. Recent investigations showed that both the Cs and C2v structures are consistent with a septuplet multiplicity19 as experimentally reported.41 In this work, the search of the ground state geometry and spin state for Cr3 have been performed starting from different guess geometries and spin multiplicities (results are summarized in Tables S10−S12). We have considered distorted initial structures having (i) a C2v bent geometry close to a triangle, (ii) a Cs bent structure close to a C2v form, and finally (iii) a two distances linear C∞v conformation. We avoided in this search fully symmetrical geometries as starting points. For starting geometries (i) and (ii), we found the same final structures while the linear choice (iii) yield high energy structures. The ground state has been found to be in a septuplet spin state in well agreement with previous reports.19,41 Other close structures appear at higher energies for quintuplet spin state frequently at more than 0.2 eV/atom indicating that the magnetic ground state is well resolved. In Figure 1a and b, we show the geometry of the ground state and spin density obtained at PBE/aug-cc-pVTZ and TPSS/aug-
minimum in the potential energy surfaces (PES) has been confirmed by inspecting the vibrational analysis. Complementary Born−Oppenheimer molecular dynamics were perfomed by using the deMon2k code.26 DFT computations have been obtained at double- and triple-ζ (DZVP,TZVP) basis sets, while the PBE and TPSS exchange and correlation functionals have been used. A Nosé−Hoover thermostat27,28 with four chain links with a coupling frequency close to the theoretical and experimental stretching vibrational frequency of Cr2 (500 cm−1) has been employed. Simulations during 10 ps have been carried out at different temperatures and spin multiplicities.
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RESULTS AND DISCUSSION Experimentally it has been reported the 7S3 ground state (GS) of the Cr atom, corresponding to a 3d54s1 electronic configuration,9,29,30 with ionization potential (IP) of 6.7665152 ± 0.0000372 eV.29 In our computations, we systematically have found a 7S3 GS configuration in well agreement with earlier reports (see Tables S1 and S2). Similarly the chromium dimer has been extensively investigated.12−14,16,18,19,30−38 Experimentally the electronic 1Σ+g GS39 is reported. In the same way, DFT computations point to the electronic 1Σ+ GS17 in an antiferromagnetic coupling33,37 even when non-collinear magnetism is included.18,36 In this work, the 1 Σg state has been found to be the electronic GS in agreement with previous reports (see Table S3). Besides, the experimental bond length (BL) has been found as 1.6788 Å.39 In contrast, DFT calculations reported BLs in a broad range (1.93 Å,37 between 1.70 and 1.75 Å,17 and between 1.61 and 2.55 Å19). We have found the BL subestimated as 1.59 Å in fair agreement with the experimental data39,40 (see Table S4). The fluorescence excitation spectra exhibit a vibrational frequency of ν = 470 cm−1,39 and the Raman line is observed at 427.5 cm−1.32 The photoionization spectroscopy experiments reported a dissociation energy (De) of 1.5374 ± 0.06199 eV.35 Once again, the previous DFT vibrational frequency and dissociation energy are within a wide range (ν = 289−405,17 180−572 cm−1,19 and De = 1.04−1.92,17 0.73−3.06 eV19 respectively). In the same way, we have obtained an overestimated normal-mode frequency (see Table S4). These discrepancies in the computed BL and vibrational frequency suggests that the PES is poorly described at these theory levels. Besides the DFT results, exhaustive state of the art computations12−14 employing fully uncontracted multireference-averaged quadratic coupled cluster,12 natural orbital functional theory,14 and the CASPT2(12e,28o)/cc-pwCV5Z theory level,13 reported highly accurate spectroscopic parameters (BL = 1.685,12 1.675−1.741,13 and 2.10−3.19 Å;14 De = 1.48,12 0.82−1.61,13 and 0.14−1.07 eV;14 ν = 45912 and 361−487 cm−113). As far as our knowledge, these highly meticulous results12,13 are the best agreement with the experimental39 ones. As mentioned above, the high localized valence electrons in Cr2+, have been observed by means of X-ray absorption spectroscopy where the bonding is mediated by 4s electrons.30 The XMCD observations concluded the high spin polarization of the dimer chromium cation with total magnetization of 11 μB.5 In opposition to the current XMCD, the previous DFT computations employing GGA functionals reported a low total magnetization of 1μB,17,37 in a antiferromagnetic 2Σ+ electronic state,17,19 with a short BL (1.67,37 1.65−1.67,17 and 1.58 Å19) and high De (2.47 eV,37 between 1.28 and 2.02 eV17) and the vibrational frequency lying between ν = 413 and 486 cm−1.17 In disagreement with these DFT computations, similar GGA and B
DOI: 10.1021/acs.jpcc.6b08575 J. Phys. Chem. C XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry C
Table 1. Cr4 Atomic Charges (in au), Local Magnetization (in μB), and Characteristic Distances d (in Å) for the Magnetic Ground State Structures Obtained for the Basis Sets B1 = Def2TZVPP, B2 = aug-cc-pVDZ, and B3 = aug-cc-pVTZ at (2) Starting Geometries (n) (1 = Cs, 2 = C(1) 2v and 3 = C2v ) Using the TPSS Functional
Figure 1. Ground state structures for the septuplet spin state of Cr3 obtained at (a) PBE/aug-cc-pVTZ and (b) TPSS/aug-cc-pVTZ theory level. In these plots, the charge density cutoff is 0.004 au−3.
cc-pVTZ theory level, respectively. Two different geometries are obtained depending on the employed density functional. In the PBE derived computations, we systematically found a dimer (d = 1.75 Å) in a sextuple-bond-like structure consistent with the free dimer, bonded to a third atom through s-like bonding at 2.49 Å and forming a 92° angle. However, for the TPSS computations, a C2v structure is found with bond distances at 2.29 Å and forming a 85° angle. The local magnetic moments show an alternating spin orientation as sketched in Figure 1. Cheng33 and Wang34 reported that the Cr3 possess a third atom in a dimer structure conserving its six unpaired electrons having a C2v structure. It is remarkable that we found both kinds of structures, depending on the density functional employed. Considering the experimental results, we conclude that the TPSS based approach reproduce reasonably well the experimental findings. The VIE has been found as theoretical (5.63 eV) or experimental (5.38 eV) in a 7A1 → 6B2 electronic transition.41 Our estimates for the VIE at different electronic transitions are summarized in Tables S12−S15 and they are labeled in the Cs ground state symmetry (7A′ → 6A′ transition). These results are found to be consistent with those previously reported.41 The chromium tetramer has been fairly investigated from a theoretical as well as experimental viewpoint. Photoionization studies reported a vertical ionization energy of 5.91 eV ± 0.05 eV.45 The expected geometry for this cluster lies between a flat rhombus in which one atom bends out of plane dihedrally in C2v symmetry until it reaches an apex on top of the remaining three atoms, to form a tetrahedron.42 Previous DFT computations agree with a D 2h flat structure 16,18,33 with 0μB in an antiferromagnetic coupling18 as a frustrated spin configuration.33 We have investigated the chromium tetramer for a large number of possible spin multiplicities starting from three guess geometries: a Cs structure adding an in-plane fourth atom to the equilateral chromium triangle, a distorted tetrahedra C(1) 2v , and a C(2) 2v rhombic flat structure. Different basis sets and two DFT functionals have been tested as summarized in Tables S16−S18. It clearly appears a competition between the triplet spin state structure and the higher spin multiplicity M = 13 structure which differs by a small amount of energy (
