Record High Magnetic Anisotropy in Three Coordinate MnIII ...
Transcript of Record High Magnetic Anisotropy in Three Coordinate MnIII ...
doi.org/10.26434/chemrxiv.14338907.v1
Record High Magnetic Anisotropy in Three Coordinate MnIII and CrIIComplexes: A Theoretical PerspectiveArup Sarkar, Reshma Jose, Harshit Ghosh, Rajaraman Gopalan
Submitted date: 30/03/2021 • Posted date: 31/03/2021Licence: CC BY-NC-ND 4.0Citation information: Sarkar, Arup; Jose, Reshma; Ghosh, Harshit; Gopalan, Rajaraman (2021): Record HighMagnetic Anisotropy in Three Coordinate MnIII and CrII Complexes: A Theoretical Perspective. ChemRxiv.Preprint. https://doi.org/10.26434/chemrxiv.14338907.v1
Ab initio calculations performed in two three-coordinate complexes [Mn{N(SiMe3)2}3] (1) and[K(18-crown-6)(Et2O)2][Cr{N(SiMe3)2}3] (2) reveal record-high magnetic anisotropy with the D values -64cm-1 and -15 cm-1 respectively, enlisting d4 ion back in the race for single-ion magnets. For the first time, adetailed spin-vibrational analysis was performed in 1 and 2 that suggest a dominant under barrier relaxationdue to flexible coordination sphere around the metal ion offering design clues for low coordinate transitionmetal SIMs.
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1
Record High Magnetic Anisotropy in Three
Coordinate MnIII and CrII Complexes: A Theoretical
Perspective
Arup Sarkar, Reshma Jose, Harshit Ghosh and Gopalan Rajaraman*
Department of Chemistry, Indian Institute of Technology Bombay, Mumbai- 400076,
Maharashtra, India
Keywords: Low-coordinate, Ab initio, NEVPT2, Zero-field Splitting, Spin-vibronic coupling
ABSTRACT: Ab initio calculations performed in two three-coordinate complexes
[Mn{N(SiMe3)2}3] (1) and [K(18-crown-6)(Et2O)2][Cr{N(SiMe3)2}3] (2) reveal record-high
magnetic anisotropy with the D values -64 cm-1 and -15 cm-1 respectively, enlisting d4 ion back in
the race for single-ion magnets. For the first time, a detailed spin-vibrational analysis was
performed in 1 and 2 that suggests a dominant under barrier relaxation due to flexible coordination
sphere around the metal ion offering design clues for low coordinate transition metal SIMs.
2
Introduction
Single-Molecule Magnets (SMMs) have become a fascinating research area as this class of
molecules exhibit magnetization just like permanent magnets below a critical temperature defined
as blocking temperature TB.1 An important parameter associated with the blocking temperature is
the barrier height for magnetization reversal (Ueff) which is correlated to the magnetic moment of
different microstate and the nature of anisotropy. While in lanthanide complexes, the first-order
spin-orbit coupling (SOC) is strong enough to produce large barrier heights,2 in transition metal
(TM) systems spin-orbit coupling is generally weak, leading to relatively smaller anisotropy which
is reflected in the axial zero-field splitting parameter (D) which can be tuned at will using ligand
field.3
There are several challenges in enhancing the blocking temperature TB in SMMs as several
relaxation mechanisms other than the Orbach process spoil the direct correlation of TB to Ueff
values. Among others, quantum tunneling of magnetization (QTM) and spin-phonon/vibrational-
mode relaxation mechanisms are a prominent source of relaxation, as shown in recent years by
various groups.4 Earlier research in the SMM area was focused on increasing the total spin (S) of
the complexes by increasing the number of metal centers. After the discovery of a very small Ueff
barrier in {Mn19} cluster possessing record high ground state S value, it becomes clear that
increasing the number of metal centers or S value diminishes the axial anisotropy (D term) as
evident from the equation proposed originally by Abragam and Bleaney5 and adapted in ab initio
calculations later on. For this reason, mononuclear TM complexes gained significant attention
leading to the birth of several single-ion magnets (SIMs) based on the low coordination number
such as Fe(II/I), Ni(II), and Co(II), exhibiting very large Ueff values.6
3
In the early years of SMMs, the focus has been on transition metal cluster particularly that of
Mn(III) ions, as this offer an easy source of negative D parameter for the chemists and unearthed
numerous SMMs albeit with smaller Ueff/TB values. 1a, 7 The Mn(III) ions are very robust and can
be easily incorporated in cluster aggregation, and are relatively redox stable6a but exhibit only small
D values of the order of ~|5| cm-1. 8 While several low-coordinate transition metal ions were
pursued recently for potential SMMs, Mn(III) has not been studied in detail, perhaps due to the
perception that the expected D values are rather small.8 Apart from Ueff values, the blocking
temperature is an important criterion which is often very small. This suggests that apart from the
QTM effect, spin-vibrational relaxations are at play in such systems.4 How these effects manifest
in these complexes are not fully understood.
To ascertain complexes that exhibit large negative D values and also to correlate the relaxation
mechanism to spin-vibrational coupling, we undertake theoretical studies based on multi-
configurational ab initio calculations SA-CASSCF/NEVPT2 using the ORCA suite.9 Here, we
have studied in detail two three-coordinate d4 systems Mn(III) and Cr(II): [Mn{N(SiMe3)2}3]10 (1)
and [K(18-crown-6)(Et2O)2] [Cr{N(SiMe3)2}3]11 (2) using their reported X-ray structure. Our
NEVPT2 calculations yield a record axial D value of -64 cm-1 and -15 cm-1 for 1 and 2,
respectively, with a negligible E/D value. The D value computed for both complexes is larger than
any examples reported to-date and suggests a potential SMMs characteristic for these robust
building block metal ions.
Computational Details
All the ab initio single point calculations have been performed using ORCA 4.0.0 program.9 DKH
(Douglas-Kroll-Hess) Hamiltonian was used to account for the scalar relativistic effect. DKH
4
contracted versions of the basis sets were used during the calculations- DKH-def2-TZVP for Mn,
Cr, Si; DKH-def2-TZVP(-f) for N and DKH-def2-SVP for the rest of the atoms. During the orbital
optimization step in SA-CASSCF (state-averaged complete active space self-consistent field)
method, 4 metal electrons in 5 metal d-orbitals were taken into consideration and optimized with
5 quintet and 35 triplet roots for Mn(III) and Cr(II) metal centers. Additional calculations have
also been carried out with 5 quintets, 45 triplet roots, and 5 quintets, 35 triplet, and 22 singlet roots
to check the effect of high-lying excited states on the Spin-Hamiltonian (SH) parameters. The
addition of extra 10 triplet roots and 22 singlet roots marginally affect the SH parameters (see
Table S1 in ESI). NEVPT2 (N-electron valence perturbation theory second-order) calculation has
also been performed on the top of converged SA-CASSCF wavefunction to include the dynamic
electron correlation. Spin-orbit interaction was accounted with quasi-degenerate perturbation
theory (QDPT) approach using SOMF (spin-orbit mean field) operator. Only spin-orbit
contributions towards zero-field splitting were computed. Final Spin-Hamiltonian parameters were
determined with effective Hamiltonian approach (EHA) formalism.12 Ab initio ligand field theory
(AILFT) calculations have also been performed to obtain the d-orbital energies.13
Geometry optimization and single point frequency calculations have been carried out in Gaussian
09 (Rev. D.01) program.14 Hybrid unrestricted B3LYP-D2 functional was used for the DFT
calculations along with Ahlrich’s triple- valence polarized (TZVP) basis set for Mn, Cr, Si, N
and Ahlrich’s spilt valence polarized (SVP) basis set for rest of the atoms.15
5
Result and Discussions
Complex 1 possesses a perfect D3h symmetry as the three N-Mn-N bond angles are 120.02,
120.02 and 119.95 and the three Mn-N bond lengths are 1.89, 1889, and 1.89 (in Å unit). It was
also noticed that the {MnN3} core was planar, and the bulky trimethylsilyl groups surrounded the
central moiety stabilizes the low coordinate molecule from further coordination via steric
arrangements (see Figure 1). The NEVPT2-QDPT calculated major anisotropy axes, i.e., Dzz and
gzz axes, were found to be exactly perpendicular to the Mn-N3 plane, i.e., exactly collinear with the
C3 axis, which describes the axial nature of anisotropy present in the molecule.
Figure 1: NEVPT2 computed Dzz axis of the molecule plotted on the X-Ray structure (left) and
three Mn-N bond lengths (in Å) and N-Mn-N angles () shown on the molecule (right). Colour
code: Mn: pink, N: blue, Si: light green, C: dark grey. Hydrogens are omitted due to clarity.
6
A record axial zero-field splitting (ZFS) was found for this complex, showing a D value of -64 cm-
1 with E/D estimated to be 0.0003, indicating strong easy-axis type anisotropy (see Table 1) for
complex 1. A very similar geometry was observed in the Cr(II) analog, and the N-Cr-N bond
angles (123.9, 115.81 and 120.29) are not exactly similar and significantly deviated from D3h
symmetry. The D value for complex 2 is less than complex 1 due to these structural deviations and
also smaller spin-orbit coupling constant () values of Cr(II) than Mn(III). For complex 2, the E/D
value is estimated to be 0.003, which is ten times larger than complex 1 (see Figure S1 and Table
S1 in ESI).
The ground state electronic configuration of complex 1 is dz21dyz
1dxz1dxy
1dx2
-y20, and this comprises
77% of the overall wavefunction. The major contribution (-62 cm-1) towards the negative D value
arises from the first excited state, which consists of dxy dx2-y
2 (same ML valued) electronic
excitation and this excited state contribute ~97% of the overall D value (see Figure 2 and Table S2
in ESI). Other electronic transitions were found to contribute negligibly to the overall D value. A
very close analysis of the NEVPT2 states reveals that the first excited quintet state is only 19 cm-
1 apart from the ground state and consequently results in a very strong second-order spin-orbit
coupling. While the first excited state is the spin-allowed quintet, the second, third and fourth
excited states arise from the spin-flipped triplet transitions. These three excited states consist of a
mixture of dxy dxz/dyz and dxy dz2 transitions (see Table S2 in ESI). The computed gx, gy and
gz values are 1.67, 1.67 and 1.14 respectively for true spin S =2 and 0.00 0.00 and 5.14, respectively
for pseudospin �� =1/2 manifold. In the case of complex 2, the first excited state contributes 96%
(-14.4 cm-1) towards the overall D value. Again, the D value is negative due to the coupling with
the prominent first excited state involving the same ML level dxy dx2
-y2 electronic excitation (see
Figure S2 in ESI). Here one major difference of complex 2 from complex 1 is that due to
7
significant distortion from D3h and lower ligand field of Cr(II), the first excited state is 756 cm-1
apart and the next three excited states are quintets (see Table S3). The computed gx, gy and gz
values are 1.97, 1.97, and 1.58 respectively for true spin S=2 and 0.00 0.00 and 6.351, respectively
for pseudospin �� =1/2 manifold.
In the case of non-Kramers ions like in these two cases studied, the tunnel-splitting is generally
larger, leading to faster relaxation via the QTM process. The tunnel-splitting strongly depends on
the local symmetry and ligand field environment around the metal ion. The high symmetry present
in complexes 1 and 2 leads to smaller tunnel splitting (see Figure S3 and Table S4 in ESI). The
first excited pseudo-KDs is separated by 154 cm-1 in case of complex 1 and 45 cm-1 in case of
Figure 2: NEVPT2-LFT d-orbital diagram of complex 1. The orange arrow indicates the first
excited spin-allowed transition.
8
complex 2. The multi-determinant nature of the ground state leads to mixing of the |+2 and |-2
states, and this is very prominent in complex 1 compared to 2 (see Table S4).
The static electronic picture is insufficient to describe the relaxation mechanism or the spin
dynamics of the system. Recent reports of spin-vibronic coupling that describe the role of
vibrational frequencies of a single molecule or of the surrounding lattice are very important to
elucidate the dynamic scenario of SMMs.4 In this regard, we have attempted to investigate the role
of molecular vibrations occurring at low temperatures on the spin-orbit or Ms levels in the two
complexes. Therefore, we have performed frequency calculations (normal modes) on the X-ray
structures of 1 and 2 using Density Functional Theory (DFT) methods (B3LYP-D2/TZVP, a
similar vibrational pattern also found for the optimized geometries, see Table S5 in ESI).
Here we have carefully analyzed five lower energy vibrational modes below 80 cm-1, and these
are 1 45.1 (40.1), 2 45.8(46.2), 3 58.4(50.3), 4 70.3(58.8) and 5 72.9 (69.9) for complex 1 (2)
(see Figure S4 in ESI). Out of the five vibrations mentioned, the 4 and 5 vibrations were found
to be IR active and also break the D3h symmetry (see Figure S4). Here 4 corresponds to N-M-
N bond angle bending and correlates to Jahn-Teller active vibration (E irreducible representation
in D3h symmetry). The 5 corresponds to out-of-plane (M-N-N-N) bending vibration of the metal
ion and associate with A2” irreducible representation. Several displacement points in 4 and 5
vibrational surfaces were considered for CASSCF/NEVPT2 calculations. The maximum
displacement scale of a particular vibration j, denoted by xj, was fixed at 2.0 for both the complexes
as suggested earlier (see Table S6 and S7 in ESI).16
An angular distortion parameter Q was introduced, which is a sum of deviation from 120 from
each of the equatorial N-M-N angles (denoted as ) (see Table S6 and S7).6e Here, in order to
9
find out the spin-vibronic coupling, the variation of D and E/D have been computed with respect
to the displacement of nuclear coordinates (x) using the following Hamiltonian:
��𝑠−𝑣𝑖𝑏 = (𝜕𝐷
𝜕𝑥)𝑥 [𝑆𝑍
2 −𝑆(𝑆 + 1)
3] + (
𝜕𝐸
𝜕𝑥)𝑥(𝑆𝑥
2 − 𝑆𝑦 2) … 𝑒𝑞𝑛. 1)
In Figure 3, we plot computed D values with respect to Q and xj, and these plots show that as the
Q diverges from zero, the magnitude of D decreases for 4 vibrations (see Figure S5 in ESI). This
is because an increase in Q breaks the D3h symmetry and, consequently, increases the gap between
the dxy and dx2-y
2 orbitals (see Fig. S6). In complex 1, the X-Ray structure shows the highest
negative D value and minimum E/D value (see Fig. S5) at equilibrium geometry or zero
displacement point, but for complex 2, the X-ray structure is significantly deviated from the ideal
D3h symmetry and therefore do not have the largest negative D or the lowest E/D at zero
Figure 3: Variation of D values in complexes 1 (left) and 2 (right) with respect to the distortion
parameter Q and displacement factor xj for 4 vibrational mode.
10
displacement point. In complex 2, at xj = 0.8 (see Fig. 3), the Q parameter shows a minimum and
predicts a D value as high as -46 cm-1.
Furthermore, we have developed a three-dimensional magneto-structural correlation to see the
effect of angle change on the D values for complex 1 and 2 (see Figure 4 and S7 in ESI). It is very
clear that the D is maximum when all the three equatorial angles are 120. For 1, the variation in
D values is found to be relatively smaller for 5 vibrations compared to 4 mode (see Table S8-S9
in ESI). For 2 no spin-vibrational coupling is detected as a much smaller change in D is noted. To
rationalize this observation, the AILFT computed d-orbitals are plotted, and this reveals that the
dxy-dx2-y
2 orbital energy gap is altered only slightly in 1 and negligibly in 2 (see Fig. S8-S9). This
suggests that 4 vibrational mode is dominant in controlling the magnetic anisotropy in trigonal
planar d4 systems, and this vibration likely offers a smaller barrier height for relaxation at lower
temperatures. Between complex 1 and 2, the spin-vibronic coupling is found to be stronger in the
former.
At the equilibrium geometries, neglecting other effects, the computed Ucal values for complexes
1 and 2 are 153.8 and 44.7 cm-1 for complexes 1 and 2, respectively. Considering the vibrational
relaxation 4 modes at the displacement scale of xj=±2, the Ueff value is expected to be diminished
to 19 cm-1 and 15 cm-1 for complexes 1 and 2, respectively (neglecting the QTM effects). This is
substantially smaller than the barrier height estimated from the Orbach process and suggests a
dominant spin-vibrational relaxation role in the magnetization relaxation in these complexes. This
may be attributed to the fact that the N-M-N bond angle bending vibration is very subtle and
does not require significant energy for structural distortion and is strongly correlated to the dxy and
dx2
-y2 gap altering the magnetic anisotropy. This advocates a design principle that a rigid structure
11
with a robust N-Mn-N angle could block such relaxation, and this is possible if a chelate type or
macrocyclic type ligands are employed.
Conclusion
To the end, we have successfully employed an accurate ab initio method to explore the zero-field
splitting and ligand field parameters in two MnIII and CrII high spin complexes. A record-high D
value of -64 cm-1 and -15 cm-1 was found for the X-ray structures of 1 and 2, respectively. These
two values are higher than any other reported D values for any mononuclear d4 systems (see Table
S10 in ESI). While a significant barrier for magnetization relaxation is found for both the
complexes, our detailed analysis revealed a strong spin-vibration coupling both the complexes that
are likely to yield smaller blocking temperatures.
Figure 4. Three-dimensional magneto-structural correlation of D obtained from 4 mode for complex 1.
12
ASSOCIATED CONTENT
The following files are available free of charge.
AUTHOR INFORMATION
Corresponding Author
Gopalan Rajaraman. Email: [email protected]
Present Addresses
†Department of Chemistry, Indian Institute of Technology Bombay, Mumbai- 400076,
Maharashtra, India
Author Contributions
The manuscript was written through contributions of all authors. All authors have given approval
to the final version of the manuscript.
Funding Sources
This work was funded by DST and SERB (CRG/2018/000430; DST/SJF/CSA-03/2018-10;
SB/SJF/2019-20/12), UGC-UKIERI (184-1/2018(IC)) and SUPRA (SPR/2019/001145).
ACKNOWLEDGMENT
RJ thanks DST-INSPIRE and AS thanks IIT Bombay for IPDF funding.
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TOC: Using Ab initio NEVPT2 calculations, we offer a design principle to enhance ZFS in high-
spin d4 complexes of first-row transition elements.
download fileview on ChemRxivManuscript_GR_final_Arxiv2.pdf (914.22 KiB)
Supporting Information
Record High Magnetic Anisotropy in Three Coordinate MnIII and CrII
Complexes: A Theoretical Perspective
Arup Sarkar, Reshma Jose, Harshit Ghosh, and Gopalan Rajaraman*
Department of Chemistry, Indian Institute of Technology Bombay, Mumbai- 400076, India
Email: [email protected]
Table S1: Comparison of the ZFS parameters using different triplet and singlet roots during
the SA-CASSCF/NEVPT2 calculations.
Sets Quintet roots Triplet roots Singlet roots D (cm-1) E/D
Complex 1 5 35 - -64.5 0.0002
Complex 1 5 45 - -64.3 0.0003
Complex 1 5 35 22 -63.5 0.0003
Complex 2 5 35 - -15.2 0.003
Complex 2 5 45 - -15.1 0.003
Complex 2 5 45 22 -14.8 0.003
Figure S1: Major anisotropic axes plotted on complex 2 from NEVPT2 level of theory
(left). Equatorial N-Cr-N bond angles and Cr-N bond lengths shown on X-Ray
structure of complex 2 (right). Colour code: Cr: green, N: blue, Si: bluish green, C: dark
grey. Hydrogens are omitted for clarity.
Table S2: NEVPT2 vertical excitation spectrum, CASSCF electronic configuration and their
respective contribution towards D and E values for ground state and six lower lying excited
states for complex 1.
Table S3: NEVPT2 vertical excitation spectrum, CASSCF electronic configuration and their
respective contribution towards D and E values for ground state and four lower lying excited
states for complex 2 (The irreducible representations are assigned according to C2v symmetry).
States Major CASSCF electronic
configuration
NEVPT2
Energy (cm-
1)
Contribution to D
(cm-1)
Contribution to
E (cm-1)
5E dz
21dyz1dxz
1dxy1dx
2-y
20 (77%)
dz21dyz
1dxz1dxy
0 dx2-y
21 (76%)
0.0
18.7
0.0
-62.16
0.0
0.00
3E
dz21dyz
1dxz2dxy
0 dx2-y
20 (37%)
dz21dyz
2dxz1dxy
0 dx2-y
20 (12%) 13593.2 -0.38 0.38
dz21dyz
2dxz1dxy
0 dx2-y
20 (38%)
dz21dyz
1dxz2dxy
0 dx2-y
20 (12%) 13597.6 -0.23 -0.38
3A2
dz22dyz
1dxz1dxy
0 dx2-y
20 (42%)
dz22dyz
1dxz0dxy
1 dx2-y
20 (15%) 13720.0 -0.09 0.09
5E dz
21dyz1dxz
0dxy1 dx
2-y
21 (74%)
dz21dyz
0dxz1dxy
1 dx2-y
21 (74%)
18929.8
18949.3
0.18
0.13
-0.18
0.18
States Major CASSCF electronic
configuration
NEVPT2
Energy (cm-
1)
Contribution to D
(cm-1)
Contribution to
E (cm-1)
5A2 dz21dyz
1dxz1dxy
1 dx2-y
20 (91%) 0.0 0.0 0.0 5A2 dz
21dyz1dxz
1dxy0 dx
2-y
21 (91%) 755.8 -14.43 0.00 5B1
dz21dyz
1dxz0dxy
1 dx2-y
21 (94%) 10368.3 0.16 -0.12 5B2
dz21dyz
0dxz1dxy
1 dx2-y
21 (94%) 10808.9 0.13 0.10
5A1 dz
20dyz1dxz
1dxy1 dx
2-y
21
(100%) 12854.9 0.00 -0.00
Table S4: Wavefunction decomposition spin-orbit coupled states (Ms) of S =2 manifold for
complex 1 and 2.
Figure S2: NEVPT2-LFT d-orbital splitting diagram for complex 2. Green arrows
indicate the first excited state electronic transition. The green arrow indicates 1st excited
state electronic excitation.
Figure S3: Energy profile diagram of the lowest five spin-orbit states of complex 1
(left) and complex 2 (right) obtained from NEVPT2/QDPT/EHA method.
Table S5: Selected structural parameters of the X-Ray structure and optimised geometries of
complex 1 and 2.
Complex 1
Spin-orbit
State S MS
Quintet Weightage
Energy
(cm-1)
1
2 2 GS 26%
0.00 2 2 1st ES 24%
2 -2 GS 26%
2 -2 1st ES 24%
2
2 2 GS 26%
0.04 2 2 1st ES 24%
2 -2 GS 26%
2 -2 1st ES 24%
3
2 1 GS 27%
153.81 2 1 1st ES 23%
2 -1 GS 27%
2 -1 1st ES 23%
4
2 1 GS 27%
153.83 2 1 1st ES 23%
2 -1 GS 27%
2 -1 1st ES 23%
5 2 0 GS 100% 296.17
Complex 2
1
2 2 GS 47%
0.00 2 2 1st ES 3%
2 -2 GS 47%
2 -2 1st ES 3%
2
2 2 GS 47%
0.01 2 2 1st ES 3%
2 -2 GS 47%
2 -2 1st ES 3%
3 2 1 GS 50%
44.69 2 -1 GS 50%
4 2 1 GS 50%
44.99 2 -1 GS 50%
5 2 0 GS 100% 60.90
Complex
N1-
Mn-N2
()
N2-
Mn-
N3()
N3-
Mn-N1
()
Mn-
N1
(Å)
Mn-
N2
(Å)
Mn1-
N3
(Å)
4 and 5
(cm-1)
Table S6: Variation of D and E/D values with respect to Q parameter along with their energies
of the first excited state for complex 1. The frequency points (P’s) are taken from 4 vibration.
*n =1 for positive xj and -1 for negative xj.
(Angle
A)
(Angle
B)
(Angle
C)
1 (X-Ray) 120.02 119.95 120.02 1.889 1.890 1.890 70.3, 72.9
1 (optimised
in toluene) 113.93 113.87 132.20 1.911 1.902 1.911 68.6, 72.6
N1-Cr-
N2 ()
(Angle
A)
N2-Cr-
N3 ()
(Angle
B)
N3-Cr-
N1 ()
(Angle
C)
Cr-N1
(Å)
Cr-N2
(Å)
Cr-N3
(Å)
2 (X-Ray) 115.81 120.29 123.90 2.021 2.027 2.033 58.7, 69.9
2 (optimised
in n-hexane) 113.28 113.08 133.65 2.051 2.038 2.050 61.0, 73.5
Figure S4: DFT computed IR spectrum of the two complexes at far-IR frequencies of
complex 1 (left) and complex 2 (right). The black parenthesis and the black arrows
indicate the N-M-N angle bending and out-of-plane bending vibrations.
4 & 5
4 &
5
Table S7: Variation of D and E/D values with respect to Q parameter along with their energies
of the first excited state for complex 2. The frequency points (P’s) are taken from the fourth
frequency point.
Bond Angle ( =
A/B/C)
D (cm-
1) |E/D|
Energy of
the 1st
excited
state (cm-
1)
Q =
n|120
- |*
D Displacement
scale (xj)
P1
A=116.50
C=111.07
B=131.89
-6.47 0.019 4445.8 -24.32 57.81 -2.0
P2
A=117.70
C=114.07
B=128.00
-8.86 0.012 3007.0 -16.23 55.42 -1.3
P3
A=118.84
C=116.98
B=124.12
-15.33 0.005 1567.1 -8.30 48.95 -0.7
P4
A=119.21
C=117.91
B=122.85
-20.63 0.003 1094.8 -5.73 43.65 -0.4
P5
(X-Ray
Structure)
A=120.02
C=120.02
B=119.95
-64.28 0.0003 18.7 0.09 0 0.0
P6
A=120.56
C=121.42
B=118.01
-27.50 0.001 750.2 3.97 36.78 0.3
P7
A=121.01
C=122.62
B=116.33
-17.05 0.002 1374.5 7.3 47.23 0.6
P8
A=122.05
C=125.42
B=112.33
-9.22 0.006 2841.3 15.14 55.06 1.2
P9
A=123.23
C=128.73
B=107.51
-6.29 0.008 4565.2 24.45 57.99 2.0
*n =1 for positive xj and -1 for negative xj.
Bond Angle ( =
A/B/C)
D
(cm-1) |E/D|
Energy of
the 1st
excited
state (cm-1)
Q =
n|120
- |*
D Displacement
scale (xj)
P1
A=106.15
B=119.75
C=133.79
-5.00 0.022 2639.6 -27.89 10.10 -2.0
P2
A=109.41
B=119.97
C=130.48
-6.37 0.014 2014.7 -21.10 8.73 -1.4
P3
A=112.18
B=120.12
C=127.64
-8.45 0.009 1471.6 -15.58 6.65 -0.8
P4
(X-Ray
Structu
re)
A=115.81
B=120.29
C=123.90
-15.10 0.003 755.8 -8.38 0 0.0
P5
A=119.69
B=120.43
C=119.84
-45.87 0.000 22.6 0.90 30.77 0.8
P6
A=122.67
B=120.49
C=116.69
-21.08 0.001 575.0 6.47 5.98 1.4
P7
A=125.29
B=120.52
C=113.88
-11.57 0.003 1069.2 11.93 3.53 2.0
Figure S5: Variation of E/D with respect to Q parameter and xj for complex 1 (left)
and for complex 2 (right) in 4 vibration.
-32 -24 -16 -8 0 8 16
0.000
0.005
0.010
0.015
0.020
0.025-2.4 -1.6 -0.8 2.40.8 1.6
E/D
Q
xj
0.0
-30 -20 -10 0 10 20 30
-2.4 -1.6 -0.8 0.0 0.8 1.6 2.4
0.000
0.005
0.010
0.015
0.020
xj
E/D
Q
Figure S6: Variation of LFT d-orbital energies with respect to Q parameter for complex
1 (left) and for complex 2 (right) in 4 vibration.
-24 -18 -12 -6 0 6 12 18 24
0
3000
6000
9000
12000
15000
18000
dxy
dx
2-y
2
En
erg
y (c
m-1
)
Angular Distortion parameter (Q)
dxy
dx
2-y
2
dz
2
dxz
dyz
dyz
dxz
dz
2
-30 -24 -18 -12 -6 0 6 12
0
2000
4000
6000
8000
10000
12000
dz
2
dxz
dyzE
ner
gy
(cm
-1)
Angular distortion parameter (Q)
dx
2-y
2
dxy
dyz
dxz
dz
2
dx
2-y
2
dxy
Figure S7. Three dimensional magneto-structural correlation of D parameter obtained
from 4 vibrational points in case of complex 2.
Table S8: Variation of D, E/D, 1st excited state NEVPT2 energy values with respect to the
displacement of Mn along z-direction for complex 1. The frequency points (P’s) are taken from
the 5 vibrations.
Coordinates of Mn ion in (x y z)
format (Å)
D (cm-1) E/D
Energy of 1st
Excited State
(cm-1) D
Displacement
scale (xj)
P1 (-0.040 -0.019 0.360) -16.2 0.004 1407.4 48.1 2.0
P2 (-0.027 -0.013 0.248) -21.5 0.002 1016.3 42.8 1.4
P3 (-0.013 -0.006 0.120) -34.8 0.001 523.6 29.5 0.7
P4
(X-Ray
Structure)
(0.000 0.001 0.000) -64.3 0.000 18.7 0.0 0.0
P5
(0.014 0.008 -0.123)
-32.2 0.002 593.1 32.1 -0.7
P6 (0.029 0.015 -0.254)
-18.3 0.006 1232.1 46.0 -1.4
P7 (0.040 0.021 -0.359) -13.4 0.011 1751.9 50.9 -2.0
-2 -1 0 1 2
-28
-24
-20
-16
-12
-8
-4
0
D (
cm-1)
Displacement scale (xj)
complex 2
-2 -1 0 1 2-70
-60
-50
-40
-30
-20
-10
0
D (
cm-1)
Displacement scale (xj)
complex 1
Figure S8: Variation of D parameter of complex 1 (left) and complex 2 (right) with respect
to 5 vibration.
Table S9: Variation of D, E/D, 1st excited state NEVPT2 energy values with respect to the
displacement of Cr along z-direction for complex 2. The frequency points (P’s) are taken from
the 5 vibration.
Coordinates of Cr ion in (x y z)
format (Å)
D (cm-1) E/D
Energy of
1st Excited
State (cm-1) D
Displacement
scale (xj)
P1 (-0.092 -0.106 0.312) -11.1 0.005 1077.6 4.0 2.0
P2 (-0.080 -0.101 0.218) -12.1 0.004 983.9 3.0 1.4
P3 (-0.066 -0.093 0.103) -13.6 0.004 868.2 1.4 0.7
P4
(X-Ray
Structure)
(-0.05 -0.086 -0.008) -15.1 0.003 755.8 0.0 0.0
P5
(-0.040 -0.080 -0.102)
-16.7 0.003 677.4 1.6 -0.6
P6 (-0.025 -0.073 -0.221)
-18.7 0.002 584.0 3.6 -1.4
P7 (-0.012 -0.067 -0.327) -20.3 0.002 515.1 5.2 -2.0
Figure S9: Variation of ab initio LFT d-orbital splitting of complex 1 (left) and complex
2 (right) with respect to 5 vibration.
-2 -1 0 1 2
0
3000
6000
9000
12000
15000
18000
dz
2
dyz
dxy
dx
2-y
2
dxz
dyz
En
ergy
(cm
-1)
Displacement scale (xj)
dxy
dx
2-y
2
dxz
dz
2
-2 -1 0 1 2
0
2000
4000
6000
8000
10000
12000
dz
2
dxz
dyzE
ner
gy
(cm
-1)
Displacement scale (xj)
dx
2-y
2
dxy
dyz
dxz
dz
2
dx
2-y
2
dxy
Table S10: Literature survey of all reported mononuclear high-spin Mn(III) and Cr(II)
complexes.
Sr. No Complex Dexp
(cm-1) |E/D|exp
Dcal
(cm-1) |E/D|cal YearRef.
1 trans-[Mn(cyclam)I2]I +0.60 0.05 - - 20021
2 [Mn(dbm)3] -4.35 0.06 -4.55 0.06 19972
3 [MnTPPCl] -2.29 0.00 - - 19993
4 [(tpfc)Mn(OPPh3)] -2.69 0.06 - - 20004
5 [(terpy)Mn(N3)3] -3.29 0.15 -3.29 0.16 20015
6 CsMn(SO4)2‚12D2O -4.52 0.06 - - 20016
7 [Mn(cyclam)Br2]Br -1.67 0.01 - - 20017
8 [Mn(OH2)6]3+ -4.49 0.06 - - 20038
9 [Mn(acac)3] - - -4.21 0.10 20069
10 [Mn(bpia)(OAc)(OCH3)]
(PF6) +3.53 0.16 +3.24 0.16 200810
11
[MnIII(5-TMAM(R)-
salmen)(H2O)-
CoIII(CN)6]·7H2O·MeCN
-3.30 - - - 201311
12 Ph4P[Mn(opbaCl2)(py)2] -3.42 0.04 -3.47 0.01 201312
13 [Mn(dbm)2(DMSO)2]
(ClO4) -3.42 0.22 -3.64 0.00 201513
14 [Mn(dbm)2(py)2]
(ClO4) -4.46 0.21 -3.95 0.00 201513
15 Na5[Mn(L-tart)2]·12H2O -3.23 0.01 - - 201514
16 [Mn(TPP)(3,5-
Me2pyNO)2]ClO4 -3.82 0.04 -3.94 0.01 201515
17 [Mn(3-OEt-salme)2]BPh4 -4.60 0.32 -3.81 0.27 201616
18 MnL(NCS)·0.4H2O +2.53 0.18 +2.66 0.20 201717
19
Mn(tpfc) (tpfc = 5,10,15-
tris(pentafluorophenyl)corrole
trianion)
-2.67 0.01 - - 202018
20 [Mn{(OPPh2)2N}3] -3.92 0.00 -3.52 0.01 202019
21 [CrII(N(TMS)2)2(py)2] -1.80 0.01 -1.50 0.04 201520
22 [CrII(N(TMS)2)2(THF)2] -2.00 0.01 -1.66 0.05 201520
23 Cr(CO)3(η
6,η6-C6H5C6H5)
Cr(Al2(OC(CF3)2H)4) -2.15 0.00 - - 201721
24
{[1-N-3,5-tBu2dp)4Cr][5-
(N,N,C,C,P))2K(1-O-
THF)2[2}
-1.86 0.01 - - 202022
25 [Cr(iPrNC(CH3)NiPr)2] -1.74 0.04 -1.50 0.02 202123
26 [Cr(CyNC(CH3)NCy)2] -1.82 0.05 -1.47 0.02 202123
27 [Cr(DippNC(CH3)NDipp)2] -1.71 0.04 -1.48 0.02 202123
28 [Cr(tBuNC(CH3)NtBu)2] -1.94 0.02 -1.68 0.00 202123
29 [Cr{N(SiMe2Ph)2}2] -2.70 0.07 -2.70 0.07 202124
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24. Freitag, K.; Stennett, C. R.; Mansikkamaki, A.; Fischer, R. A.; Power, P. P., Two-Coordinate,
Nonlinear Vanadium (II) and Chromium (II) Complexes of the Silylamide Ligand–N (SiMePh2) 2:
Characterization and Confirmation of Orbitally Quenched Magnetic Moments in Complexes with Sub-
d5 Electron Configurations. Inorg. Chem. 2021.
download fileview on ChemRxivSupporting_Information.pdf (1.06 MiB)
Record High Magnetic Anisotropy in Three
Coordinate MnIII and CrII Complexes: A Theoretical
Perspective
Arup Sarkar, Reshma Jose, Harshit Ghosh and Gopalan Rajaraman*
Department of Chemistry, Indian Institute of Technology Bombay, Mumbai- 400076,Maharashtra, India
Keywords: Low-coordinate, Ab initio, NEVPT2, Zero-field Splitting, Spin-vibronic coupling
ABSTRACT: Ab initio calculations performed in two three-coordinate complexes
[Mn{N(SiMe3)2}3] (1) and [K(18-crown-6)(Et2O)2][Cr{N(SiMe3)2}3] (2) reveal record-high
magnetic anisotropy with the D values -64 cm-1 and -15 cm-1 respectively, enlisting d4 ion back in
the race for single-ion magnets. For the first time, a detailed spin-vibrational analysis was
performed in 1 and 2 that suggests a dominant under barrier relaxation due to flexible
coordination sphere around the metal ion offering design clues for low coordinate transition
metal SIMs.
1
Introduction
Single-Molecule Magnets (SMMs) have become a fascinating research area as this class of
molecules exhibit magnetization just like permanent magnets below a critical temperature
defined as blocking temperature TB.1 An important parameter associated with the blocking
temperature is the barrier height for magnetization reversal (Ueff) which is correlated to the
magnetic moment of different microstate and the nature of anisotropy. While in lanthanide
complexes, the first-order spin-orbit coupling (SOC) is strong enough to produce large barrier
heights,2 in transition metal (TM) systems spin-orbit coupling is generally weak, leading to
relatively smaller anisotropy which is reflected in the axial zero-field splitting parameter (D)
which can be tuned at will using ligand field.3
There are several challenges in enhancing the blocking temperature TB in SMMs as several
relaxation mechanisms other than the Orbach process spoil the direct correlation of TB to Ueff
values. Among others, quantum tunneling of magnetization (QTM) and
spin-phonon/vibrational-mode relaxation mechanisms are a prominent source of relaxation, as
shown in recent years by various groups.4 Earlier research in the SMM area was focused on
increasing the total spin (S) of the complexes by increasing the number of metal centers. After
2
the discovery of a very small Ueff barrier in {Mn19} cluster possessing record high ground state S
value, it becomes clear that increasing the number of metal centers or S value diminishes the
axial anisotropy (D term) as evident from the equation proposed originally by Abragam and
Bleaney5 and adapted in ab initio calculations later on. For this reason, mononuclear TM
complexes gained significant attention leading to the birth of several single-ion magnets (SIMs)
based on the low coordination number such as Fe(II/I), Ni(II), and Co(II), exhibiting very large
Ueff values.6
In the early years of SMMs, the focus has been on transition metal cluster particularly that of
Mn(III) ions, as this offer an easy source of negative D parameter for the chemists and unearthed
numerous SMMs albeit with smaller Ueff/TB values. 1a, 7 The Mn(III) ions are very robust and can
be easily incorporated in cluster aggregation, and are relatively redox stable6a but exhibit only
small D values of the order of ~|5| cm-1. 8 While several low-coordinate transition metal ions were
pursued recently for potential SMMs, Mn(III) has not been studied in detail, perhaps due to the
perception that the expected D values are rather small.8 Apart from Ueff values, the blocking
temperature is an important criterion which is often very small. This suggests that apart from the
QTM effect, spin-vibrational relaxations are at play in such systems.4 How these effects manifest
in these complexes are not fully understood.
To ascertain complexes that exhibit large negative D values and also to correlate the relaxation
mechanism to spin-vibrational coupling, we undertake theoretical studies based on multi-
3
configurational ab initio calculations SA-CASSCF/NEVPT2 using the ORCA suite.9 Here, we
have studied in detail two three-coordinate d4 systems Mn(III) and Cr(II): [Mn{N(SiMe3)2}3]10
(1) and [K(18-crown-6)(Et2O)2] [Cr{N(SiMe3)2}3]11 (2) using their reported X-ray structure.
Our NEVPT2 calculations yield a record axial D value of -64 cm-1 and -15 cm-1 for 1 and 2,
respectively, with a negligible E/D value. The D value computed for both complexes is larger
than any examples reported to-date and suggests a potential SMMs characteristic for these robust
building block metal ions.
Computational Details
All the ab initio single point calculations have been performed using ORCA 4.0.0 program.9
DKH (Douglas-Kroll-Hess) Hamiltonian was used to account for the scalar relativistic effect.
DKH contracted versions of the basis sets were used during the calculations- DKH-def2-TZVP
for Mn, Cr, Si; DKH-def2-TZVP(-f) for N and DKH-def2-SVP for the rest of the atoms. During
the orbital optimization step in SA-CASSCF (state-averaged complete active space self-
consistent field) method, 4 metal electrons in 5 metal d-orbitals were taken into consideration
and optimized with 5 quintet and 35 triplet roots for Mn(III) and Cr(II) metal centers. Additional
calculations have also been carried out with 5 quintets, 45 triplet roots, and 5 quintets, 35 triplet,
and 22 singlet roots to check the effect of high-lying excited states on the Spin-Hamiltonian (SH)
parameters. The addition of extra 10 triplet roots and 22 singlet roots marginally affect the SH
parameters (see Table S1 in ESI). NEVPT2 (N-electron valence perturbation theory second-
4
order) calculation has also been performed on the top of converged SA-CASSCF wavefunction
to include the dynamic electron correlation. Spin-orbit interaction was accounted with quasi-
degenerate perturbation theory (QDPT) approach using SOMF (spin-orbit mean field) operator.
Only spin-orbit contributions towards zero-field splitting were computed. Final Spin-
Hamiltonian parameters were determined with effective Hamiltonian approach (EHA)
formalism.12 Ab initio ligand field theory (AILFT) calculations have also been performed to
obtain the d-orbital energies.13
Geometry optimization and single point frequency calculations have been carried out in Gaussian
09 (Rev. D.01) program.14 Hybrid unrestricted B3LYP-D2 functional was used for the DFT
calculations along with Ahlrich’s triple- valence polarized (TZVP) basis set for Mn, Cr, Si, N
and Ahlrich’s spilt valence polarized (SVP) basis set for rest of the atoms.15
Result and Discussions
Complex 1 possesses a perfect D3h symmetry as the three N-Mn-N bond angles are 120.02,
120.02 and 119.95 and the three Mn-N bond lengths are 1.89, 1889, and 1.89 (in Å unit). It was
5
Figure 1: NEVPT2 computed Dzz axis of the molecule plotted on the X-Ray structure (left) and three Mn-N bond lengths (in Å) and N-Mn-N angles () shown on the molecule (right). Colour code: Mn: pink, N: blue, Si: light green, C: dark grey. Hydrogens are omitted due to clarity.
also noticed that the {MnN3} core was planar, and the bulky trimethylsilyl groups surrounded the
central moiety stabilizes the low coordinate molecule from further coordination via steric
arrangements (see Figure 1). The NEVPT2-QDPT calculated major anisotropy axes, i.e., Dzz and
gzz axes, were found to be exactly perpendicular to the Mn-N3 plane, i.e., exactly collinear with
the C3 axis, which describes the axial nature of anisotropy present in the molecule.
A record axial zero-field splitting (ZFS) was found for this complex, showing a D value of -64
cm-1 with E/D estimated to be 0.0003, indicating strong easy-axis type anisotropy (see Table 1)
for complex 1. A very similar geometry was observed in the Cr(II) analog, and the N-Cr-N
6
bond angles (123.9, 115.81 and 120.29) are not exactly similar and significantly deviated from
D3h symmetry. The D value for complex 2 is less than complex 1 due to these structural
deviations and also smaller spin-orbit coupling constant () values of Cr(II) than Mn(III). For
complex 2, the E/D value is estimated to be 0.003, which is ten times larger than complex 1 (see
Figure S1 and Table S1 in ESI).
The ground state electronic configuration of complex 1 is dz21dyz
1dxz1dxy
1dx2-y
20, and this comprises
77% of the overall wavefunction. The major contribution (-62 cm-1) towards the negative D value
arises from the first excited state, which consists of dxy dx2-y
2 (same ML valued) electronic
excitation and this excited state contribute ~97% of the overall D value (see Figure 2 and Table
S2 in ESI). Other electronic transitions were found to contribute negligibly to the overall D
value. A very close analysis of the NEVPT2 states reveals that the first excited quintet state is
only 19 cm-1 apart from the ground state and consequently results in a very strong second-order
spin-orbit coupling. While the first excited state is the spin-allowed quintet, the second, third and
fourth excited states arise from the spin-flipped triplet transitions. These three excited states
consist of a mixture of dxy dxz/dyz and dxy dz2 transitions (see Table S2 in ESI). The computed
gx, gy and gz values are 1.67, 1.67 and 1.14 respectively for true spin S =2 and 0.00 0.00 and 5.14,
respectively for pseudospin S =1/2 manifold. In the case of complex 2, the first excited state
contributes 96% (-14.4 cm-1) towards the overall D value. Again, the D value is negative due to
the coupling with the prominent first excited state involving the same ML level dxy dx2-y
2
7
Figure 2: NEVPT2-LFT d-orbital diagram of complex 1. The orange arrow indicates the first excited spin-allowed transition.
electronic excitation (see Figure S2 in ESI). Here one major difference of complex 2 from
complex 1 is that due to significant distortion from D3h and lower ligand field of Cr(II), the first
excited state is 756 cm-1 apart and the next three excited states are quintets (see Table S3). The
computed gx, gy and gz values are 1.97, 1.97, and 1.58 respectively for true spin S=2 and 0.00
0.00 and 6.351, respectively for pseudospin S =1/2 manifold.
In the case of non-Kramers ions like in these two cases studied, the tunnel-splitting is generally
larger, leading to faster relaxation via the QTM process. The tunnel-splitting strongly depends on
the local symmetry and ligand field environment around the metal ion. The high symmetry
8
present in complexes 1 and 2 leads to smaller tunnel splitting (see Figure S3 and Table S4 in
ESI). The first excited pseudo-KDs is separated by 154 cm-1 in case of complex 1 and 45 cm-1 in
case of complex 2. The multi-determinant nature of the ground state leads to mixing of the |+2
and |-2 states, and this is very prominent in complex 1 compared to 2 (see Table S4).
The static electronic picture is insufficient to describe the relaxation mechanism or the spin
dynamics of the system. Recent reports of spin-vibronic coupling that describe the role of
vibrational frequencies of a single molecule or of the surrounding lattice are very important to
elucidate the dynamic scenario of SMMs.4 In this regard, we have attempted to investigate the
role of molecular vibrations occurring at low temperatures on the spin-orbit or Ms levels in the
two complexes. Therefore, we have performed frequency calculations (normal modes) on the X-
ray structures of 1 and 2 using Density Functional Theory (DFT) methods (B3LYP-D2/TZVP, a
similar vibrational pattern also found for the optimized geometries, see Table S5 in ESI).
Here we have carefully analyzed five lower energy vibrational modes below 80 cm-1, and these
are 1 45.1 (40.1), 2 45.8(46.2), 3 58.4(50.3), 4 70.3(58.8) and 5 72.9 (69.9) for complex 1 (2)
(see Figure S4 in ESI). Out of the five vibrations mentioned, the 4 and 5 vibrations were found
to be IR active and also break the D3h symmetry (see Figure S4). Here 4 corresponds to N-M-
N bond angle bending and correlates to Jahn-Teller active vibration (E irreducible
representation in D3h symmetry). The 5 corresponds to out-of-plane (M-N-N-N) bending
vibration of the metal ion and associate with A2” irreducible representation. Several displacement
9
Figure 3: Variation of D values in complexes 1 (left) and 2 (right) with respect to the distortion parameter Q and displacement factor xj for 4 vibrational mode.
points in 4 and 5 vibrational surfaces were considered for CASSCF/NEVPT2 calculations. The
maximum displacement scale of a particular vibration j, denoted by xj, was fixed at 2.0 for both
the complexes as suggested earlier (see Table S6 and S7 in ESI).16
An angular distortion parameter Q was introduced, which is a sum of deviation from 120 from
each of the equatorial N-M-N angles (denoted as ) (see Table S6 and S7).6e Here, in order to
find out the spin-vibronic coupling, the variation of D and E/D have been computed with respect
to the displacement of nuclear coordinates (x) using the following Hamiltonian:
H s−vib=(∂ D∂x
) x [SZ2−S (S+1 )
3 ]+(∂E∂ x
)x (Sx2−Sy
2)…eqn.1¿
10
In Figure 3, we plot computed D values with respect to Q and xj, and these plots show that as
the Q diverges from zero, the magnitude of D decreases for 4 vibrations (see Figure S5 in ESI).
This is because an increase in Q breaks the D3h symmetry and, consequently, increases the gap
between the dxy and dx2-y
2 orbitals (see Fig. S6). In complex 1, the X-Ray structure shows the
highest negative D value and minimum E/D value (see Fig. S5) at equilibrium geometry or zero
displacement point, but for complex 2, the X-ray structure is significantly deviated from the ideal
D3h symmetry and therefore do not have the largest negative D or the lowest E/D at zero
displacement point. In complex 2, at xj = 0.8 (see Fig. 3), the Q parameter shows a minimum and
predicts a D value as high as -46 cm-1.
Furthermore, we have developed a three-dimensional magneto-structural correlation to see the
effect of angle change on the D values for complex 1 and 2 (see Figure 4 and S7 in ESI). It is
very clear that the D is maximum when all the three equatorial angles are 120. For 1, the
variation in D values is found to be relatively smaller for 5 vibrations compared to 4 mode (see
Table S8-S9 in ESI). For 2 no spin-vibrational coupling is detected as a much smaller change in
D is noted. To rationalize this observation, the AILFT computed d-orbitals are plotted, and this
reveals that the dxy-dx2-y
2 orbital energy gap is altered only slightly in 1 and negligibly in 2 (see
Fig. S8-S9). This suggests that 4 vibrational mode is dominant in controlling the magnetic
anisotropy in trigonal planar d4 systems, and this vibration likely offers a smaller barrier height
11
for relaxation at lower temperatures. Between complex 1 and 2, the spin-vibronic coupling is
found to be stronger in the former.
At the equilibrium geometries, neglecting other effects, the computed Ucal values for complexes
1 and 2 are 153.8 and 44.7 cm-1 for complexes 1 and 2, respectively. Considering the vibrational
relaxation 4 modes at the displacement scale of xj=±2, the Ueff value is expected to be diminished
to 19 cm-1 and 15 cm-1 for complexes 1 and 2, respectively (neglecting the QTM effects). This is
substantially smaller than the barrier height estimated from the Orbach process and suggests a
dominant spin-vibrational relaxation role in the magnetization relaxation in these complexes.
This may be attributed to the fact that the N-M-N bond angle bending vibration is very subtle
and does not require significant energy for structural distortion and is strongly correlated to the
dxy and dx2-y
2 gap altering the magnetic anisotropy. This advocates a design principle that a rigid
structure with a robust N-Mn-N angle could block such relaxation, and this is possible if a
chelate type or macrocyclic type ligands are employed.
12
Figure 4. Three-dimensional magneto-structural correlation of D obtained from 4 mode for complex 1.
Conclusion
To the end, we have successfully employed an accurate ab initio method to explore the zero-field
splitting and ligand field parameters in two MnIII and CrII high spin complexes. A record-high D
value of -64 cm-1 and -15 cm-1 was found for the X-ray structures of 1 and 2, respectively. These
two values are higher than any other reported D values for any mononuclear d4 systems (see
Table S10 in ESI). While a significant barrier for magnetization relaxation is found for both the
complexes, our detailed analysis revealed a strong spin-vibration coupling both the complexes
that are likely to yield smaller blocking temperatures.
13
ASSOCIATED CONTENT
The following files are available free of charge.
AUTHOR INFORMATION
Corresponding Author
Gopalan Rajaraman. Email: [email protected]
Present Addresses
†Department of Chemistry, Indian Institute of Technology Bombay, Mumbai- 400076,
Maharashtra, India
Author Contributions
The manuscript was written through contributions of all authors. All authors have given approval
to the final version of the manuscript.
Funding Sources
This work was funded by DST and SERB (CRG/2018/000430; DST/SJF/CSA-03/2018-10;
SB/SJF/2019-20/12), UGC-UKIERI (184-1/2018(IC)) and SUPRA (SPR/2019/001145).
ACKNOWLEDGMENT
14
RJ thanks DST-INSPIRE and AS thanks IIT Bombay for IPDF funding.
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17
TOC: Using Ab initio NEVPT2 calculations, we offer a design principle to enhance ZFS inhigh-spin d4 complexes of first-row transition elements.
18
download fileview on ChemRxivManuscript_GR_final_Arxiv2.docx (4.55 MiB)
Supporting Information
Record High Magnetic Anisotropy in Three Coordinate MnIII and CrII
Complexes: A Theoretical Perspective
Arup Sarkar, Reshma Jose, Harshit Ghosh, and Gopalan Rajaraman*
Department of Chemistry, Indian Institute of Technology Bombay, Mumbai- 400076, India
Email: [email protected]
Figure S1: Major anisotropic axes plotted on complex 2 from NEVPT2 level of theory (left). Equatorial N-Cr-N bond angles and Cr-N bond lengths shown on X-Ray structure of complex 2 (right). Colour code: Cr: green, N: blue, Si: bluish green, C: dark grey. Hydrogens are omitted for clarity.
Table S1: Comparison of the ZFS parameters using different triplet and singlet roots during the SA-CASSCF/NEVPT2 calculations.
Sets Quintet roots Triplet roots Singlet roots D (cm-1) E/D
Complex 1 5 35 - -64.5 0.0002
Complex 1 5 45 - -64.3 0.0003
Complex 1 5 35 22 -63.5 0.0003
Complex 2 5 35 - -15.2 0.003
Complex 2 5 45 - -15.1 0.003
Complex 2 5 45 22 -14.8 0.003
Table S2: NEVPT2 vertical excitation spectrum, CASSCF electronic configuration and theirrespective contribution towards D and E values for ground state and six lower lying excitedstates for complex 1.
StatesMajor CASSCF electronic
configuration
NEVPT2Energy (cm-
1)
Contribution to D(cm-1)
Contribution toE (cm-1)
5Edz
21dyz1dxz
1dxy1dx
2-y
20 (77%)dz
21dyz1dxz
1dxy0 dx
2-y
21 (76%)0.018.7
0.0-62.16
0.00.00
3E
dz21dyz
1dxz2dxy
0 dx2-y
20 (37%)dz
21dyz2dxz
1dxy0 dx
2-y
20 (12%)13593.2 -0.38 0.38
dz21dyz
2dxz1dxy
0 dx2-y
20 (38%)dz
21dyz1dxz
2dxy0 dx
2-y
20 (12%)13597.6 -0.23 -0.38
3A2dz
22dyz1dxz
1dxy0 dx
2-y
20 (42%)dz
22dyz1dxz
0dxy1 dx
2-y
20 (15%)13720.0 -0.09 0.09
5Edz
21dyz1dxz
0dxy1 dx
2-y
21 (74%)dz
21dyz0dxz
1dxy1 dx
2-y
21 (74%)18929.818949.3
0.180.13
-0.180.18
Table S3: NEVPT2 vertical excitation spectrum, CASSCF electronic configuration and theirrespective contribution towards D and E values for ground state and four lower lying excitedstates for complex 2 (The irreducible representations are assigned according to C2v
symmetry).
StatesMajor CASSCF electronic
configuration
NEVPT2Energy (cm-
1)
Contribution to D(cm-1)
Contribution toE (cm-1)
5A2 dz21dyz
1dxz1dxy
1 dx2-y
20 (91%) 0.0 0.0 0.05A2 dz
21dyz1dxz
1dxy0 dx
2-y
21 (91%) 755.8 -14.43 0.005B1 dz
21dyz1dxz
0dxy1 dx
2-y
21 (94%) 10368.3 0.16 -0.125B2 dz
21dyz0dxz
1dxy1 dx
2-y
21 (94%) 10808.9 0.13 0.105A1 dz
20dyz1dxz
1dxy1 dx
2-y
21 (100%) 12854.9 0.00 -0.00
Figure S2: NEVPT2-LFT d-orbital splitting diagram for complex 2. Green arrows indicate the first excited state electronic transition. The green arrow indicates 1st excited state electronic excitation.
Figure S3: Energy profile diagram of the lowest five spin-orbit states of complex 1 (left) and complex 2 (right) obtained from NEVPT2/QDPT/EHA method.
Complex 1Spin-orbit
StateS MS
QuintetWeightage
Energy (cm-
1)
1
2 2 GS 26%
0.002 2 1st ES 24%2 -2 GS 26%2 -2 1st ES 24%
2 2 2 GS 26% 0.04
2 2 1st ES 24%2 -2 GS 26%2 -2 1st ES 24%
3
2 1 GS 27%
153.812 1 1st ES 23%2 -1 GS 27%2 -1 1st ES 23%
4
2 1 GS 27%
153.832 1 1st ES 23%2 -1 GS 27%2 -1 1st ES 23%
5 2 0 GS 100% 296.17Complex 2
1
2 2 GS 47%
0.002 2 1st ES 3%2 -2 GS 47%2 -2 1st ES 3%
2
2 2 GS 47%
0.012 2 1st ES 3%2 -2 GS 47%2 -2 1st ES 3%
32 1 GS 50%
44.692 -1 GS 50%
42 1 GS 50%
44.992 -1 GS 50%
5 2 0 GS 100% 60.90Table S4: Wavefunction decomposition spin-orbit coupled states (Ms) of S =2 manifold for complex 1 and 2.
Table S5: Selected structural parameters of the X-Ray structure and optimised geometries of complex 1 and 2.
Complex N1-Mn-N2
()(Angle
N2-Mn-N3()
(AngleB)
N3-Mn-N1
()(Angle
Mn-N1(Å)
Mn-N2(Å)
Mn1-N3(Å)
4 and 5 (cm-
1)
Figure S4: DFT computed IR spectrum of the two complexes at far-IR frequencies of complex 1 (left) and complex 2 (right). The black parenthesis and the black arrows indicate the N-M-N angle bending and out-of-plane bending vibrations.
4 & 5
A) C)1 (X-Ray) 120.02 119.95 120.02 1.889 1.890 1.890 70.3, 72.9
1 (optimisedin toluene)
113.93 113.87 132.20 1.911 1.902 1.911 68.6, 72.6
N1-Cr-N2 ()(Angle
A)
N2-Cr-N3 ()(Angle
B)
N3-Cr-N1 ()(Angle
C)
Cr-N1(Å)
Cr-N2(Å)
Cr-N3(Å)
2 (X-Ray) 115.81 120.29 123.90 2.021 2.027 2.033 58.7, 69.92 (optimisedin n-hexane)
113.28 113.08 133.65 2.051 2.038 2.050 61.0, 73.5
Table S6: Variation of D and E/D values with respect to Q parameter along with theirenergies of the first excited state for complex 1. The frequency points (P’s) are taken from 4
vibration.
*n =1 for positive xj and -1 for negative xj.
Bond Angle ( = A/B/C)
D (cm-
1)|E/D|
Energy ofthe 1st
excitedstate (cm-
1)
Q =n|120- |*
DDisplacement
scale (xj)
P1A=116.50C=111.07B=131.89
-6.47 0.019 4445.8 -24.32 57.81 -2.0
P2A=117.70C=114.07B=128.00
-8.86 0.012 3007.0 -16.23 55.42 -1.3
P3A=118.84C=116.98B=124.12
-15.33 0.005 1567.1 -8.30 48.95 -0.7
P4A=119.21C=117.91B=122.85
-20.63 0.003 1094.8 -5.73 43.65 -0.4
P5(X-Ray
Structure)
A=120.02C=120.02B=119.95
-64.28 0.0003 18.7 0.09 0 0.0
P6A=120.56C=121.42B=118.01
-27.50 0.001 750.2 3.97 36.78 0.3
P7A=121.01C=122.62B=116.33
-17.05 0.002 1374.5 7.3 47.23 0.6
P8A=122.05C=125.42B=112.33
-9.22 0.006 2841.3 15.14 55.06 1.2
P9A=123.23C=128.73B=107.51
-6.29 0.008 4565.2 24.45 57.99 2.0
Table S7: Variation of D and E/D values with respect to Q parameter along with theirenergies of the first excited state for complex 2. The frequency points (P’s) are taken from thefourth frequency point.
*n =1 for positive xj and -1 for negative xj.
Bond Angle ( = A/B/C)
D(cm-1)
|E/D|
Energy ofthe 1st
excitedstate (cm-1)
Q = n|120 - |
*D
Displacementscale (xj)
P1A=106.15B=119.75C=133.79
-5.00 0.022 2639.6 -27.89 10.10 -2.0
P2A=109.41B=119.97C=130.48
-6.37 0.014 2014.7 -21.10 8.73 -1.4
P3A=112.18B=120.12C=127.64
-8.45 0.009 1471.6 -15.58 6.65 -0.8
P4(X-RayStructu
re)
A=115.81B=120.29C=123.90
-15.10 0.003 755.8 -8.38 0 0.0
P5A=119.69B=120.43C=119.84
-45.87 0.000 22.6 0.90 30.77 0.8
P6A=122.67B=120.49C=116.69
-21.08 0.001 575.0 6.47 5.98 1.4
P7A=125.29B=120.52C=113.88
-11.57 0.003 1069.2 11.93 3.53 2.0
Figure S5: Variation of E/D with respect to Q parameter and xj for complex 1 (left) and for complex 2 (right) in 4 vibration.
-32 -24 -16 -8 0 8 16
0.000
0.005
0.010
0.015
0.020
0.025-2.4 -1.6 -0.8 2.40.8 1.6
E/D
Q
xj
0.0
-30 -20 -10 0 10 20 30
-2.4 -1.6 -0.8 0.0 0.8 1.6 2.4
0.000
0.005
0.010
0.015
0.020
xj
E/D
Q
Figure S6: Variation of LFT d-orbital energies with respect to Q parameter for complex 1 (left) and for complex 2 (right) in 4 vibration.
-24 -18 -12 -6 0 6 12 18 24
0
3000
6000
9000
12000
15000
18000
dxy
dx2-y2
En
ergy
(cm
-1)
Angular Distortion parameter (Q)
dxy
dx2-y2
dz2
dxz
dyz
dyz
dxz
dz2
-30 -24 -18 -12 -6 0 6 12
0
2000
4000
6000
8000
10000
12000
dz2
dxz
dyzE
nerg
y (c
m-1
)
Angular distortion parameter (Q)
dx2-y2
dxy
dyz
dxz
dz2
dx2-y2
dxy
Figure S7. Three dimensional magneto-structural correlation of D parameter obtained from 4 vibrational points in case of complex 2.
-2 -1 0 1 2
-28
-24
-20
-16
-12
-8
-4
0
D (
cm-1)
Displacement scale (xj)
complex 2
-2 -1 0 1 2-70
-60
-50
-40
-30
-20
-10
0
D (
cm-1)
Displacement scale (xj)
complex 1
Figure S8: Variation of D parameter of complex 1 (left) and complex 2 (right) with respect to 5 vibration.
Table S8: Variation of D, E/D, 1st excited state NEVPT2 energy values with respect to thedisplacement of Mn along z-direction for complex 1. The frequency points (P’s) are takenfrom the 5 vibrations.
Coordinates of Mn ion in (x y z)format (Å) D (cm-1) E/D
Energy of 1st
Excited State(cm-1)
DDisplacemen
t scale (xj)
P1 (-0.040 -0.019 0.360) -16.2 0.004 1407.4 48.1 2.0
P2 (-0.027 -0.013 0.248) -21.5 0.002 1016.3 42.8 1.4
P3 (-0.013 -0.006 0.120) -34.8 0.001 523.6 29.5 0.7
P4(X-Ray
Structure)(0.000 0.001 0.000) -64.3 0.000 18.7 0.0 0.0
P5 (0.014 0.008 -0.123)-32.2 0.002 593.1 32.1 -0.7
P6(0.029 0.015 -0.254)
-18.3 0.006 1232.1 46.0 -1.4
P7 (0.040 0.021 -0.359) -13.4 0.011 1751.9 50.9 -2.0
Figure S9: Variation of ab initio LFT d-orbital splitting of complex 1 (left) and complex 2 (right) with respect to 5 vibration.
-2 -1 0 1 2
0
3000
6000
9000
12000
15000
18000
dz2
dyz
dxy
dx
2-y
2
dxz
dyz
Ene
rgy
(cm
-1)
Displacement scale (xj)
dxy
dx2-y2
dxz
dz2
-2 -1 0 1 2
0
2000
4000
6000
8000
10000
12000
dz2
dxz
dyzE
nerg
y (c
m-1)
Displacement scale (xj)
dx2-y2
dxy
dyz
dxz
dz2
dx2-y2
dxy
Table S9: Variation of D, E/D, 1st excited state NEVPT2 energy values with respect to thedisplacement of Cr along z-direction for complex 2. The frequency points (P’s) are takenfrom the 5 vibration.
Coordinates of Cr ion in (x y z)format (Å) D (cm-1) E/D
Energy of1st ExcitedState (cm-1)
DDisplacement
scale (xj)
P1 (-0.092 -0.106 0.312) -11.1 0.005 1077.6 4.0 2.0
P2 (-0.080 -0.101 0.218) -12.1 0.004 983.9 3.0 1.4
P3 (-0.066 -0.093 0.103) -13.6 0.004 868.2 1.4 0.7
P4(X-Ray
Structure)(-0.05 -0.086 -0.008) -15.1 0.003 755.8 0.0 0.0
P5 (-0.040 -0.080 -0.102)-16.7 0.003 677.4 1.6 -0.6
P6(-0.025 -0.073 -0.221)
-18.7 0.002 584.0 3.6 -1.4
P7 (-0.012 -0.067 -0.327) -20.3 0.002 515.1 5.2 -2.0
Table S10: Literature survey of all reported mononuclear high-spin Mn(III) and Cr(II)complexes.
Sr. No ComplexDexp
(cm-1)|E/D|exp
Dcal
(cm-1)|E/D|cal YearRef.
1 trans-[Mn(cyclam)I2]I +0.60 0.05 - - 20021 2 [Mn(dbm)3] -4.35 0.06 -4.55 0.06 19972
3 [MnTPPCl] -2.29 0.00 - - 19993
4 [(tpfc)Mn(OPPh3)] -2.69 0.06 - - 20004
5 [(terpy)Mn(N3)3] -3.29 0.15 -3.29 0.16 20015 6 CsMn(SO4)2‚12D2O -4.52 0.06 - - 20016 7 [Mn(cyclam)Br2]Br -1.67 0.01 - - 20017
8 [Mn(OH2)6]3+ -4.49 0.06 - - 20038
9 [Mn(acac)3] - - -4.21 0.10 20069
10[Mn(bpia)(OAc)(OCH3)]
(PF6)+3.53 0.16 +3.24 0.16 200810
11[MnIII(5-TMAM(R)-salmen)
(H2O)-CoIII(CN)6]·7H2O·MeCN
-3.30 - - - 201311
12 Ph4P[Mn(opbaCl2)(py)2] -3.42 0.04 -3.47 0.01 201312
13[Mn(dbm)2(DMSO)2]
(ClO4)-3.42 0.22 -3.64 0.00 201513
14[Mn(dbm)2(py)2]
(ClO4)-4.46 0.21 -3.95 0.00 201513
15 Na5[Mn(L-tart)2]·12H2O -3.23 0.01 - - 201514
16[Mn(TPP)(3,5-
Me2pyNO)2]ClO4-3.82 0.04 -3.94 0.01 201515
17 [Mn(3-OEt-salme)2]BPh4 -4.60 0.32 -3.81 0.27 201616 18 MnL(NCS)·0.4H2O +2.53 0.18 +2.66 0.20 201717
19Mn(tpfc) (tpfc = 5,10,15-
tris(pentafluorophenyl)corroletrianion)
-2.67 0.01 - - 202018
20 [Mn{(OPPh2)2N}3] -3.92 0.00 -3.52 0.01 202019
21 [CrII(N(TMS)2)2(py)2] -1.80 0.01 -1.50 0.04 201520
22 [CrII(N(TMS)2)2(THF)2] -2.00 0.01 -1.66 0.05 201520
23Cr(CO)3(η6,η6-C6H5C6H5)
Cr(Al2(OC(CF3)2H)4)-2.15 0.00 - - 201721
24{[1-N-3,5-tBu2dp)4Cr][5-
(N,N,C,C,P))2K(1-O-THF)2[2}
-1.86 0.01 - - 202022
25 [Cr(iPrNC(CH3)NiPr)2] -1.74 0.04 -1.50 0.02 202123
26 [Cr(CyNC(CH3)NCy)2] -1.82 0.05 -1.47 0.02 202123
27 [Cr(DippNC(CH3)NDipp)2] -1.71 0.04 -1.48 0.02 202123
28 [Cr(tBuNC(CH3)NtBu)2] -1.94 0.02 -1.68 0.00 202123
29 [Cr{N(SiMe2Ph)2}2] -2.70 0.07 -2.70 0.07 202124
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