Investigations of the Magnetic and Spectroscopic Properties of V(III) and V(IV) Complexes

Article

pubs.acs.org/IC

Cite This: Inorg. Chem. XXXX, XXX, XXX −XXX

Investigations of the Magnetic and Spectroscopic Properties of V(III)

and V(IV) Complexes

Casey Van Stappen,^†Dimitrios Maganas,^‡Serena DeBeer,^†Eckhard Bill,^‡and Frank Neese*^,‡

^†Max-Planck Institute for Chemical Energy Conversion, Stiftstrasse 34-36, Mulheim an der Ruhr, 45470 North Rhine-Westphalia,

̈

Germany

^‡Max-Planck-Institut fur Kohlenforschung, Kaiser-Wilhelm-Platz 1, Mulheim an der Ruhr, 45470 North Rhine-Westphalia, Germany

̈

S

* Supporting Information

ABSTRACT: Herein, we utilize a variety of physical methods

including magnetometry (SQUID), electron paramagnetic resonance

(EPR), and magnetic circular dichroism (MCD), in conjunction with

high-level ab initio theory to probe both the ground and ligand-ﬁeld

excited electronic states of a series of V(IV) (S = ¹/₂) and V(III) (S =

1) molecular complexes. The ligand ﬁelds of the central metal ions are

analyzed with the aid of ab initio ligand-ﬁeld theory (AILFT), which

allows for a chemically meaningful interpretation of multireference

electronic structure calculations at the level of the complete-active-

space self-consistent ﬁeld with second-order N-electron valence

perturbation theory. Our calculations are in good agreement with all

experimentally investigated observables (magnetic properties, EPR, and

MCD), making our extracted ligand-ﬁeld theory parameters realistic. The ligand ﬁelds predicted by AILFT are further analyzed

with conventional angular overlap parametrization, allowing the ligand ﬁeld to be decomposed into individual σ- and π-donor

contributions from individual ligands. The results demonstrate in VO²⁺complexes that while the axial vanadium−oxo interaction

dominates both the ground- and excited-state properties of vanadyl complexes, proximal coordination can signiﬁcantly modulate

the vanadyl bond covalency. Similarly, the electronic properties of V(III) complexes are particularly sensitive to the available σ

and π interactions with the surrounding ligands. The results of this study demonstrate the power of AILFT-based analysis and

provide the groundwork for the future analysis of vanadium centers in homogeneous and heterogeneous catalysts.

relatively limited, particularly since the 1970s. More speciﬁcally,

only a handful of examples exist that have utilized magnetic

circular dichroism (MCD) to probe these properties.^22,23This

is especially surprising in the case of V(IV) because the S = ¹/₂

ground state should provide relatively simple and easily

interpreted spectra in the frame of a one-electron picture.

Even so, there is only one reported study that describes the C

terms of complexes bearing a VO²⁺core.²³Similarly, only a

single report has been made that utilizes MCD as a probe of

V(III).²²

Herein, we present our investigation of the ground- and

excited-state electronic properties of vanadium in the V(IV)

and V(III) oxidation states. More speciﬁcally, we investigate the

optical and magnetic properties of V(IV) and V(III) in a series

of coordination environments, as shown in Figure 1. The V(IV)

complexes all employ acetyl acetonate (acac⁻) as an equatorial

ligand, with this series consisting of VO(acac)₂(1), VO-

(acac)₂nPrCN (2), VO(acac)₂Py (3), and VCl₂(acac)₂(4).

These particular complexes were selected to represent both

vanadyl (1−3) and “bare”, also known as nonoxo (4),

vanadium species in 5- and 6-coordinate environments. Since

1. INTRODUCTION

Vanadium (V) is an abundant and widely distributed element

that plays a critical role in both biology and modern catalysis,^1,2

where its ability to access a variety of oxidation states lends

itself to applications requiring either oxidizing or reducing

behavior. Industrially, the oxidative capabilities of V₂O₅are

exploited in several critical processes, including the synthesis of

sulfuric acid, maleic and phthalic anhydride,³⁻⁵and the

decomposition of the NO_xspecies responsible for acid rain.⁶

Additionally, great interest has arisen in recent decades toward

the use of vanadium oxide catalysts for the selective oxidative−

dehydrogenation of short alkanes.⁷⁻¹⁵Biologically, vanadium is

found in marine-haloperoxidases,¹⁶amavadin,¹⁷vanadium

nitrogenase,^18,19and other organisms spanning a range of

oxidation states from V(III) to V(V).^20,21In many of these

systems, the active vanadium species still remains controversial.

Therefore, developing ways to understand the electronic and

geometric structures of vanadium in such environments

remains critical to the development and improvement of

these applications.

Despite the intensive eﬀorts present in the literature to

understand vanadium ions in their many facets, the number of

studies set forth to understand the spectroscopic and magnetic

properties of molecular vanadium complexes has remained

Received: February 22, 2018

A

DOI: 10.1021/acs.inorgchem.8b00486

Inorg. Chem. XXXX, XXX, XXX−XXX

Inorganic Chemistry

Article

Since D may be either positive or negative, values on both sides were

explored. The value of E was constrained such that |E| < |D/3|. An

averaged, isotropic g tensor (g_av) was employed in all modeling, in

(g_i)²

3

which

g_av

=

∑

. Values for E, D, and g were optimized by a

least-squares minimization using data from all ﬁelds and temperatures

simultaneously.

2.3. EPR Measurements. EPR measurements were recorded at

temperatures of 30 K for complexes 1−3 using continuous-wave (cw)

X-band EPR spectra recorded on a Bruker E500 ELEXSYS

spectrometer equipped with

a Bruker dual-mode cavity

Figure 1. Vanadium complexes under investigation.

(ER4116DM) and an Oxford Instruments helium-ﬂow cryostat

(ESR 900). A high-sensitivity Bruker Super-X (ER-049X) bridge

with an integrated microwave-frequency counter was employed as the

microwave unit. A magnetic ﬁeld controller (ER032T) was externally

calibrated with a Bruker NMR ﬁeld probe (ER035M). cw Q-band EPR

measurements performed on complex 4 utilized a Bruker ESP-300E

spectrometer with a Bruker Q-band cavity (ER5106QT) with a Bruker

ﬂexline support and an Oxford Instruments helium-ﬂow cryostat

(CF935). Microwave frequencies were calibrated using a Hewlett-

Packard frequency counter (HP5352B), and the ﬁeld control was

calibrated using a Bruker NMR ﬁeld probe (ER035M). Spectra were

recorded on frozen solutions of complexes 1−3, where 1 was dissolved

in dichloromethane (DCM), 2 in nPrCN, and 3 in pyridine (Py).

Spectra of 4 were recorded on a solid powder at 30 and 50 K in the X-

band and Q-band experiments, respectively. X-band measurements

utilized a 0.2 mW microwave power and 0.75 mT and 100 kHz

modulation, while 0.1 mW microwave power and 0.01 mT modulation

were used in Q-band measurements. Spectra were analyzed in both the

local software package esim_gfit (available from E.B.) and the software

package EasySpin (version 5.1.9), as implemented in Matlab.³⁰

2.4. Optical and MCD Measurements. All presented optical

measurements of all compounds, with the exception of 2, were

prepared as ﬁnely dispersed powders embedded in KBr. Because the

coordination of nPrCN in VO(acac)₂nPrCN is not strong enough to

form an isolable complex,²⁷the presented samples for optical and EPR

samples of 2 were made in a glassed nPrCN solution at concentrations

of 2 and 1 mM, respectively. All samples, with the exception of 2, were

prepared in a strictly anaerobic, moisture-free glovebox. Electronic

absorption and VTVH-MCD measurements were recorded using an

OLIS DSM17 UV−vis/NIR CD spectropolarimeter in conjunction

with an Oxford Instruments Spectromag SM4000 magnetocryostat

over ranges of 2−80 K and ﬁelds of 1−7 T. Additional UV−vis/NIR

absorption measurements were performed using a Cary 6000i UV−

vis/NIR spectrophotometer in conjuction with an Oxford Instruments

Optistat-DN cryostat at temperatures of 80 K. All low-temperature

measurements were performed on samples prepared in MCD cells

using either 0.1 or 0.3 mM quartz windows. MCD and electronic

absorption data were analyzed using local software (developed by E.B.

V(III) is most commonly found in an octahedral environment,

the V(acac)₃(5), VCl₃(thf)₃(6), and VCl₃ttcn (7) complexes

were selected to provide both a variety of octahedral distortions

and ligand-ﬁeld environments. Magnetic susceptibility, electron

paramagnetic resonance (EPR), and variable-temperature

variable-ﬁeld magnetic circular dichroism (VTVH-MCD)

techniques are used to investigate the ground-state electronic

properties of the outlined complexes, while absorption [UV−

vis/near-IR (NIR)] and MCD spectroscopies are used to probe

excited electronic states. To provide further insight into the

electronic structures of these complexes, high-level ab initio

theory has been employed in the form of the complete-active-

space self-consistent-ﬁeld method in conjunction with N-

electron valence perturbation theory (CASSCF/NEVPT2).

2. METHODS

2.1. Complexes and Models. Compound 1 was purchased from

Sigma-Aldrich and used to generate complex 2 in the presence of

butyronitrile (nPrCN). Complexes 3−7 were synthesized according to

literature methods.²⁴⁻²⁹Further details regarding the synthesis and

crystallographic data of complexes 1 and 2 are provided in the

Supporting Information. Renderings of the available crystal structures

of these complexes are provided in Figure D1.

2.2. Magnetic Measurements. Bulk magnetization measure-

ments were performed for the V(III) complexes using a Quantum

Design MPMS-7 SQUID magnetometer, calibrated with a standard

palladium reference sample (error < 2%). All samples consisted of

randomly oriented microcrystals, with total masses of 18.1 mg for 5,

25.4 mg for 6, and 30.40 mg for 7, which were placed in anaerobic

quartz-glass holders for measurement. Minute amounts of eicosane

(melting point of 310 K) were used to prevent torqueing of the

material under large applied magnetic ﬁelds. The temperature

dependence of the magnetic susceptibility was measured from 2 to

290 K at a magnetic ﬁeld of 0.1 T. Magnetization versus ﬁeld

measurements were performed at multiple temperatures at magnetic

ﬁelds of 1, 4, and 7 T over a range of 2−260 K. Blank measurements of

the quartz-glass holder were performed for background subtraction.

Desired magnetization data were acquired by ﬁtting amplitudes from

the appropriately corrected SQUID response curves. Values for the

sample magnetization were divided by the number of moles and

converted to units of molar susceptibility using the deﬁnition χ =

μ_BM/B. Values of χ were then corrected for any temperature-

independent paramagnetism or underlying diamagnetism by the use of

tabulated Pascal’s constants. The temperature-dependent magnetic

susceptibility and ﬁeld-dependent magnetization data were handled

and simulated using the julX and julX_2S software packages, which

employ the spin Hamiltonian described by eq 1 to calculate true

powder averages in three dimensions, assuming the presence of an

isolated spin ground state and collinear D and g matrixes, where the g

matrix may be isotropic, axial, or rhombic.

at the MPI-KOFO, Mulheim an der Ruhr, Germany). MCD spectra

̈

were ﬁt simultaneously by a number of Gaussians as a function of the

temperature and ﬁeld dependence in conjunction with their

corresponding 80 K UV−vis/NIR spectrum. Spectra were analyzed

using the global ﬁtting procedure in the program BF, with a bandwidth

restriction whereby the largest bandwidth was not allowed to vary

higher than ∼2 times the smallest bandwidth measured for a given

compound; exceptions to this approach are noted where applicable.

To probe the magnetic and polarization properties of the observed

C terms, VTVH-MCD measurements were performed by measuring

the MCD intensity at a ﬁxed wavelength for varying ﬁelds at multiple

temperatures. The resulting isotherms of the MCD intensity are

present as a function of μ_BB/2kT, where μ_Bis the Bohr magneton, B is

the strength of the applied magnetic ﬁeld, k is the Boltzmann constant,

and T is the temperature (K). It has been shown that the saturation

1

behavior of systems with S > /₂depends on a combination of the

spin-Hamiltonian parameters and transition polarizations, allowing

insight into the properties of both the ground and excited states.³¹

Using the equation for the orthorhombic approximation,

2

H = D[S_z− S(S + 1)/3 + (E/D)(S_x− S_y²)] + μ ·B·g·S

B

(1)

B

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Inorganic Chemistry

Article

π

2π

spin-Hamiltonian parameters. In order to accurately model the ligand-

ﬁeld structure of the V(III) and V(IV) complexes, active spaces were

chosen to encompass the dominate bonding/antibonding orbitals

formed between vanadium and the surrounding ligand. A total size of

(9,9) was used for complexes 1−4 with a minimum of 5 doublet roots

to describe the ligand-ﬁeld excited states. Active spaces of (12,10)

along with 10 triplet roots and 15 singlet roots were selected for the

V(III) series 5−7. Additionally, minimal active spaces of (2,5) and

(1,5) were calculated for all V(III) and V(IV) complexes, respectively,

to investigate the signiﬁcance of including of bonding orbitals in these

calculations. AILFT analysis^52,53was requested by canonicalizing the

active orbitals in a speciﬁc manner (keyword actorbs = dorbs in

ORCA).

Δε

γ

eff

=

∑ N(l_x⟨S_x⟩_iM + l_y⟨S_y⟩_iM

_4πS∫ ∫

i

yz

xz

E

0

i

+ l_z⟨S_z⟩_iM_x^e_y^ff) sin θ dθ dϕr

(2)

as implemented in the local program mcd3D_2S (available from E.B.),

global ﬁttings of the recorded VTVH magnetization curves were

simulated. In this equation, Δε/E is the MCD intensity, γ represents a

collection of constants, S is the total spin of the ground state, N_iis the

Boltzmann population of the ith magnetic sublevel of the electronic

ground state, l_x,y,zare the directional cosines of the spin Hamiltonian,

and ⟨S_x,y,z⟩_iare the expectation values of the x, y, and z components of

the spin operator S over the ith magnetic eigenstate, respectively. For

complexes 5 and 6, VTVH-MCD curves were ﬁt using several sets of

spin-Hamiltonian parameters, including those determined in the

present study by magnetic susceptibility measurements and those

previously reported from high-ﬁeld EPR (HFEPR) studies by Krzystek

and co-workers.²²Similarly, the VTVH-MCD curves of 7 were ﬁt in

several sets using the spin-Hamiltonian parameters, as determined by

magnetic susceptibility (presented here) and previous HFEPR

2.6. Ligand-Field Analysis. The program AOMX was utilized for

the analysis of all data in terms of ligand-ﬁeld parameters.⁵⁴AOMX

calculates the dⁿelectron terms in the framework of either the crystal

ﬁeld or angular overlap model (AOM).

The ability to fully determine the ligand-ﬁeld parameters of a given

complex experimentally is highly dependent on the number of

available observable electronic transitions and choice of their

assignment. In practice, one is typically limited to a low-energy subset

of spin-allowed ligand-ﬁeld transitions, such that the problem usually

requires more parameters than can be determined by the available

information. Meanwhile, calculations are capable of providing all

ligand-ﬁeld states of interest. The discrepancy in the available

information has often led to considerable disagreement between the

calculated and experimentally determined parameters. In particular, a

lower number of experimental points require a greater number of

assumptions to be made in the applied interpretive model. Therefore,

ligand-ﬁeld parameters determined from CASSCF/NEVPT2 calcu-

measurements.²²The polarization factors M (v, w = x, y, z) are

eﬀective transition dipole moments, which are independently

determined for each transition. Using these, the individual polarization

of a given MCD band may be calculated using the relationship

eff

vw

eff eff

2

(M M_xz

)

xy

% x = 100 ×

(M M_x^e_z^ff)²+ (M M_y^e_z^ff)²+ (M M_yz

)

eff

xy

eff

xy

eff eff 2

xz

(3)

for the percentage of x polarization and the complementing

permutations for the corresponding percentage y and z components.

2.5. Computational Details. All calculations were performed

using the quantum computing suite ORCA 4.0.³²Because the recorded

spectra were performed on solid complexes, it was natural to utilize the

originally reported crystal structures, with optimization steps only

being performed for hydrogen atoms. Geometry optimizations of

hydrogen atoms were performed at the level of density functional

theory with the pure exchange correlation functional BP86, which

utilizes Becke’s 1988 exchange functional along with the gradient

corrections of Perdew as well as Perdew’s 1981 local correlation

functional,^33,34in conjunction with the second-deﬁnition triple-ζ

valence-polarized (def2-TZVP) basis of Alrich and co-workers and the

complementing def2/J auxiliary basis set.^35,36

Scheme 1. Descriptive Angles of (a) V(IV) Complexes, (b

a

and c) V(acac)₃, and (d and e) VCl₃ttcn

The initial structures for complexes 3−7 were obtained from the

reported crystallographic structures.^29,37−40Because of the lack of an

axially unperturbed crystal structure of 1, the inﬂuence of proximal

ligation to 1 was investigated through the generation of a clear series of

models based on the VO(acac)₂Py crystal structure 3. To this end,

four models were generated that involve the presence/absence of the

Py ligand and its trans eﬀect on the VO bond. These model

structures include (a) VO(acac)₂(1a), generated by the simple

removal of Py from the VO(acac)₂Py structure, with no further

structural modiﬁcations, (b) VO(acac)₂(1b) again generated by the

removal of Py from VO(acac)₂Py, but with the VO bond length

shortened from 1.573 to 1.543 Å and no further optimization steps,

(c) VO(acac)₂Py (3a), and (d) VO(acac)₂Py (3b), with the VO

bond length shortened from 1.573 to 1.543 Å (3b). The combination

of these four models allows us to look individually at the inﬂuences of

the Py coordination and VO bond length on the ligand-ﬁeld

manifold of these complexes.

Calculations of the ground- and excited-state properties, including

MCD, were performed using the complete-active-space self-consistent-

ﬁeld method with consideration of spin−orbit coupling (SOC-

CASSCF)^41,42in conjunction with N-electron valence perturbation

theory to second order (NEVPT2)^43,44in order to recover missing

dynamic electron correlation. These calculations were performed using

the triple-ζ atomic natural orbital basis ano-pVTZ⁴⁵along with the

AutoAux basis⁴⁶option of ORCA, in conjuction with second-order

Douglas−Kroll−Hess (DKH2) to account for scalar relativistic eﬀects.

SOC was treated through the mean-ﬁeld (SOMF) approximation,^47,48

and the eﬀective Hamiltonian approach⁴⁹⁻⁵¹was used to compute the

a

In parts b and c, θ is deﬁned as the angle between the unique C₃axis,

the central V, and the coordinating ligand atom. In part b, α is deﬁned

by the chelating ligand bite angle, while in part c, it is used to describe

the angle between ligands that lie in-plane orthogonal to the unique C₃

axis. The projection “X”, which lies in-plane with the C₃axis and a

coordinating ligand, is needed to help describe ψ and ϕ. Here, ϕ

describes the twist angle between the projection X and a component

ligand in the C₃orthogonal plane, while ψ describes the dihedral angle

V−L−X−(L + 1) (for example, in part b, V−O1−X−O2).

C

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Inorganic Chemistry

Article

Scheme 2. (a) Orbital Overlap Scheme of V(IV) with O²⁻

and acac⁻Ligands To Form the VO(acac)₂Complex with

(b) Corresponding Orbitals

lated excited states were derived by using both (a) all calculated ligand-

ﬁeld states and (b) an “abbreviated” number of excited states to match

those assigned experimentally.

a

3. GEOMETRIC STRUCTURE

Embedding V(IV) in an equatorial bis(acac⁻) environment

generates a pseudo-C_4v-symmetric complex (within the ﬁrst

coordination sphere), as depicted in Scheme 1a. At present, we

deﬁne the primary z axis to run along the V−X bond, with the

xz plane bisecting the two acac⁻ligands and the yz plane

bisecting between the acac⁻ligands. In complex 3, for which

the crystal structure is known, the vanadium sits above the

equatorial plane (∠X−V−O = 100°) such that the internal bite

angle (α_int) of the acac⁻ligands is ∼89° and that between either

acac⁻(α_ext) is ∼87°. Meanwhile in complex 4, vanadium

actually sits within the equatorial plane (average ∠X−V−O =

90°), leading to an internal bite angle of 86.6° and an external

bite angle of 93.4°. Therefore, while ligation of acac⁻implies

that these complexes are strictly either C_2v(1−3) or D_2h(4)

symmetric in geometry, the relatively small diﬀerences between

α_intand α_extimply that these systems may behave as minor

distortions from their respective higher-order counterparts, C_4v

and D_4h.

Of the V(III) complexes, the trigonal distortion of tris-

bidentate complexes such as 5 may be described in terms of the

polar angle θ, twist angle ϕ, bite angle α, and dihedral angle ψ

(Scheme 1b). In perfect octahedral symmetry, θ = 54.74°, ϕ =

60°, α = 90°, and ψ = 60°. In 5, these angles average to θ =

54.4°, ϕ = 60°, α = 88°, and ψ = 43.5°. The signiﬁcant decrease

in ψ implies a considerable trigonal expansion in this complex.

Meanwhile, while 7 is also trigonally distorted, the meridonal

faces of the complex along the C₃axis are no longer equal

(Scheme 1c). This requires individual parameters for the polar

angle θ and the angle α for each face. We ﬁnd here that θ_Cl

=

63.0°, θ_S= 49.5°, ϕ = 60°, α_Cl= 101°, α_S= 82°, and ψ = 61.0°.

The combination of θ_Cl> 60° and α_Cl> 90° implies

compression along the Cl2−Cl4−Cl6 face, while θ_S< 60°

and α_S< 90° show elongation along the S1−S3−S5 face.

Complex 6 can be described more simply in terms of several

polar angles θ and dihedral angles ψ to describe the out-of-

plane twists of the tetrahydrofuran (thf) ligands. The highest-

order axis, which C₂, is oriented along the near-linear Cl−V−thf

coordinate, giving θ_Cl= 92.5° and θ_thf= 93.4°. Two dihedral

angles are needed to describe each the equatorial and axial thf

ligands. The parameter ψ_eqdescribes deviations from the

equatorial plane, while ψ_axdescribes deviations from an axial

plane containing the C₂axis and all three Cl ligands. With these

deﬁnitions, ψ_eq= 34.6° and ψ_ax= 43.3°.

a

Orbitals were generated using an isosurface value of 0.05.

prevailing.⁵⁵This consists of a single unpaired electron of

V(IV) predominately occupying the 3d_xyorbital and the 3d_z

2

and 3d_xz,yzorbitals undergoing several strong interactions with

the terminal oxo to form a highly covalent bond. While the

ligation of acac⁻implies that these complexes are strictly either

C_2v(1−3) or D_2h(4) symmetric, the axial distortion is usually

considered to be the primary perturber, while the equatorial

distortion is only a minor perturbation. Upon axial compression

or elongation, the orbitals that are able to interact along the z

axis will either increase or decrease in energy, respectively.

Therefore, axial compression results in an approximate ordering

4. ELECTRONIC STRUCTURE

2

of 3d_xy< 3d_xz,yz< 3d_{x −y}< 3d_z, in which the relative ordering

of 3d_xz,yzand 3d_{x −y}depends upon the degree of compression.

Similarly, axial elongation is anticipated to result in a 3d_xz,yz

Under the C_4vaxially compressed distortion, the d manifold of

2

V(IV) is split such that b₂(d_xy) < e(d_xz,d_yz) < b₁(d_{x −y}) <

2

<

a₁(d_z). The ligand ﬁelds of vanadyl complexes have classically

2

3d_xy< 3d_z< 3d_{x −y}ordering. In turn, the D free-ion state of a

been interpreted by the model developed by Ballhausen and

Gray for VO(H₂O)₅²⁺; here, the b₂orbital is noninteracting

with the surrounding ligand ﬁeld, while the e, b₁, and a₁orbitals

overlap with the oxo-π, equatorial H₂O-σ, and oxo-σ orbitals,

respectively.⁵⁵In the present case, the equatorial σ interaction

arises from the acac⁻ligand, as summarized in Scheme 2.

The electronic structure of the VO²⁺center embedded within

5- and 6-coordinate complexes is a topic with considerable

history.^6,56−64Although heavily debated in the 1960s, the most

popular model proposed by Ballhausen and Gray in 1961 is still

d¹system, which is split into the T_2gground state and E_g

excited state in the presence of an O_hﬁeld, will be further split

in C_4vunder an axial compression to ²B₂< ²E < ²B₁₂< ²A₁, while

2

axial elongation in D_4hresults in E_g< B_2g< A_1g< B_1g

(Figure D2).

3

V(III) presents a d²system (S = 1), in which the F and P

3

free-ion states are split to form a T₁(F) ground state and

³T₂(F), T₁(P), and A₂(P) excited states in an octahedral

3

environment. The addition of trigonal distortion (as in

D

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complexes 5 and 7) lowers the eﬀective symmetry to D₃/C_3v,

further splitting the triplet states from ³T₁→ ³A₂, ³E and ³T₂→

Table 1. Spin-Hamiltonian Parameters of V(III) Complexes

5−7 As Simulated for the Present Magnetic Susceptibility/

a

3

³A₁, E (described in Figure D3). For even larger distortions,

Molar Magnetization and VTVH-MCD Measurements

such as in the meridonal complex 6 with C₂symmetry, all

degeneracy is lost.

compound

method

magn.

g_⊥

g_∥

1.75

D (cm⁻¹

)

E/D

5

1.75

6.9

7.1

0.132

0.14

VTVH-

MCD

1.75

SOC-C/N

1.73, 1.75

1.94

9.6

0.06

b

HFEPR

1.833(4),

1.72(2)

2.03(2)

7.470(1)

0.256

b

magn.

1.7

7.4

0.324

0.33

6

magn.

1.7

10−14

10

VTVH-

MCD

1.85

SOC-C/N

1.59, 1.69

1.95

16.2

0.18

0.33

0.16

b

HFEPR

11.85

11−15

−10

b

magn.

1.7

1.8

1.7

1.8

VTVH-

MCD

b

7

magn.

1.77

1.8

1.77

1.8

6.1

0−0.1

0.0

VTVH-

MCD

SOC-C/N

1.73, 1.75

1.93

9.5

0.06

a

Additionally, the SOC-CASSCF(12,10)/NEVPT2 (abbreviated as

b

SOC-C/N)-calculated parameters are provided. Literature values

previously determined by HFEPR and magnetization simulations are

also included.²²

magnetic susceptibility data favor |D| = 14−15 cm⁻¹, while

simulations of the magnetization data favor |D| = 10 cm⁻¹.

5.2. EPR Measurements. 5.2.1. X-Band EPR Spectroscopy

of the VO(acac)₂Series. The X-band EPR spectra of complexes

1−3 measured on frozen solutions in DCM, nPrCN, and Py,

respectively, display the typical eight-line pattern of vanadium,

which has a nuclear spin of I = ⁷/₂(natural abundance of ⁵¹V =

99.8%).⁶⁷A high degree of agreement between the simulation

and experiment is found for all spectra, which are presented in

Figure 3 along with corresponding simulated parameters of the

S = ¹/₂spin Hamiltonian in Table 2. The resulting simulations

imply a small degree of orthorhombicity in the Zeeman

splitting and hyperﬁne interaction tensors g and A. All ﬁt g

tensors appear relatively close to that of the free electron,

implying well-isolated ground states in all three complexes.

The directionally dependent g tensor may be approximated

using the rotational relationships of the real d orbitals and the

equation

Figure 2. Temperature and ﬁeld dependence of the molar magnet-

ization and magnetic susceptibilities (insets) of complexes 5−7. Solid

lines represent the S = 1 simulated spin Hamiltonians. Multiﬁeld

measurements of the molar magnetization were performed at 7 T

(blue), 3 T (green), and 1 T (red). Magnetic susceptibilities were

measured at 0.1 T.

5. RESULTS AND ANALYSIS

5.1. Magnetic Susceptibility Measurements. Variable-

temperature variable-ﬁeld direct-current SQUID measurements

were performed for complexes 5−7 in order to determine their

magnetic ground-state characteristics. The ﬁt eﬀective magnetic

moment and magnetization curves are presented in Figure 2.

The χT values for all three V(III) complexes decrease

drastically below 50 K, indicating the presence of zero-ﬁeld-

splitting (ZFS) eﬀects.⁶⁵Susceptibility and magnetization data

were ﬁt simultaneously, and the resulting spin-Hamiltonian

parameters are presented in Table 1 along with literature values

for reference.

For 5, reasonable ﬁts were achieved with positive values of D

ranging from 6.9 to 8 cm⁻¹and g_av= 1.75. These values are in

good agreement with those reported previously by both

Krzystek et al.²²and Gregson et al.⁶⁶Similarly, reasonable ﬁts

of 7 were only achievable using positive D with a value of 6.1

cm⁻¹. Notably, values of E/D for 7 were quite ﬂexible with little

perturbation to the ﬁt across a range of 0−0.1; however, values

closer to zero were still favored. Simulations of 6 proved to be

somewhat more diﬃcult; using g_av= 1.7 and E/D = 0.33,

⎛

e

⎞

⎟

⎠

n_iζ

2SΔ

g = g 1 +

⎜

i

⎝

(4)

i

where S is the total spin, g_eis the g value of the free electron,

and n_x= (id_xz)², n_y= (−id_yz)², and n_z= (−2id_{x −y}) . Therefore,

g_x= g_e− ζ/SΔ_x, g_y= g_e− ζ/SΔ_y, and g_x= g_e− 4ζ/SΔ_z. Because

the one-electron SOC constant is necessarily positive, this

equation predicts that all principle g values will be smaller than

that of the free electron and that Δ_x,y,zcorresponds to the

2

energy diﬀerences between the 3d_xyand 3d_xz, 3d_yz, and 3d_{x −y}

,

orbitals, respectively. From eq 4, it is also notable that, as Δ_x,y,z

increases, g_iapproaches g_e, implying an increase in electronic

isolation of the ground state.

Despite clear visual diﬀerences in the spectra, only minute

variations in the simulated g-tensor values are found. We have

assigned the spectral features such that g_z< g_y< g_x; upon

moving from 1 to 3, g_xdecreases slightly while g_yincreases,

E

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Table 2. Summary of Spin-Hamiltonian Parameters of 1−4

compound/model

solvent

g_x

g_y

g_z

A_x

A_y

A_z

1

2

3

4

DCM

nPrCN

Py

1.983

1.982

1.984

1.975

1.977

1.981

1.943

1.950

1.949

1.947

1.807

166.6

164.0

171.2

175.8

184.6

184.8

497.9

505.6

500.4

solid

1a

1b

3a

3b

4

1.975

1.976

1.978

1.928

1.976

1.977

1.974

1.979

1.843

1.933

1.931

1.932

1.736

Figure 4. Gaussian-deconvoluted MCD spectra of (a) powder 1 in

KBr, (b) 2 (1 mM) in nPrCN, (c) powder 3 in KBr, and (d) powder 4

in KBr. The presented spectra were obtained at 2 K and 5 T. The

presented band deconvolutions were acquired through the simulta-

neous ﬁtting of temperature- and ﬁeld-dependent series in which the

peak positions and bandwidths were ﬁxed, allowing only the intensities

to vary between measurements; this includes the ﬁtting of measure-

ments at 2, 5, 10, 20, and 40 K for a ﬁeld of 5 T and ﬁelds of 3, 5, and

7 T at a temperature of 5 K.

supports the presence of a low-lying ligand-ﬁeld excited state at

∼1000 cm¹, according to eq 4.

Figure 3. (a) Frozen-solution X-band EPR (solid) and simulated (red

dot) spectra of 1 in DCM, 2 in nPrCN, and 3 in Py. Spectra were

acquired at 30 K and 9.63 GHz using a power of 0.2 mW and a 7.46 G

modulation amplitude. All samples were prepared at a 1 mM

concentration. (b) Powder Q-band EPR (solid line) and simulated

(red dot line) spectra of complex 4 acquired at 40 K and 34.08 GHz

using a power of 0.01 mW and a 0.97 G modulation amplitude.

5.3. Optical and MCD Measurements. 5.3.1. V(IV)

Complexes. The deconvoluted MCD spectra of complexes

1−4 are presented in Figure 4, with the corresponding ﬁt

components presented in Table 3 and the absorption spectrum

in Figure D4. Interpretation of the spectra was achieved

through the application of a quantitative Gaussian deconvolu-

tion of both temperature- and ﬁeld-dependent series for each

complex using a minimum set of bands, which were ﬁxed in

energy and bandwidth for all ﬁelds and temperatures, with only

the intensity allowed to vary. In particular, a set of 4 bands were

used for complexes 1 and 3, 6 for complex 2, and 12 for

complex 4.

becoming nearly equivalent in complex 3. These changes result

from the coordination of an axial ligand to the VO²⁺core in

complexes 2 and 3, which results in a more axially symmetric

coordination environment.

5.2.2. Q-Band EPR Spectroscopy of 4. Powder X-band

5.3.1.1. VO²⁺Complexes (1−3). The lower-energy spectral

region of complexes 1−3 (Figure 4) shows three distinct

features between 5000 and 20000 cm⁻¹, beginning with a small

negative dip at lower energy, followed by a more intense

positive band to form a quasi-derivative shape. This is followed

by a second positive feature that appears between 17000 and

1

measurements of 4 resulted in a relatively broad, axial S = /₂

signal. To better resolve this spectrum, powder Q-band EPR

measurements of 4 were performed, as provided in Figure 3b,

with the corresponding simulated spin-Hamiltonian parameters

in Table 2. Complex 4 presents a distorted axial spectrum that

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spectrum of 4, is provided in Figure D6. The low-energy

portion of the spectrum from 13000 to 17000 cm⁻¹shows a

weak positive MCD signal while exhibiting an intense (ε =

∼6000 M⁻¹cm⁻¹) feature in the absorption spectrum. This is

followed by several distinguishable features at 18060 and 19400

cm⁻¹(bands 3 and 4), which exhibit reasonable intensity in

both the absorption and MCD spectra. These are, in turn,

followed by a negative pseudo-A term centered at 21100 cm⁻¹,

which is formed by bands 5 and 6. Next, a broad feature

centered at 24600 cm⁻¹in the absorption spectrum correlates

with a positive pseudo-A term from the overlap of bands 7 and

8. Several additional features appear at higher energies (bands

9−12), although these appear fairly weak in the MCD relative

to the absorption spectra.

5.3.2. V(III) Complexes. To date, only the diﬀuse-reﬂectance

electronic absorption spectrum of 7 has been reported,²⁴and

discrepancies in the literature on the assignments and analysis

of electronic absorption and MCD spectra of 5 and 6 merit

additional investigations.^22,68,69These data are also particularly

critical to formulating objective comparisons with theory, which

will be presented later. The band-ﬁt MCD spectra of complexes

5−7 are presented in Figure 5. Deconvolutions of these spectra

were performed in a manner identical with those described

above for compounds 1−4, in which a minimum number of

bands with consistent energies and bandwidths were optimized

for all temperatures and ﬁelds measured, allowing only the

Table 3. Summary of Experimentally Deconvoluted MCD

Bands of Complexes 1−4

energy/sign

band

1

2

3

4

1

12500

−

+

10550

−

+

9850

−

+

14150

+

2

13730

17030

23390

12390

17580

23800

25000

28550

12150

17520

23760

16070

18060

19400

20650

21810

23860

25600

26510

28920

30600

32360

+

3

+

−

+

4

−

5

6

−

+

7

8

9

+

10

11

12

−

+

−

Table 4. Summary of Experimentally Deconvoluted MCD

Bands of Complexes 5−7.

energy/sign

band

5

6

7

1

2

3

4

5

6

7

8

9

18090

19380

21570

25050

26540

28390

30650

32760

−

+

z

13400

18980

20340

24170

29690

32600

35860

−

+

z

12910

18446

21510

25050

26850

28180

30150

31840

33290

+

−

+

−

+

x

z

+

y, z

+

−

+

z

y

−

17600 cm⁻¹for all three complexes. All bands exhibit strong

temperature dependence (Figure D5), indicating that these

signals arise through a C-term mechanism. In all three

complexes, a somewhat poorly resolved vibrational progression

is present in both the ﬁrst and second bands, both of which

may be ﬁt with the same frequency. A frequency of 695 cm⁻¹

was used in the case of 1 and 680 cm⁻¹for 2 and 3. On this

basis, it is likely that these features compose a pseudo-A-term

signal, which arises from the overlap of two related C terms.

Several additional features arise at energies above 20000 cm⁻¹

in all three complexes. For 1, a broad negative band around

approximately 23400 cm⁻¹is seen. In 2, the energy range is

somewhat better resolved, and several additional positive

features appear at 23800 and 25000 cm⁻¹. Last, an additional

positive feature may be resolved in 3 at 23760 cm⁻¹.

Unfortunately, because of low intensity and signiﬁcant issues

in achieving reasonable S/N ratios, the energy ranges of the

MCD spectra for complexes 1−3 remain relatively limited,

particularly for the solid-state spectra acquired for complexes 1

and 3.

5.3.1.2. Compound 4. In the nonoxo “bare” V(IV) complex

4, the spectrum appears drastically diﬀerent from those of

complexes 1−3 (Figure 4). All bands exhibit direct temperature

and ﬁeld dependence and are therefore assigned as features

arising through a C-term mechanism. Both the UV−vis

absorption and MCD spectra are highly featured, allowing a

reasonable correlation between the two to be made and making

it possible to postulate which bands of the MCD form pseudo-

A terms and which arise as independent C terms. This more

detailed deconvolution, in conjunction with the absorption

Figure 5. Band-deconvoluted 5 K and 5 T MCD spectra of (top) 5,

(middle) 6, and (bottom) 7. All spectra were obtained as ﬁnely ground

powders pressed in KBr.

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intensity to vary. A summary of ﬁt bands for complexes 5−7 is

provided in Table 4 and the temperature-dependent series in

Figure D7. Additionally, the UV−vis absorption spectra are

provided in Figure D8.

temperatures, it forms its own distinguishable maximum

(Figure D7). The intense, narrower negative feature at 32560

cm⁻¹, in turn, overlaps with a strong positive feature ﬁt by a

band centered at 35860 cm⁻¹to form a second pseudo-A term

with an isosbestic point at 34000 cm⁻¹.

5.3.2.1. Compound 5. Complex 5 presents a rich MCD

spectrum containing both relatively weak and intense features

(Figure 5), all of which exhibit strong temperature and ﬁeld

dependencies and therefore likely arise through a C-term

mechanism. The spectrum is dominated by a large positive

feature around 28000 cm⁻¹and its lower-energy shoulder,

which together may be ﬁt by three bands centered at 25050,

26540, and 28390 cm⁻¹. These are followed by several negative

features centered at 30650 and 32760 cm⁻¹. Lower in energy,

two weak negative features centered around 18500 and 21500

cm⁻¹arise. The unusual broadness of the ﬁrst feature at 18500

cm⁻¹requires two Gaussian bands centered at 18090 and

19380 cm⁻¹for an adequate ﬁt to be obtained, while the second

may be simulated with a single Gaussian centered at 21570

cm⁻¹. The slight positive signal seen around 16000 cm⁻¹does

not exhibit any signiﬁcant temperature or ﬁeld dependence and

likely arises from background scattering.

Optical measurements of 5 have been reported by several

groups, most recently by Krzystek and co-workers, who

presented the temperature-dependent MCD spectrum up to

32000 cm⁻¹.²²However, the spectra presented in their work

was performed using a mulled sample with an unknown ratio of

the α- and β- crystalline forms, while the present study utilizes

the pure α form. Diﬀerences between the present spectrum and

that of Krzystek and co-workers are discussed in greater detail

in the Supporting Information. Generally, trivalent M^III(acac)₃

complexes commonly exhibit solvent- and temperature-depend-

ent crystalline polymorphism, which can lead to discrepant

results between several groups or even between several

preparations of the same compound.^70,71

5.3.2.2. Compound 6. Similar to 5, optical measurements of

6 have also been reported by Krzystek and co-workers, who

have presented the temperature-dependent MCD spectrum up

to 26000 cm⁻¹.²²The spectrum presented in Figure 5 resolves

the MCD of 6 from 5000 to 40000 cm⁻¹. All features across the

spectrum exhibit a strong temperature dependence and thus

must arise through a C-term mechanism. Similar to the

previously reported spectrum, a low, sloping baseline of

increasing intensity is present across the low-energy range of

the spectrum. This baseline is ﬁrst interrupted by a negative

feature centered at 13400 cm⁻¹; while a very small increase

above the baseline is seen around 12000 cm⁻¹, this cannot be ﬁt

objectively as a unique feature without additional experimental

corroboration. This is again followed by a mild, sloping increase

in the intensity, leading to two positive features centered at

18980 and 20340 cm⁻¹. The remaining spectrum is composed

of a series of four very broad features. Three of these are so

broad that the standard ﬁtting procedure applied thus far, in

which a maximum bandwidth is restricted to no greater than

∼2 times the minimum bandwidth, would require the use of

numerous bands. However, applying such an approach to these

features would supply no additional useful information because

they do not contain any clear additional inﬂection points. The

ﬁrst broad, positive feature is centered at 23900 cm⁻¹, which

overlaps with a second, intense negative band centered at

∼29700 cm⁻¹to form a negative pseudo-A term with an

isosbestic point at 25840 cm⁻¹. At lower temperatures, the

negative component appears as a shoulder to a sharper, even

more intense band centered at 32560 cm⁻¹, while at higher

5.3.2.3. Compound 7. While the major absorption features

of 7 via diﬀuse reﬂectance were originally reported by Davies et

al.,²⁴the absorption spectrum of this compound is absent in the

literature. The UV−vis/NIR spectrum (Figure D8) presents a

weak, broad absorption peak centered at 12900 cm⁻¹, followed

by a larger and somewhat sharper feature at 18500 cm⁻¹. The

last easily discernible peak appears at 27250 cm⁻¹before rising

into a more intense series of high-energy features starting at

37000 cm⁻¹. In the MCD (Figure 5), the feature at 12900 cm⁻¹

may be adequately ﬁt using either a single, broader Gaussian

band or two smaller Gaussian bands centered at 12500 and

13250 cm⁻¹. Similar to 6, 7 shows a continuous positive sloping

background across the entire low-energy range of the spectrum;

this has also been seen for VBr₃(thf)₃.²²Next, the large positive

peak centered at 18400 cm⁻¹is easily ﬁt using a single Gaussian

band. This is followed by several negative peaks centered at

21510 and 25050 cm⁻¹. The following positive feature appears

as a convolution of three bands, with the dominant

contribution centered at 28180 cm⁻¹and shoulders at 26850

and 30150 cm⁻¹.

5.4. VTVH-MCD. VTVH-MCD was collected for the three

V(III) complexes in order to determine the polarizations of the

observed electronic transitions, as well as to gain additional

insight into the ground-state electronic properties of these

molecules. Because of the large parameter space available

during ﬁtting (D, E/D, g_x,y,z, M_xz,yz,xy, and A_sat), modeling of the

observed isotherms was restricted such that g_x= g_y= g_z, and D,

E/D, and g_av.were initially ﬁxed to the values determined by

SQUID in order to ﬁt M_xz,yz,xyand A_sat. Following initial ﬁtting

of M_xz,yz,xyand A_sat, values of D, E/D, and g_avwere allowed to

vary.

VTVH-MCD measurements were performed at 18450,

21460, and 23810 cm⁻¹for 5 (Figure D9), 13370, 15380,

19120, 20240, 24100, 28570, and 32360 cm⁻¹for 6 (Figure

D10), and 12900, 18240, 21550, 25000, 28250, 29940, and

31950 cm⁻¹for 7 (Figure D11). The initial modeling of 5 was

performed starting from the spin-Hamiltonian parameters

determined from the present SQUID study, as well as from

previously reported HFEPR measurements.²²Analysis of the

global-ﬁt error surfaces from either approach support an

intermediate rhombicity (E/D = 0.14) with g_av= 1.75 and D =

7.1 cm⁻¹. The ﬁrst three bands appear strictly z-polarized, while

band 4 is a convolution of 42% y-polarized and 53% z-

polarized. In complex 6, simultaneous ﬁtting of the spin-

Hamiltonian and band polarizations for all bands supports a

highly rhombic ground state (E/D = 0.33) with a relatively

large ZFS (|D| = 10 cm⁻¹) and g_av= 1.85. Interestingly, while

ﬁtting of the susceptibility and magnetization data of 6 did not

show a particularly strong preference to D = 10 cm⁻¹versus D

= 14 cm⁻¹, the VTVH-MCD isotherms cannot be reasonable ﬁt

using |D| > 10 cm⁻¹, thus supporting the smaller value. All

bands are predominately z-polarized, although there is

considerable mixing (15−30% x, y contribution). Finally, in

complex 7, analysis of the global-ﬁt error surfaces support a

small rhombicity (E/D = 0) with g_av= 1.8. Simulations for

measurements at 29940 and 31950 cm⁻¹were bettered

considerably when D was allowed to vary up to 9.6 cm⁻¹,

although this only resulted in nominal improvements for

H

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Table 5. Energies and Signs of the First Four SA-CASSCF(9,9)/NEVPT2-Calculated Excited States of Models 1a−3b and 4

CASSCF(9,9)/NEVPT2 energy/sign

state

1a

1b

3a

3b

4

1

2

3

4

14490

15250

18240

31510

−

+

15580

16370

17850

33100

−

+

15140

15930

18120

37380

−

+

16180

16990

17740

38770

+

1010

3860

+

−

+

−

20440

24510

−

2

simulations of measurements at other energies. The most

noticeable feature of any ﬁt is that all observed VTVH-MCD

follows single, pure polarizations; this implies that while the

ground state contains very low rhombicity, the measured

excited states are considerably rhombic in nature.

where E increases by ∼1040−1060 cm⁻¹and A₁by ∼1300−

1570 cm⁻¹. Here, B₁decreases by ∼380 cm⁻¹. Taking these

2

two sets of comparisons into consideration, one can now pose

the question of how these eﬀects combine for a ﬁnal outcome.

Considering that the ligation of Py to VO(acac)₂results in a

trans eﬀect that weakens the VO bond, something already

known from the observed VO stretching frequencies

reported in previous IR studies,²⁷it is fairest to draw our

comparisons between 3a and 1b. With both coordination of Py

and a lengthening of the VO bond by 0.03 Å, it is seen that

the energy of the ²E state decreases by ∼440 cm⁻¹, while that of

²A₁increases by ∼4400 cm⁻¹. Additionally, ²B₁is nearly

invariant, increasing by only 270 cm⁻¹.

5.5. Theoretical Calculations. 5.5.1. MCD and Spin-

Hamiltonian Calculations of V(IV) Complexes. 5.5.1.1. Calcu-

lations of the VO²⁺Model Complexes (1a, 1b, 3a, and 3b).

The SOC-CASSCF(9,9)/NEVPT2-calculated spin-Hamilto-

nian parameters of models 1a−3b are provided in Table 2.

1

The well-isolated S = /₂ground states of models 1a−3b all

consist of a single unpaired electron that occupies a

predominately V d_xy-centered orbital. As expected, coordination

of Py or shortening of the VO bond, which produces minor

increases in g_xand g_y, is found because of the increased

interaction along the z axis, while g_zremains, for the most part,

invariant.

With these correlations in hand, we may return to the task of

interpreting the observed spectra of 1−3. As was just shown,

our calculations predict a drop in the energy of the E state

upon coordination of an additional axial substituent and

subsequent weakening of the VO bond; similarly, we have

seen that the energies of bands 1 and 2 are decreased in

complexes 2 and 3, relative to complex 1 (Figure 6). Therefore,

we assign bands 1 and 2 to the E state. Additionally, the

relatively energy-invariant band 3 is assigned to the B₁state.

2

The calculated energies, MCD signs, and state assignments

under C_4vsymmetry for the ﬁrst four ligand-ﬁeld excited states

of 1a, 1b, 3a, and 3b are presented in Table 5 and Figure 6, and

2

Meanwhile, our calculations predict the ²A₁state to be

considerably higher in energy, well outside of the observed

range and unfortunately preventing the assignment of this state

for 1−3 in the present study. However, the ligand-ﬁeld

transition energies of VO(acac)₂have recently been reported

by resonant inelastic X-ray scattering (RIXS) studies of

VO(acac)₂. These reported values are in good agreement

with those observed presently, and an additional higher-lying

state around ∼26000 cm⁻¹has been observed and assigned to

72

2

²B₂→ A₁. With this estimate of the A₁state, our current

calculation overestimates this transition by ∼5000 cm⁻¹, which

is still not unreasonable for the employed method.

Figure 6. SA-CASSCF(9,9)/NEVPT2-calculated excitation energies

for the ﬁrst ﬁve states of model complexes 1a−3b.

To further support our assignments, we can individually

determine the signs of the two ²B₂→ ²E transitions, which give

rise to the pseudo-A term formed by bands 1 and 2 in

complexes 1−3. This term arises predominately through SOC

the calculated spectra in Figure D12. The ﬁrst two excited

electronic states involve excitations of the single unpaired

electron from b₂(d_xy) → e(d_xz,d_yz) to generate the degenerate

2

between the E_y(d_xy→d_yz) and E_x(d_xy→d_xz) states; because of

the asymmetry imposed by the acac⁻ligand in 1 and 2 (as well

as by Py in 3), ²E_y(d_xy→d_yz) < ²E_x(d_xy→d_xz). As d−d

transitions are parity-forbidden, the transition dipole moments

²E state. The third excited state (²B₁) arises from the b₂(d_xy) →

2

b₁(d_{x −y}) and the ﬁnal A₁from the b₂(d_xy) → a₁(d_z).

In this system, the Py ligand acts primarily as a σ donor

through the two unpaired electrons present on nitrogen (Figure

D13). This is clear upon comparison of the state energies of

2

of the B₂→ E excitations must arise through overlap of the

metal-centered d orbitals with the ligand O p orbitals. In

1

general, the MCD C-term parameter C₀for an S = /₂system

2

3a/1a or 3b/1b. In both cases, the energy of A₁increases

greatly (5700−6000 cm⁻¹), while the E state increases by a

2

between the 2S + 1 (with S being the total spin of the state)

components of the spatially nondegenerate ground state A, the

spatially nondegenerate excited J set of states, and the

intermediate K set of states, in the presence of SOC, is

described by the following equation:³¹

mere ∼600−650 cm⁻¹, implying that π interaction of Py with

either V d_xzor d_yzis only a minor perturbation. Meanwhile, a

comparison of 3a with 3b or 1a with 1b reveals that shortening

2

of the VO bond signiﬁcantly impacts the E and A₁states,

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1

6

underestimation of the experimentally determined g_x= 1.984, g_y

= 1.943, and g_z= 1.807, particularly in terms of g_z, likely due to

an overestimation of the calculated 1-²A_gand 2-²A_gstates.

The calculated SA-CASSCF(9,9)/NEVPT2 excited states of

4 presented in Table 5 (with spectra provided in Figure D14)

imply that only the 1-²A_g(20440 cm⁻¹) and 2-²A_g(24510

cm⁻¹) states may be assigned within the observed experimental

range. The overlap of these two terms forms a pseudo-A term

with a predominately negative component. Experimentally, the

C/D ratios of bands 3−6 (Table D1) all lie within a reasonable

range (0.03−0.04) for a ligand-ﬁeld-type assignment. Addi-

tionally, an even higher C/D ratio is found for band 9 (0.06),

but the extinction coeﬃcient of this band is also considerably

higher (∼6130 M⁻¹cm⁻¹) and therefore unlikely to be ligand-

ﬁeld-centered. These high ratios are due to the considerable

SOC induced by Cl (ζ = −587 cm⁻¹), allowing charge-transfer

(CT)-type transitions between V(IV) and Cl⁻to gain

considerable intensity in the MCD and therefore making a

clear assignment of the ligand-ﬁeld transitions diﬃcult. On the

basis of the calculated sign and relative energy splitting, we

assign the experimental bands 4 and 5 of 4 in Table 5 to the

1-²A_gand 2-²A_gstates.

C₀= − ∑ ϵ_xyzg ∑ ^{^Δ_KJ⁻¹D_x^AKD_y^AJL_z^KJ}

z

xyz

K≠A,J

+ {Δ_KJ⁻¹D_x^AJD_y^AKL_z^AK

where D^I_i^Jdescribes the Cartesian component (i = x, y, or z) of

the eﬀective transition dipole moment between states I and J,

}

(5)

−1

Δ_IJis their energy diﬀerence, and ϵ is the Levi−Civitta

symbol.

Focusing on the lower energy transition, we will assign A =

²B₂(d_xy) and J = ²E_y(d_xy→d_yz). To simplify this equation, ﬁrst all

other excited states besides ²E_x(d_xy→d_yz) = A → K are

neglected. Rotating d_yzcounterclockwise into d_xzleads to a

KJ

positive overlap, and thus L_z> 0. Additionally, we

approximate that D^A_x^J≪ D_x^AKand D_y^AK≪ D^A_y^J, allowing us to

reduce eq 5 to

KJ

⎧

⎨

⎩

⎫

⎬

⎭

L_z

1

6

C₀= −

ϵ g

D_x^AKD_y^AJ

∑

xyz

z

Δ

KJ

xyz

(6)

This allows the sign of the resulting MCD C term at the

saturation limit to be evaluated following

L_z^KJ

Δ_KJ

Table 6. Energies and Signs of the First 10 SA-

CASSCF(12,10)/NEVPT2-Calculated Triplet States of

Complexes 5−7

C₀(E_y) ∝ −⟨S_z⟩

(D_x^AK)(D_y^AJ) < 0

(7)

when Δ_KJ= E_K− E_J> 0. From the calculated transition dipole

moments, it then follows that positive Δ_KJresults in the

absorption of right-handed photons, producing a negative

MCD signal. Meanwhile, if we assign the higher energy E_x

transition as A → J and E_yas A → K, a positive sign will result

CASSCF(12,10)/NEVPT2 energy/sign

eigenstate

³T₁

5

6

7

6.42

+

10.81

892

−

+

6.35

+

810

+

1191

as Δ_KJ= E_K− E_J< 0. Together, the transitions E(d_xy→d_xz,yz

)

961

+

1305

−

+

1390

³T₂

³T₁

³A₂

18574

18909

19109

26149

26768

27788

38122

−

+

13374

13534

14244

21094

21598

23111

28004

12494

12669

13080

19493

19690

20153

25747

form a positive pseudo-A term, which corresponds well with the

MCD bands 1 and 2 observed for complexes 1−3.

−

+

5.5.1.2. Calculations of the VCl₂(acac)₂Complex (4).

Unlike the vanadyl series, 4 lacks the strong axial oxo bond

that dominates the electronic structure of complexes 1−3.

Instead, the softer binding Cl⁻ligands result in a mild axial

elongation and approximate D_4hsymmetry. Under this

−

+

−

+

2

assumption, the ground state would be characterized as E_g

arising from the singly occupied e_g(d_yz,d_xz), and the relative

energetic ordering of the d manifold of 4 follows an e_g(d_yz,d_xz)

2

< b_2g(d_xy) ≪ a_1g(d_z) < b_1g(d_{x −y}) motif. In reality, as evidenced

2

from EPR (Figure 3a) and in our calculations, the E_gground

state is split signiﬁcantly. Indeed, the relative energies of the

ligand-ﬁeld orbitals from our calculations predict d_yz< d_xy< d_xz

−

2

≪ d_z< d_{x −y}, implying that π interactions between acac and

V(IV) are signiﬁcant. Therefore, we will proceed with our

discussion of the excited states using D_2hsymmetry labeling

from here forward.

2

Under D_2hsymmetry, the B_3gground state arises

predominately from the singly occupied V d_yz, and the relative

energetic ordering of the d manifold of 4 follows a b_3g(d_yz) <

2

b_1g(d_xy) < b_2g(d_xz) ≪ 1a_g(d_z) < 2a_g(d_{x −y}) motif. Similar to the

VO(acac)₂series, the ligand-ﬁeld excited states arise from a

2

series of one-electron excitations, starting with the B_1g

originating from the b_3g(d_yz) → b_1g(d_xy) transition (state 1 of

Table 5). Slightly higher in energy, b_3g(d_yz) → b_2g(d_xz)

2

generates the B_2gstate, while b_3g(d_yz) → 1a_g(d_z) and

2

2a_g(d_{x −y}) comprise the 1- A_gand 2- A_g, respectively. The

SOC-CASSCF(9,9)/NEVPT2 magnetic S = 1/2 ground state

spin-Hamiltonian parameters present a rhombic ground state

with g_x= 1.928, g_y= 1.843, and g_z= 1.736. This is a signiﬁcant

Figure 7. Comparison of the SA-CASSCF(12,10)/NEVPT2-calcu-

lated triplet states of 5−7 with ligand-ﬁeld state assigments (black)

alongside the experimentally assigned states (red).

J

DOI: 10.1021/acs.inorgchem.8b00486

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Inorganic Chemistry

Article

5.5.2. MCD and Spin-Hamiltonian Calculations of V(III)

Complexes. The state-averaged (SA)-CASSCF(12,10)/

NEVPT2-calculated triplet-state energies of complexes 5−7

are presented in Table 6 and Figure 7, while the corresponding

spectra are provided in Figure D15. The ﬁrst 10 triplet and 15

singlet roots were calculated for 5−7.

(Table 6). Here, the calculated energy of this negative feature is

in excellent energetic agreement with the negatively signed

band 1 of the experimental MCD and is therefore assigned in

this manner. 2-³T₁is considerably more distorted, with ³E < ³A

by 1770 cm⁻¹and ³E further split by 500 cm⁻¹. Interestingly, all

three components are calculated to generate a positive sign in

the MCD; while overestimating by ∼2000−3000 cm⁻¹, which

is still quite reasonable by CASSCF/NEVPT2, these excited

states correspond well with the positive bands 2 and 3 of the

5.5.2.1. Calculations of the V(acac)₃Complex (5). The

SOC-CASSCF(12,10)/NEVPT2-calculated ground state of 5 is

3

comprised of the nondegenerate A₂state. Here, the calculated

3

spin-Hamiltonian parameters (Table 1) describe the ground

state as near-axial (E/D = 0.06, g_⊥= 1.747 and 1.729, and g_∥=

1.937), with a ZFS of D = 9.6 cm⁻¹.

experimental spectrum. Last, the A₂transition is calculated to

have a positive sign at 28000 cm⁻¹. While this may very well be

present in some respect, the relatively low calculated intensity

(compared to 2-³T₁) and the presence of a large, broad negative

feature in this region prevent us from ascertaining a precise

experimental assignment of this transition.

The calculated ground state of 5 consists of a near-axially

3

split 1-³T₁term to form A₂and E, with A₂(T_1g) < E(T_1g)

split by 880 cm⁻¹and E(T_1g) further split by 150 cm⁻¹, with

3

all transitions resulting in positive MCD signs (Table 6). The

ﬁrst excited state (³T₂) is calculated to be only very mildly split

(400 cm⁻¹), and similar to the ground state, ³A₁(T_2g) <

5.5.2.3. Calculations of the VCl₃ttcn Complex (7). The

SOC-CASSCF(12,10)/NEVPT2-calculated spin-Hamiltonian

parameters of 7 produce a considerable axial splitting of D =

9.53 and a relatively low rhombicity of E/D = 0.057, both of

which are somewhat overestimated compared to the exper-

imentally determined values presented in Table 1. Meanwhile,

the calculated g-tensor values of 1.921, 1.728, and 1.743 (g_av=

1.797) are in excellent agreement with the experiment

[g_av(Magn.) = 1.77; g_av(VTVH-MCD) = 1.8]. The calculated

triplet excited-state energies are presented in Table 6. Similar to

5, the calculated MCD spectrum mirrors a distorted

pseudooctahedral spectrum, forming three dominant positive

3

³E(T_2g). Here, E(T_2g) is split by 200 cm⁻¹. Together, these

form a (−, −, + ) motif in terms of the MCD sign, with the

combined negative components having about 4 times greater

intensity than the positive. The energetic proximity of the

observed bands 1−3 (all negative) to these calculated

3

transitions suggests that they also belong to T_2g; while no

positive feature is observed, this may be masked by the strong,

positive band 4. Moving forward, the calculated 2-³T₁forms a

negative feature split as ³E(2-³T_1g) < ³A₁(2-³T_1g) by 1330 cm⁻¹,

with ³E(2-³T_1g) further split by 620 cm⁻¹. This transition

appears with an intensity ∼18 times greater than that of ³T₂. In

this energetic region, experimental bands 5 and 6, which are

split by 1900 cm⁻¹, present two very large positive features. It is

notable that the absolute intensity of band 6 is ∼20 times

greater than that of band 4, which we have assigned as part of

³T₂. Therefore, based on the good agreement between the

experimental and calculated energies and relative intensities,

bands 5 and 6 are assigned to 2-³T₁. This assignment is also in

excellent agreement with recent RIXS studies of complex 5,

which have assigned 2-³T₁to two transitions around ∼27400

and ∼29800 cm⁻¹, respectively.⁷²Discrepancies between the

calculated and experimental signs may arise through the

coupling of 2-³T₁with a neighboring CT states; since CT

states are not accounted for in the present calculation, such

eﬀects are not presently taken into account. At present, we have

not taken this into consideration because doing so often

requires forbiddingly large active spaces to fully and accurately

describe the CT states.

3

features that correspond to the T₂, 2-³T₁, and A₂states (in

order of increasing energy). As seen previously for both 5 and

6, the splitting of the ³T₂and ³T₁terms follows a pseudotrigonal

3

distortion, in which each T term is split into the A and E

3

states and E is further split to a lesser degree. In the ground

state, A and E of 1-³T₁are strongly split by 1290 cm⁻¹, with

3

³A < E, while both T₂and 2-³T₁follow a E < A motif and

3

are more mildly split, by 500 and 560 cm⁻¹, respectively. The

³E states of 1-³T₁, T₂, and 2-³T₁are further split by 200, 175,

3

and 200 cm⁻¹each.

As noted before, all triplet excited states calculated for 7

3

result in a net positive MCD intensity. The calculated T₂

matches well with band 1 in terms of both energy and sign and

is assigned thusly. Furthermore, the single large band 2 is

assigned to 2-³T₁because of its excellent correlation with

calculated values. Last, the small positive band 5 is assigned to

³A₂, again because of strong support in terms of the calculated

energy, sign, and relative intensity.

5.5.3. Ligand-Field Treatment of Parameters. In this

section, we interpret the ligand-ﬁeld properties of complexes

1−7 from the experimental and calculated data above

determined in a stepwise fashion through the AOM. In this

5.5.2.2. Calculations of the VCl₃(thf)₃Complex (6). The

SOC-CASSCF(12,10)/NEVPT2-calculated ground state of 6 is

considerably rhombic (E/D = 0.18), with a large ZFS of D =

16.2 cm⁻¹. Values of g_⊥= 1.594 and 1.689 and g_∥= 1.946 (g_av=

1.743) were obtained, in reasonable agreement with what we

have seen thus far experimentally (Table 1; g_av= 1.72).

While truly meridonal in geometry, the calculated triplet

states of 6 appear to follow a pseudotrigonal distortion, in which

2

well-established ansatz, the 3d-t_2g(d_xy,d_xz,d_yz) and e_g(d_{x −y},d_z)

orbitals of metal complexes containing anionic ligands are

destabilized through σ- and π-type interactions, giving rise to

antibonding orbital energies of 3e_σand 4e_π, respectively. These

are further perturbed by asymmetry, requiring the employed

AOM model to be customized on a case-by-case basis. The

formulations of these customized approaches are described

below, while the resulting calculated ligand-ﬁeld parameters are

summarized in Table 7 for complexes 1−4 and in Table 8 for

complexes 5−7.

3

each T is split into E + A states, similar to the case of 5.

Because of this behavior, it is useful to continue the use of this

nomenclature for later comparisons of complexes 5−7. The

3

calculated ground-state 1-³T₁is split in a A < E fashion by

1100 cm⁻¹, with E being further split by 400 cm⁻¹. The ﬁrst

3

calculated excited state, T₂, is split as E < A by 790 cm⁻¹,

3

5.5.3.1. VO²⁺Complexes (1−3). The AOM analysis protocol

developed to extract the ligand-ﬁeld parameters from the

experimental data of complexes 1−3 and the computed data of

with ³E further split by 160 cm⁻¹, resulting in a (+, −, −) motif

3

in the MCD. Here, E forms a negative pseudo-A term, which

overlaps with the additional negative component from ³A

K

DOI: 10.1021/acs.inorgchem.8b00486

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Inorganic Chemistry

Article

model complexes 1a, 1b, 3a, and 3b are presented in section C

of the Supporting Information. In complexes 1−3, bands 1 and

2 of Table 3 have been assigned in C_4vsymmetry to the split ²E

3, the e_σ(acac) interaction is increased somewhat as expected

because of the movement of vanadium into the acac⁻plane

(Table 7).

2

state, while band 3 is assigned to B₁; as mentioned before, we

5.5.3.3. Complex 5. The deceptively simple complex 5 has a

considerable history of previous ligand-ﬁeld assignments, which

contain numerous discrepancies. The ﬁrst proposed assignment

of the ligand ﬁeld of 5 was made by Piper and Carlin,⁶⁹who

hypothesized that the features observed at 18200 and 21700

unfortunately have not been able to conclusively assign the ²A₁

state of these complexes based upon our current observations.

Therefore, our analysis is limited to the accurate determination

of parameters e_π(O), Δe_πs(acac), and e_σ(acac) (Table 7). To

provide estimates of 10Dq and e_σ(acac), placeholder values of

the 2-²A₁state were used based upon previous RIXS studies of

1 and the relative shift seen between 1b and 3a in our

CASSCF(9,9)/NEVPT2 calculations, employing 26000 cm⁻¹

(for 1) and 31000 cm⁻¹(2 and 3).⁷²In 1, this assignment

results in values of e_σ(O) ≅ 20730 cm⁻¹and 10Dq ≅ 14080

cm⁻¹.

3

cm⁻¹arise from the T_1g→ T_2g, T_1gtransitions, respectively.

The same assignment was later proposed by Machin and

Murray,⁶⁸who proposed B = 285 cm⁻¹[B = 860 cm⁻¹for the

free V(III) ion] and 10Dq = 18900 cm⁻¹under the assumption

of O_hsymmetry using the equations of Griﬃth.⁷³This

abnormally small value of B led Gregson et al.⁶⁶to reanalyze

these data; while they propose that B = 600 cm⁻¹and 10Dq =

22250 cm⁻¹would be reasonable considering similar values for

other V(III) complexes, their reassignment of the observed

While the fourth ligand-ﬁeld transition of complexes 1−3

cannot be conclusively assigned experimentally, this informa-

tion is readily available from theory in models 1a−3b. The

ligand-ﬁeld parameters presented in Table 7 were modeled by

the assignment of excited states 1 and 2 to ²E, 3 to ²B₁, and 4 to

²A₁, as previously mentioned.

3

transitions at 18200 and 21700 cm⁻¹as A₂[³T₁] → E[³T₂]

and ³A₂[³T₁], assuming a trigonal-ﬁeld distortion, required B =

328 cm⁻¹and 10Dq = 18060 cm⁻¹. More recently, Krzystek et

al.²²oﬀered a revision of these assignments on the basis of

MCD. In their work, the transitions observed at 18200 and

21700 cm⁻¹were assigned to ³A₂[³T₁] → ³A₁[³T₂] and

³E[³T₂], while ³A₂[³T₁] → ³A₁[³T₁] and ³E[³T₁] were proposed

to correspond to features observed at 27400 and 29700 cm⁻¹.

With this new set of assignments, ligand-ﬁeld parameters of B =

684 cm⁻¹and 10Dq ≈ 20000 cm⁻¹were proposed. This ﬁt also

requires a relatively large trigonal splitting of 2100 cm⁻¹,

although this is not particularly unusual because the trigonal

splitting of V(H₂O)₆³⁺has been reported to be as large as 1940

cm⁻¹.⁷⁴

Shortening of the VO bond (comparing 1a/1b or 3a/3b)

interestingly results in a relatively small decrease in 10Dq. This

arises from the strong π interaction of the terminal oxo with

vanadium; while both σ and π-oxo interactions strengthen with

a shortened VO distance, the π interaction increases at a

greater rate, resulting in a decrease in 10Dq. Meanwhile,

coordination of Py (comparing 1a/3a or 1b/3b) drastically

increases 10Dq by ∼2400 cm⁻¹. This occurs predominately

through the overall increased σ interaction, raising the energy of

²A₁signiﬁcantly. Meanwhile, coordination of Py only nominally

increases the ﬁt values of e_π(O) by 270 cm⁻¹, a signiﬁcantly

smaller eﬀect than decreasing of the VO coordinate.

5.5.3.2. Complex 4. We have just seen that the ligand ﬁelds

of complexes 1−3 are dominated by the VO interaction, with

the acac⁻ligands acting as a relatively minor perturbation. In

the case of complex 4, on the other hand, the interaction of

acac⁻with V(IV) becomes a more signiﬁcant force. According

to our calculations, the ²E_g(in D_4h) ground state of 4 is split by

∼3800 cm⁻¹to form the ²B_3gand ²B_2gstates (in D_2h), with ²B_3g

As noted previously, the in-plane (e_πc) and out-of-plane (e_πs)

π interactions in ligands such as acac⁻are inequivalent.

Additionally, as mentioned for the case of complexes 1−3, the

extended out-of-place π-electron network of acac⁻leads to

phase relations of the out-of-plane ligand orbitals, forming

symmetric (ψ, in-phase) and antisymmetric (χ, out-of-phase)

sets as described by Orgel⁷⁵and elaborated by Ceulemans et

al.⁷⁶(see Scheme C1). This further requires the out-of-plane π

interaction e_πsto be described as an average of the in-phase

e_πs(ψ) and out-of-phase e_πs′(χ).

2

< B_2g. In a one-electron picture, the B_3gground state is

predominately composed of a singly occupied V 3d_yz-centered

orbital. The energies of V d_yzand d_xzin 4 depend upon both

the cylindrical e_π(Cl) and e_πs(acac)/e_πs′(acac) interactions,

while the energy of V d_xydepends on e_πc(acac). As also

employed for complexes 1−3, we may introduce the parameter

Δe_πs(acac) = e_πs(acac) − e_πs′(acac) to provide insight into the

Orgel eﬀect described above. However, our previous

assumption that e_πc(acac) ≈ 0 is no longer valid, and it is not

possible to deconvolute e_πc(acac), e_πs(acac), and e_π(Cl) without

making further assumptions. We may then ﬁt the system using

the approximation that e_π(Cl) = 0; this is done based upon the

relatively small (>3%) contribution of Cl⁻to the unoccupied V

d_xz,yz-dominated molecular orbitals. This allows us to at least

determine a parameter that contains a convolution of e_πc(acac)

and e_πs(acac), which provide a gauge of how much greater

e_πc(acac) is than e_πs(acac). We will refer to this as e_πc*(acac).

This leaves our model with two σ-based parameters [e_σ(Cl) and

e_σ(acac)], as well as two π-based parameters [Δe_πs(acac) and

e_πc*(acac)]. While all four parameters may be ﬁt based on the

SA-CASSCF(9,9)/NEVPT2-calculated excited states, only

1-²A_gand 2-²A_gare seen in experiment, limiting our ability to

ﬁt Δe_πs(acac) and e_πc*(acac). Upon a comparison of 4 with 1−

A model coordinate system of 5 described in terms of the

polar angle θ, twist angle ϕ, bite angle α, and dihedral angle ψ

(Scheme 2) was generated by averaging these angles in the core

geometry of the observed crystal structure to generate a trigonal

model with eﬀective D₃symmetry, where θ = 54.43°, ϕ = 60°,

α = 88°, and ψ = 43.5°. When this model was applied, the

3

following experimental assignments were made: A₂(³T_1g) →

³E(T_2g) to the average of 18090 and 19380 cm⁻¹, ³A₂(³T_1g) →

3

³A₁(T_2g) to 21570 cm⁻¹, A₂(³T_1g) → E(T_1g) to 26540 cm⁻¹,

and A₂(³T_1g) → A₁(T_2g) to 28390 cm⁻¹. Because of the

limited number of observables, e_πcwas ﬁxed to two-thirds that

of e_πs. Using the full matrix method, these assignments provided

excellent ﬁts (within 60 cm⁻¹for transitions to ³T_2gand 180

3

cm⁻¹for transitions to T_1g) with the use of B = 519 cm⁻¹,

3

10Dq = 19730 cm⁻¹, e_σ= 8280 cm⁻¹, e_πs= 1532 cm⁻¹, and e_πc=

1021 cm⁻¹. The signiﬁcantly large values of e_σand e_π, combined

with a small B, imply a considerable degree of covalency in the

complex.

Similarly, an AOM ﬁt was performed for the SA-CASSCF-

(12,10)/NEVPT2-calculated excited states of 5. Using a model

identical with that implemented for the experimental

L

DOI: 10.1021/acs.inorgchem.8b00486

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Inorganic Chemistry

Article

a

Table 7. Summary of Fit AOM Parameters for Complexes 1−4

ligand-ﬁeld parameters

e_π(O)

complex

10Dq

e_σ(O)

e_σ(acac)

Δe_πs(acac)

c

1

exp.

17090

16450

16280

26730

25950

27660

11690

13620

6000

6420

6280

740

413

433

b

1a

C(9,9)/N

b

1b

14730

ligand-ﬁeld parameters

complex

10Dq

e_σ(O,N)

15740

e_π(O,N)

e_σ(acac)

Δe_πs(acac)

d

2

exp.

20920

4870

6210

1120

ligand-ﬁeld parameters

complex

10Dq

e_σ(O,N)

e_π(O)

e_σ(acac)

Δe_πs(acac)

e_π(N)

d

3

exp.

21130

15720

15980

16680

8830

13910

14980

6200

6370

1410

413

460

770

730

b

3a

C(9,9)/N

18920

18640

b

3b

6240

433

ligand-ﬁeld parameters

c

complex

10Dq

e_σ(Cl)

e_πc(acac)

e_σ(acac)

Δe_πs(acac)

4

exp.

20060

24940

20950

6240

7850

6110

6910

8550

8200

e

C(9,9)/N abbr.

C(9,9)/N

270

1825

a

b

c

The CASSCF(9,9)/NEVPT2 method is abbreviated as C(9,9)/N. Derived using SA-CASSCF(9,9)/NEVPT2-calculated energies. Supplemented

using the RIXS-assigned 2-A₁energy of 1 for ﬁtting of the experiment at 10Dq.⁷²Supplemented with a 2-A₁-calculated energy shift in conjunction

d

with the RIXS-assigned 2-A₁energy of 1 for ﬁtting of experimental at 10Dq.⁷²abbr. = “abbreviated” use of calculated roots to match those observed

e

experimentally.

parameters, the calculated triplet electronic states were assigned

5.5.3.5. Complex 7. The ligand ﬁeld of complex 7 shares

commonalities with both 5 and 6 because it contains an

eﬀective trigonal symmetry (approximately C_3v) and cylindrical

π bonding from the three coordinating Cl ligands. Additionally,

the sulfur atoms of the 1,4,7-trithiacyclononane ligand are

restricted in their ability to interact with the V(III) center

because they are thioethers rather than thiols. This means that

only one of the two open lobes of sp³-hybridized sulfur is

capable of overlapping with the central metal and thus only

undergoes a σ-donor interaction. Therefore, 7 must be

described in terms of an averaged e_σfor the Cl and S

constituents, while e_πarises solely from interactions with Cl. In

turn, we will treat 10Dq = 3e_σ(Cl/S) − 2e_π(Cl). Following from

the MCD of 7 shown in Figure 5, the single broad band found

3

as follows: A₂(³T_1g) → E(T_2g) to the average of 18574 and

3

18909 cm⁻¹, A₂(³T_1g) → A₁(T_2g) to 19109 cm⁻¹, A₂(³T_1g)

→ E(T_1g) to the average of 26149 and 26786 cm⁻¹, and

3

³A₂(³T_1g) → ³A₁(T_2g) to 27778 cm⁻¹. The resulting best ﬁt was

accomplished using B = 632 cm⁻¹, 10Dq = 19627 cm⁻¹, e_σ=

7128 cm⁻¹, e_πs= 528 cm⁻¹, and e_πc= 352 cm⁻¹, which provided

errors of 240 cm⁻¹for transitions to ³T_2gand 330 cm⁻¹for

transitions to ³T_1g. The signiﬁcant increase in B along with the

drastic decreases in e_σand e_πarises from the failure of

CASSCF/NEVPT2 to fully account for electron correlation, a

well-known problem with the method.

5.5.3.4. Complex 6. For analysis⁷⁷of the rhombic complex 6,

the lowered strict C₂symmetry of the complex allows π

contributions of the thf and Cl ligands to be diﬀerentiated.

While the Cl⁻ligands are treated cylindrically, in which e_πs= e_πc,

this is not applicable for the thf ligands, which are capable of

only the contribution from the out-of-plane e_πs. Therefore, we

may initially deﬁne the ligand-ﬁeld strength in terms of 10Dq =

3e_σ− 2e_π(Cl) − e_πs(thf). Furthermore, the thf ligands are

twisted an average of 34.6° out of the equatorial plane, while

the axial thf is twisted by 43.3° out of the axial plane containing

the three Cl ligands. Using the C₂-symmetrized model, a

reasonable ﬁt was obtained in which e_σ= 5290 cm⁻¹, e_π(Cl) =

700 cm⁻¹, and e_πs(thf) = 450 cm⁻¹with errors of 100−160

cm⁻¹and B = 465 cm⁻¹with an error of 2 cm⁻¹. Additionally,

the ligand ﬁeld of 6 was calculated for the SA-CASSCF(12,10)/

NEVPT2-calculated excited states. To equate our calculations

3

at 12910 cm⁻¹is assigned to the A₂(³T_1g) → E(T_2g) and

³A₁(T_2g) transitions. Similarly, the single band at 18450 cm¹is

attributed to the ³A₂(³T_1g) → ³E(T_1g) and ³A₂(T_1g) transitions.

Finally, the small feature at 26850 cm⁻¹is assigned as ³A₂(³T_1g)

3

→ A₂(A_2g). With these assignments, good agreement was

found using 10Dq = 13800 cm⁻¹, B = 423 cm⁻¹, e_σ= 5310

cm⁻¹, and e_π(Cl) = 1060 cm⁻¹. Deviations of the corresponding

transitions predicted with these parameters are ∼ 100 cm⁻¹.

Furthermore, ligand-ﬁeld analysis of the SA-CASSCF-

(12,10)/NEVPT2-calculated electronic states of 7 was

performed. Here, the included states were averaged to imitate

the experimental assignments. To do so, the three components

3

with the experiment, excited states belonging to T₂and 2-³T₁

3

of each of the T₂and T₁excited states provided in Table 6

were averaged and used in the ligand-ﬁeld analysis, giving a

total of three bands (at 12748, 19779, and 25747 cm⁻¹)

available for the ﬁtting process. Doing so resulted in a

reasonable ﬁt using 10Dq = 13470 cm⁻¹, B = 533 cm⁻¹, e_σ=

5180 cm⁻¹, and e_π= 1040 cm⁻¹; deviations in the

corresponding transitions generated by this set of parameters

are ∼ 170 cm⁻¹.

were averaged as necessary to match experimental resolution. A

further ﬁt utilizing all calculated triplet roots was also

performed, as summarized in Table 8. While the calculations

reasonably estimate 10Dq, it is clear that a large overestimation

of B is implicit regardless of the number of roots employed in

the AOM model. As mentioned in the case of 5, this is an

inherent problem that arises from a failure to completely

account for the electron correlation energy.

M

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Inorg. Chem. XXXX, XXX, XXX−XXX

Inorganic Chemistry

Article

a

Table 8. Summary of Experimental and Calculated Ligand-Field Parameters of Complexes 5−7

ligand-ﬁeld parameters

complex

10Dq

B

B/B₀

e_σ

e_πs

e_πc

5

exp.

19730

19630

19480

18540

519

632

638

829

0.603

0.734

0.741

0.963

8280

7130

1530

530

1110

350

C(12,10)/N abbr.

C(12,10)/N

C(2,5)/N

580

380

ligand-ﬁeld parameters

s

complex

10Dq

B

B/B₀

e_σ

e_π(Cl)

e_π(thf)

6

exp.

14040

14450

14280

13490

465

625

622

865

0.540

0.726

0.722

1.004

5210

5620

5780

700

910

450

590

670

C(12,10)/N abbr.

C(12,10)/N

C(2,5)/N

1180

ligand-ﬁeld parameters

complex

10Dq

B

B/B₀

e_σ

e_π(Cl)

7

exp.

13800

13470

13500

12630

423

553

560

826

0.491

0.642

0.650

0.959

5310

5180

5190

1060

1040

C(12,10)/N abbr.

C(12,10)/N

C(2,5)/N

a

B/B₀calculated using the free-ion value of B = 861 cm⁻¹for V(III). The CASSCF(12,10)/NEVPT2 and CASSCF(2,5)/NEVPT2 methods are

abbreviated as C(12,10)/N and C(2,5)/N, respectively. abbr. = “abbreviated” use of calculated roots to match those observed experimentally.

0.02). At this limit, we approach the degree of error in our

simulations, making clear trends diﬃcult to formulate with EPR

alone. The MCD, however, is a much more sensitive, and

therefore more appropriate, method to observe these shifts

because this technique directly probes the corresponding

electronic excited states.

6. DISCUSSION

In the V(IV) series, we have investigated both common

“vanadyl” and rarer nonoxo “bare” vanadium complexes. In the

vanadyl series, the ligand ﬁeld is dominated by the strong,

covalent VO interaction, which is responsible for determin-

ing the primary structure of the ligand-ﬁeld manifold. Here, we

have found that both our experiments and calculations support

the general ligand-ﬁeld scheme proposed by Ballhausen and

Gray for the vanadyl hexaaqua ([VO(H₂O)₅]²⁺) complex.⁵⁵

Despite the high covalency of the VO bond, these complexes

are quite sensitive to the sixth-ligand coordination. This is

abundantly clear in both the experimental MCD spectra and

calculated transition energies for models 1a−3b. Upon a

comparison of the MCD of complexes 1−3, the low-energy

pseudo-A-term feature is clearly dependent upon the axial

coordination of the sixth ligand, shifting to increasingly lower

energy when moving from 1 to 2 to 3. The donor interactions

of a variety of solvents with VO(acac)₂have been reported

previously by Linert and co-workers, who have shown through

observation of the VO stretching frequency that Py

coordinates more strongly than acetonitrile.²⁷Because one

would anticipate that nPrCN and acetonitrile have similar

donor properties, it is expected that nPrCN also coordinates

more weakly to VO(acac)₂than Py. This is most clearly

manifested in the fact that VO(acac)₂Py may be precipitated

and isolated, whereas VO(acac)₂nPrCN cannot. As the strength

of the coordination is increased from uncoordinated in 1 to

weakly coordinated in 2 to relatively strongly coordinated in 3,

the energetic position of the ﬁrst pseudo-A term, assigned as ²E,

is decreased by approximately 1600 cm⁻¹. Interestingly, this

eﬀect is not as strongly reﬂected in the EPR spectra of these

complexes. This is not particularly surprising; a σ-type axial

perturbation will likely have the greatest eﬀect on the energy of

According to our calculations, we predict a signiﬁcant

2

increase in the energy of the A₁state (by ∼4000 cm⁻¹)

upon coordination of a sixth ligand, which accounts for the

corresponding ∼2000 cm⁻¹increase in 10Dq. Unfortunately,

2

the energy of the B₂→ A₁transition is predicted to be well

outside of our current observable range because of the presence

of a strongly absorbing feature (presumably of VO ligand-to-

metal CT character), and therefore this increase cannot be

experimentally conﬁrmed at present. Meanwhile, the ²B₁state is

2

calculated to be nearly invariant, while E actually decreases in

energy when accounting for the expected trans inﬂuence, which

arises upon sixth-ligand coordination. Here, the calculated ²E is

2

predicted to produce a pseudo-A term, and the B₁a single

positive C term. Indeed, this matches well with what has been

experimentally observed in MCD in terms of both sign and

behavior, where the lowest-energy observed transitions shift to

lower energy upon coordination, and a singly, slightly higher

energy positive C-term appears to be nearly invariant.

2

Therefore, the E transition provides a promising gauge in

determining the coordinative saturation of V(IV) vanadyl

complexes. A comparison of the vanadyl series with the bare

vanadium complex 4 further illustrates how the presence of a

terminal oxo dominates the ligand ﬁeld of the vanadyl

complexes. While both 3 and 4 experience similar ligand-ﬁeld

splittings 10Dq, the ground state is now dominated by the

single-electron occupation of V d_yz, and the predicted electronic

structure is much closer to that of an octahedral complex.

In the V(III) series, considerable insight into the general

electronic and magnetic properties of this ion in a distorted

octahedral environment, including the trigonally distorted 5,

meridonal 6, and facial 7, has been gained by the combination

of the determined spin-Hamiltonian parameters, electronic

excited states, and corresponding calculations. Perhaps the

2

the V d_zorbital, which, according to the rotational relation-

ships described above in eq 4, will not have a direct inﬂuence

on the resulting g-tensor values. Furthermore, the ground states

of the complexes are relatively well isolated (by at least 10000

cm⁻¹), and thus shifts in g_effdue to perturbations in the energies

of excited ligand-ﬁeld states will also be fairly small (0.01−

N

DOI: 10.1021/acs.inorgchem.8b00486

Inorg. Chem. XXXX, XXX, XXX−XXX

Inorganic Chemistry

Article

clearest trend among the V(III) complexes is the nephelauxetic

eﬀect (as diagnosed by B/B₀) observed as we move from 6O

(harder) to 3Cl/3O to 3Cl/3SR₂(softer) ligation. This is also

reﬂected by the decrease in 10Dq across the series in a similar

trend.

Table 9. Summary of the Experimental and Calculated

Ligand-Field Parameters of Complexes 1−7

a

experimental

calculated

complex

10Dq

B

B/B₀

10Dq

B

B/B₀

b

d

e

The observation of a positive ZFS D for both 5 and 7 (as

well as for 6, although the large rhombicity present in this

complex prevents us from assigning an absolute sign) implies

1

2

3

4

5

6

7

17090

20920

21130

16450 , 16280

c

d

18920 , 18640

3

that the T₁ground state is split such that A < E in these

20060

19730

14040

13800

20950

19480

14280

13500

3

complexes, counter to E < A predicted by ligand-ﬁeld theory

for the geometries of these complexes; this is also supported by

the observed MCD and our current calculations, as well as by

previous high-ﬁeld EPR measurements.²²It is also particularly

519

465

423

0.603

0.540

0.491

638

622

560

0.741

0.722

0.650

a

The presented calculated parameters are ﬁt to the full set of ligand-

ﬁeld transitions as described in the text using the CASSCF(9,9)/

NEVPT2 method for complexes 1−4 and the CASSCF(12,10)/

3

interesting to note that no T term in either of the three

complexes presents a clear pseudo-A term, as may be expected,

b

3

NEVPT2 method for 5−7. Supplemented using RIXS-assigned 2-A₁

with all assigned terms corresponding to a T type transition

c

energy of 1 for ﬁtting of the experiment 10Dq.⁷²Supplemented with a

showing a single sign in MCD. This behavior has also been

observed for the VBr₃(thf)₃complex,²²and therefore this may

present a characteristic of distorted octahedral V(III).

2-A₁-calculated energy shift in conjunction with RIXS-assigned 2-A₁

d

energy of 1 for ﬁtting of the experimental 10Dq.⁷²Calculated for

e

models 1a and 3a. Calculated for models 1b and 3b.

The state energies predicted by the SA-CASSCF(12,10)/

NEVPT2 method for all three V(III) complexes are in excellent

agreement with the experimentally observed transitions, well

within the currently accepted error range for such calculations.

Additionally, the spin-Hamiltonian parameters are reasonably

well reproduced in terms of their sign and magnitude, implying

again that the (12,10) active space utilized suﬃciently captures

the metal−ligand interactions in these complexes. It should be

emphasized that employing a minimal (2,5) active-space

calculation results in a large overestimation of the Racah

parameter B (nearly the free-ion value), highlighting the

importance of accounting for both the bonding and

antibonding ligand-ﬁeld orbital combinations in these com-

plexes when utilizing a multiconﬁgurational method such as

CASSCF. Our calculations also predict varying degrees of

pseudotrigonal splitting in the ³T states for all three complexes;

while this is not surprising for 5 and 7, it is interesting to

observe for 6 because this complex does not contain a C₃axis.

In accordance with the expectations from the ligand-ﬁeld

theory, we ﬁnd that, by adding a single electron to the V(IV)

ion, the system preferentially moves from an orbitally

nondegenerate to a near-orbitally degenerate ground state.

This is evidenced most clearly between the nonoxo 4 and all

three of the presented V(III) complexes. From the presented

spectroscopy, this is manifested for 4 in the Q-band EPR,

where despite possessing eﬀective D_4hsymmetry, the complex

undergoes a signiﬁcant distortion to remove the degeneracy.

This point is emphasized even further in our calculations, in

utilized as an extremely information-rich technique that allows

for both the unique assignment of ligand-ﬁeld electronic

transitions and discernment of the magnetic properties of

paramagnetic systems. To this end, we have provided insight

into the electronic and magnetic structures for a variety of

molecular V(IV) and pseudooctahedral V(III) complexes. We

have also shown that the SA-CASSCF/NEVPT2 method serves

as a valuable tool for the accurate ab initio calculation of MCD

of vanadium complexes.

As a further step, we have provided additional detailed

insight into the electronic structures of these complexes

through the development of a ligand-ﬁeld analysis protocol

based upon conventional AOM and ab initio ligand-ﬁeld

analysis. Through these methods, we have shown that the

electronic properties of 5- and 6-coordinate V(IV) complexes

depend signiﬁcantly on the presence and type of sixth-

coordination ligand, while the electronic properties of 6-

coordinate V(III) complexes are quite sensitive to the σ- and π-

donor abilities of the coordinating ligands.

Collectively, we hope that the combined experimental and

computational analysis protocols presented here will aid in the

characterization of vanadium in more complicated systems and

the sagacious design of future vanadium-based complexes with

the desired electronic and geometric properties. Further

investigations are underway in our laboratories to apply the

protocols presented here to challenging vanadium chemical

systems in the ﬁelds of bioinorganic chemistry and heteroge-

neous catalysis.

2

which the splitting of the E ground state is calculated to be

3860 cm⁻¹. Meanwhile, despite ligand-ﬁeld theory predictions,

the observed (VTVH-MCD and SQUID) and calculated

positive ZFSs of all three V(III) complexes immediately

3

indicate that all possess a near-orbitally degenerate A₂ground

ASSOCIATED CONTENT

state.

■

Finally, we have provided a summary of the most pertinent

calculated and experimentally determined ligand-ﬁeld parame-

ters in Table 9.

S

* Supporting Information

The Supporting Information is available free of charge on the

ACS Publications website at DOI: 10.1021/acs.inorg-

chem.8b00486.

7. CONCLUSIONS

Sample preparation, a comparison of the present

V(acac)₃to the literature and between α- and β-V(acac)₃,

details of the AOMX models, and supplementary ﬁgures,

tables, and schemes (PDF)

We have provided a detailed study of the magnetic and

electronic properties of a series of V(IV) and V(III) complexes

using a combination of complementing spectroscopic methods

(magnetometry, EPR, and MCD) and high-level ab initio

theory (SA-CASSCF/NEVPT2). Speciﬁcally, MCD has been

Structural coordinates (ZIP)

O

DOI: 10.1021/acs.inorgchem.8b00486

Inorg. Chem. XXXX, XXX, XXX−XXX

Inorganic Chemistry

Article

Present State-of-the-Art and Outlooks. Appl. Catal., A 1995, 127 (1−

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AUTHOR INFORMATION

■

Corresponding Author

*E-mail: frank.neese@kofo.cec.mpg

ORCID

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dependent peroxidase from Ascophyllum nodosum. Phytochemistry

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Casey Van Stappen: 0000-0002-1770-2231

Dimitrios Maganas: 0000-0002-1550-5162

Serena DeBeer: 0000-0002-5196-3400

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Vanadium Compound Occuring in Amanita Muscaria. Z. Naturforsch.,

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Notes

The authors declare no competing ﬁnancial interest.

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ACKNOWLEDGMENTS

■

C.V.S., D.M., S.B., E.B., and F.N. thank the Max-Planck Society

for funding and support. C.V.S. thanks the International Max-

Planck Research School on Reactive Structure Analysis for

Chemical Reactions (IMPRS-RECHARGE) for funding and

Mihail Atanasov for his insightful discussions regarding ligand-

ﬁeld theory and assistance in utilizing the AOMX program. We

also thank Dr. Claudi Weidenthaler and Jan Ternieden for their

measurement of the powder X-ray diﬀraction pattern of

V(acac)₃.

(22) Krzystek, J.; Fiedler, A. T.; Sokol, J. J.; Ozarowski, A.; Zvyagin,

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DOI: 10.1021/acs.inorgchem.8b00486

Inorg. Chem. XXXX, XXX, XXX−XXX

Inorganic Chemistry

Article

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DOI: 10.1021/acs.inorgchem.8b00486

Inorg. Chem. XXXX, XXX, XXX−XXX

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Investigations of the Magnetic and Spectroscopic Properties of V(III) and V(IV) Complexes

DOI: 10.1021/acs.inorgchem.8b00486

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