Computational and Theoretical Chemistry 1069 (2015) 96–104

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Computational and Theoretical Chemistry

journal homepage: www.elsevier .com/locate /comptc

Probing thermal and solvent effects on hyperfine interactions and spinrelaxation rate of d-FeOOH(100) and [MnH3buea(OH)]2�: Toward newMRI probes

http://dx.doi.org/10.1016/j.comptc.2015.07.0062210-271X/� 2015 Elsevier B.V. All rights reserved.

⇑ Corresponding author at: Department of Chemistry, Federal University ofLavras, P.O. Box 3037, 37200-000 Lavras, MG, Brazil. Tel.: +55 35 3829 1522; fax:+55 35 3829 1271.

E-mail addresses: teo@dqi.ufla.br, teodorico.ramalho@gmail.com (T.C. Ramalho).

Mateus A. Gonçalves a, Elaine F.F. da Cunha a, Fernando C. Peixoto b, Teodorico C. Ramalho a,c,⇑a Department of Chemistry, Federal University of Lavras, P.O. Box 3037, 37200-000 Lavras, MG, Brazilb Department of Chemical and Petroleum Engineering (UFF), Rua Passo da Pátria, 156, Niterói, RJ, Brazilc Center for Basic and Applied Research, Faculty of Informatics and Management, University of Hradec Kralove, Hradec Kralove, Czech Republic

a r t i c l e i n f o

Article history:Received 13 May 2015Received in revised form 4 July 2015Accepted 4 July 2015Available online 21 July 2015

Keywords:Contrast agentsMRIMolecular dynamics

a b s t r a c t

Cancer is a global epidemic, which significantly affects all ages and socio-economic groups and one rea-son is the great difficulty of the initial diagnostic phase. The Magnetic Resonance Imaging (MRI), througheffective contrast agents, has greatly helped in the diagnosis at the initial stage. Recently, superparamag-netic iron oxide nanoparticles and complexes with Mn2+ have received great attention due to their appli-cations as contrast agents for Magnetic Resonance Imaging (MRI). Those materials can shorten the T2 andT2⁄ transverse relaxation times. Thus, in this work, the face 100 of the d-FeOOH and the complex

[MnH3buea(OH)]2� were studied with explicit water molecules in order to obtain the 1H and 17O hyper-fine coupling constants (HFCCs). Molecular dynamics (MD) simulations were performed using the ReaxFFprogram for subsequent statistical inefficiency calculations. Thus, the structures from the MD simulationwere selected for HFCC calculations. The theoretical results suggest that the d-FeOOH and[MnH3buea(OH)]2� considerably increase the 1H and 17O hyperfine coupling constants of the water mole-cules. In addition, d-FeOOH is sensitive to 1H and 17O HFCCs parameters, however, in the complex[MnH3buea(OH)]2�, 17O is much more sensitive than 1H in relation to the HFCC parameters. Our findingspoint out d-FeOOH as a promising alternative to conventional contrast agents.

� 2015 Elsevier B.V. All rights reserved.

1. Introduction

Despite recent technological advances, cancer is still one of themost serious problems of humanity. This outlook is aggravated dueto difficulty of diagnosis preoperatively and postoperatively. In thisline, one of the greatest challenges of diagnostic imaging is todevelop a system able to locate species in different environmentswith high resolution for detecting foci of cancer in surgical marginsfor clinical use [1].

Among the most used diagnostic techniques for cancer, such asTomography and Ultrasonic Endoscopy, the Magnetic ResonanceImaging (MRI) is one of the most successful [2]. Although it is oftendifficult to get sharp images by using RMI, paramagnetic com-pounds are able to act as contrast enhancing agents, increasingrelaxation of water molecules in the human body thereby enhanc-ing the NMR signal [3]. This mechanism is mediated by hyperfine

interactions of paramagnetic species and affect both longitudinaland transverse relaxation times T1 and T2, respectively. In general,the interactions between electron and nuclear spins, which can beprobed by EPR spectroscopy, are denoted hyperfine interactions. Inthis context, the hyperfine coupling (A) phenomenon occurs, whichis characterized by the isotropic (Aiso) and dipolar (Adip) hyperfinecoupling constants, as reported in Eq. (1) [4,5].

A ¼ Aiso þ Adip ð1Þ

The isotropic contribution results from unpaired spin in s orbi-tals, since only s orbitals have finite electron density at the nucleus[4]. The anisotropic contribution comes from both direct (local)and indirect (nonlocal) dipolar coupling. However, it is importantto mention that the dipolar coupling is averaged to zero in fluidsolution [4,5].

Currently, EPR spectroscopy is a suitable tool for studying para-magnetic species, providing information about the oxidationstates, coordination modes and types of ligand sites [4]. Actually,the NMR technique is analogous to EPR, which is related to excita-tion of electron spins, instead of spins of atomic nuclei.

Mn

NN

N

NH

O

But

OH

NH

But

NH

O

O

But

Fig. 1. Structure of the complex [MnH3buea(OH)]�2.

M.A. Gonçalves et al. / Computational and Theoretical Chemistry 1069 (2015) 96–104 97

It should be kept in mind that hyperfine interactions stronglyaffect both relaxation rates (R1 = 1/T1 and R2 = 1/T2) in the con-densed phase. In this line, paramagnetic species, such as iron oxideand paramagnetic ion metal complexes can be used as contrastagents for MRI, because they are able to increase the relaxationof water molecules, thus enhancing the NMR signal [4,5].

Currently, iron oxide nanocrystals have attracted considerableinterest in nanoscience and nanotechnology due to their nanomet-ric dimension, nontoxic nature and superior magnetic propertiesover nanocrystals of similar compositions, which can be synthe-sized by co-precipitation methods [6]. Iron oxide compounds havebeen highly used with contrast agents (CAs) for diagnosticMagnetic Resonance Imaging (MRI) [7].

It is well-known that Iron Oxide Nanoparticles shorten thetransverse relaxation times T2 and T2

⁄ and can be used as negativecontrast agents, because they can lead to a decrease in the MRIimage intensity [8,9], that makes them attractive to act as CAs inMRI [8]. On the other hand, the longitudinal relaxation time T1 isshortened by gadolinium-based contract agents [8,9]. Another fac-tor that affects T1 and T2 is the spin distribution, in particular, thespin exchange will not affect T1, but it will affect T2. T1 is notaffected because the spin distribution between the upper andlower states is not changed. On the other hand, T2 will be affectedbecause phase coherence of the transverse magnetization is lostduring the exchange [10]. In fact, both relaxation rates (R1 = 1/T1

and R2 = 1/T2) depend on the hyperfine coupling constant (A)between the electron spin of the metal ion and the 1H or 17Onuclear spin, the study of nuclear spin relaxation rates, therefore,provides information on local structure and dynamics in solution[9,11]. In solution, the main contribution to hyperfine couplingconstant (A) is the isotropic term (Eq. (1)) [4,5]. Despite a very richexperimental corpus of data, there is a dearth of systematic under-standing of the influence of thermal and solvent effects on hyper-fine interactions and spin relaxation rate [12].

Among the Iron Oxide Nanoparticles, magnetite (Fe3O4) hasbeen widely used as a contrast agent [13] due to its magnetic nat-ure. It should be kept in mind that, although, magnetic propertieshave great importance and are explored in many ways for biomed-ical applications [14], the usefulness of the magnetic colloids inthis field depends on their biocompatibility and the stability ofthe magnetic nanoparticles in solution at neutral pHs [15].Certainly, that is a critical point for the use of magnetic nanoparti-cles in biochemical media, and several groups have invested effortsto develop magnetic materials that are stable in biological media[16]. To circumvent this scenario, other magnetic iron oxides oroxyhydroxides, such as maghemite (c-Fe2O3) [16,17] or feroxyhyte(d-FeOOH) [18] could, in principle, be used as well.

The d-FeOOH is a polymorph of several known iron oxyhydrox-ides with a structure that is based on a hexagonal closed-packedoxygen lattice similar to that of hematite (a-Fe2O3), an octahedronformed by coordination Fe–O [7]. Despite the d-FeOOH havingpromising magnetic properties [19], this oxide is currently one ofthe less extensively investigated polymorph irons (III). In fact, tothe best of our knowledge, there is no report in the literature aboutthe use of d-FeOOH as CA. It is expected that the face 100 of thed-FeOOH has a chiral subdomain like the face 100 of the a-Fe2O3,which can be promising to explore by theoretical calculations [20].

Besides the Iron Oxide Nanoparticles, paramagnetic stablemetal ion complexes in aqueous solutions have gained increasinginterest in recent years due to their importance as CAs in MRI [21].

Currently, Gd3+ complexes are the most used CAs, because theypossess paramagnetic ions and show a slow electronic relaxationdue to their electronic configuration 4f7. CAs based on a chelatecomplex coordinated with the Gd+3 should contain at least a watermolecule for the metal ion for a rapid exchange with the bulkwater system [22].

Recently, block d5 metals, such as the Mn2+ ion, have been usedas an alternative for the classic CAs based on Gd3+ [22]. The Mn2+

complexes have relatively high magnetic moments, slow electronicrelaxation rate and a relatively fast exchange rate of the innersphere water molecules, thus leading to an efficient mechanismfor the longitudinal and transverse system relaxation timeenhancement [23]. The Mn2+ presents a 3d5 electronic structure.Depending on the symmetry of the ligand field, energy levels areunfolded so that the resulting electron spin is S = 5/2 (high spin),quantum numbers can be ±1/2, ±3/2, ±5/2, each line of the EPRMn2+ is split into six hyperfine lines of equal intensity [24].

It should also be kept in mind that manganese and iron com-plexes, with terminal ligands oxo and hydroxo, can mimic catalyticsites of a variety of metalloproteins [25]. The protonation state is akey factor in the reactivity of these intermediates. Biomimeticcomplexes provide insight into the protonation effects ofmetal-oxo species without the complexity introduced by the prox-imity of the protein structure. As for example the ligand tris[(N0-tertbutylureaylato)-Nethylene]aminato ([H3buea]3�), which hasboth monomeric forms M–OH and M–OXO (M = Fe, Mn) in com-plex with several oxidation states [26]. Despite this complex hav-ing several oxidation states, the more common structure insolution is [MnH3buea(OH)]2� (Fig. 1) with the metal having a2 + oxidation state (Mn+2). The isotropic hyperfine coupling con-stant can be calculated by DFT calculations. In fact, different com-putational studies have shown that the 1H and 17O hyperfinecoupling constants can be accurately calculated by the DFT method[27,28].

Despite the great importance of evaluating the spectroscopicproperties of MRI probes in solution or solid state, surprisingly lit-tle computational work on the subject has appeared. In 1948,Bloembergen, Purcell and Pound had already shown that the relax-ation of 1H nuclear spins in water is associated to the localBrownian motion [11,28].

Although much research has been devoted in recent years to thestudy of spectroscopy properties of contrast agents for MRI, knowl-edge of the influence of solvent and thermal effects on the NMRrelaxation parameters has lagged behind. A deep understandingof this phenomenon can require the use of Molecular Dynamicssimulations with a proper empirical force field. Turning now tothe NMR and HFCC calculations, given the size of these systems,the most promising computational approach is to use density func-tional theory (DFT), which has been employed with success to reli-ably predict the chemical shifts of large compounds and complexes[29]. This method is interesting because it includes the effect ofelectronic correlation and allows the calculation of larger systems.

98 M.A. Gonçalves et al. / Computational and Theoretical Chemistry 1069 (2015) 96–104

In the present work, coordinated water molecules in the face100 of d-FeOOH as well as in the complex [MnH3buea(OH)]2� wereinvestigated in order to evaluate the thermal effects on hyperfineinteractions through theoretical calculations at the DFT level call-ing attention to its applicability to MRI probes.

2. Computational methods

2.1. Construction and optimization of structures

Initially, the following coordinates for the d-FeOOH structurewere used: Space Group: P-3m1; network parameters:a = 2.946(2) Å, c = 4.552 Å; and the atoms position parameterswere: Fe: x, y, z = 0; O: x = 0.3333, y = 0.6667, z = 0.2468; H:x = 0.3333, y = 0.6667, z = 0.5100 [18]. A structure optimization ofd-FeOOH was performed using the program ADF [30] with thefunctional PBE1PBE and the base Slater triple-double-zeta (TZP)for the iron, oxygen and hydrogen atoms.

For the complex [MnH3buea(OH)]2�, the structure was con-structed in the program GaussView 5, the optimization procedurewas performed by using the program Gaussian 09 [31] at the DFTlevel with the functional PBE1PBE and the basis set Slatertriple-double-zeta (TZP), for the manganese, oxygen, carbon andhydrogen atoms [32–34]. To account for solvent effects from wateron the HFCC values, single point energy calculations were obtainedusing the polarizable continuum model (PCM) [35,36].

2.2. Molecular dynamics simulations

After the optimization step, Molecular Dynamics (MD) simula-tions were performed for the d-FeOOH and [MnH3buea(OH)]2�

using the REAX-FF program, which was developed and validatedby van Duin and coworkers (REAX-FF) [37]. The MD simulationswere performed at 310.65 K (physiologic temperature). In fact, thistemperature is suitable to simulate the behavior of compounds inbiological systems [38]. As usual, periodic boundary conditions(PBC) and a cutoff distance of 10.0 Å have been applied. The systemconsists of 300 water molecules in a cubic cell with a side of 20 Å.The volume of the cube was determined by the density of liquidwater (q = 0.996 g cm�3). The constant atom number, temperatureand volume (NVT) ensemble, known as the canonical ensemble,was applied for both systems. First, the initial configuration wasminimized using the steepest descent and the conjugate gradientalgorithm until an energy gradient of 0.01 kcal mol�1 Å�1 wasreached. For the d-FeOOH and [MnH3buea(OH)]2� systems, a ther-malization phase of 500 ps, followed an additional period of 2.0 nswas employed.

The desired molecular properties of the FEOOH and[MnH3buea(OH)]2� were calculated from molecular dynamics sim-ulations using the FEOCH force field [39], which was developedand validated for the iron oxides and some metallic complexes.

2.3. Statistical inefficiency and hyperfine coupling constant (HFCC)calculations

The uncorrelated configurations from MD results were selectedfrom statistical calculations inefficiency using SciLab 2.7 software[40]. After MD simulations, uncorrelated structures of d-FeOOHand [MnH3buea(OH)]2� with water molecules were used for thehyperfine coupling constant (HFCC) calculations.

Hyperfine coupling constant (Aiso) calculations taking intoaccount the non-relativistic and relativistic effects were carriedout with uncorrelated structures from MD simulation. For bothsystems d-FeOOH and [MnH3buea(OH)]2�, the non-relativistic Aiso

calculations were performed using the functional PBE1PBE with

the basis set EPR-III for the hydrogen, oxygen and iron atoms inthe Gaussian 09 program and PBE1PBE with the basis set TZP[41] for all atoms in the ADF program. The relativistic effects weretaken into account by using the zero-order regular approximationincluding scalar and spin–orbit (SO) corrections (ZORA-SO) withthe functional PBE1PBE and basis set TZP [41] in the program ADF.

For the discussions of Aiso calculations, we used the followingnotation: level of Aiso computation//level of geometry optimizationor MD simulation. For example: (PBE1PBE(H2O)//PBE1PBE(H2O))means Aiso computation with explicit solvent//geometry optimiza-tion with explicit solvent; (PBE1PBE(H2O)/PCM//PBE1PBE(H2O))means Aiso computation with explicit and implicit solvent(PCM)//geometry optimization with explicit solvent molecules.Both situations consist of 300 water molecules in a cubic cell witha side of 20 Å. The (PBE1PBE(H2O)//PBE1PBE(H2O)) structures wereused as the start point for the MD simulations. The same notationis utilized when including the dynamic effect (MD simulation).

3. Results and discussion

3.1. Time correlation

The combination of NMR and MD can be studied to show andprovide a comprehensive description of fast conformationaldynamics of small molecules [42,43] in condensed phase. Thus,there are problems with working with a large number of confor-mations, because the number of quantum mechanical (QM) calcu-lations required is very high, since in every step an energyevaluation of the system is needed [44]. In the present study, wehave used statistically uncorrelated structures for quantummechanical calculations by using the energy autocorrelation func-tion from MD simulations [45,46]. This procedure was previouslydeveloped and validated by the Coutinho and Canuto’s group.

The statistical interval obtained from the energy autocorrela-tion function, C(n), is very important. For a markovian process,C(n) follows an exponential decay as demonstrated by theCanuto and Coutinho’s group [47]. The interval between uncorre-lated configurations, or the correlation step s, is calculated by inte-gration from zero to infinity of C(n). The theory shows thatconfigurations separated by 2s, or larger intervals, are considereduncorrelated [48,49]. This exponential decay can be seen in Fig. 2.

From the MD simulation, as seen in Fig. 2, the correlation timesfor water with d-FeOOH and [MnH3buea(OH)]2� were of 0.48 and0.13 ps, respectively. Thus, an increase of the d-FeOOH correlationtime compared with [MnH3buea(OH)]2� was observed.

3.2. Electronic and geometric effects on the hyperfine couplingconstant

The choice of computational methods for the HyperfineCoupling Constant calculation was based on a previous investiga-tion of Esteban-Gómez [50], which reported that the functionalPBE1PBE and the basis set EPR-III were closer to the experimentalvalues. In fact, the EPR-III basis set of Barone [11], is well optimizedfor hyperfine coupling constant calculations. It is a triple-zeta basisset including diffuse functions, double d-polarizations and a singleset of f-polarization functions. Also in this case the s-part isimproved to better describe the nucleus for hydrogen, boron andfluorine [50]. It is important to notice, however, that other basissets can be used for HFCC calculations as suggest by the JacobKongsted group, for example the basis set aug-cc-pVTZ-J [51,52].

It is well known that the NMR relaxation theory has been thesubject of numerous articles and books [53]. Along the years, theNMR relaxation parameters have been considered as one of themost useful methods for investigation of MRI probes as well as

Fig. 2. Graph of the auto-correlation function for the time in picoseconds. (a) d-FeOOH and (b) [MnH3buea(OH)]�2�. The blue curve is the correction and the redcurve the adjustment done. (For interpretation of the references to colour in thisfigure legend, the reader is referred to the web version of this article.)

M.A. Gonçalves et al. / Computational and Theoretical Chemistry 1069 (2015) 96–104 99

for detailed studies of molecular motion. The water proton magne-tization can be tipped into the transverse plane by supplyingenergy to the spin system with an RF pulse. Magnetic dipolar inter-actions between water protons with other local interactions, suchas magnetic fields produced by unpaired electrons, graduallyrestores the original orientation of the magnetization vector alongthe main magnetic field. This energy exchange process is opti-mized in the presence of paramagnetic atoms, which can drasti-cally reduce the solvent molecule relaxation time constants[47,54] according to Eqs. ((2) and (3)). Those equations representthe longitudinal and transverse relaxation time induced by param-agnetic ions in aqueous solution.

R1 ¼1T1ffi 1

15SðSþ 1Þg2b2g2

Nb2N

�h2r6þ A

�h

� �2 SðSþ 1Þ3

2se

1þ ðxIseÞ2

" #ð2Þ

R2 ¼1T2

ffi 115

SðSþ 1Þg2eb

2g2Nb2

N

h2r6þ A

�h

� �2 SðSþ 1Þ3

sC þsC

1þ ðxSseÞ2

" #ð3Þ

The relaxation time constant (T1 and T2) depends on the elec-tron spin (S), the electronic and proton g factors (ge and gN, respec-tively), the Bohr magneton (b), the nuclear magneton (bN), thehyperfine coupling constant (A), the ion-nucleus distance (r), and

the Larmor frequencies for the proton and electron spins (xI andxS, respectively). The transverse NMR relaxation of bound watermolecules is dominated by the scalar contribution, 1/T1 and 1/T2,as given in Eqs. ((1) and (2)) [55]. The correlation times sc and se

are characteristic of the rate of change of the interactions betweenthe metallic species and neighboring protons. Each of the relax-ation rates is a sum of two terms. The first term comes from thedipolar coupling and the second term from the scalar coupling.Hence, there is a dependence of the relaxation time on the s andhyperfine coupling constants values. This dependence is valid forall types of collisions, which leads to an expression for the relax-ation time (Eqs. (1) and (2)) [47]. The T1 and T2 paramagnetic ionsmost commonly found depend on the correlation times, sc and se,as well as hyperfine coupling constants [56]. Of particular signifi-cance here is that the electronic correlation time sc for the ferricand the ferrous ions is markedly different and their abilities to pro-mote spin relaxation differ considerably. This effect could, in prin-ciple, be one of the factors responsible for the T2 decrease [48]. Wehave used the relativistic (spin–orbit, SO) and non-relativistic(Fermi Contact, FC) effects for the hyperfine constant calculationsof the equilibrium structure, Aeq

iso, [57]. In fact, relativistic calcula-tions beyond FC have the contribution of the pseudocontact term(PC), which is very important to describe the relativistic systemproperties, Eq. (2). It is important to keep in mind, however, thatnon-relativistic calculations of hyperfine coupling constants are,then, equal to the Fermi contact (Aiso = AFC).

Aiso ¼ AFC þ APC ð4Þ

The psedocontact term can be assessed by various procedures.Corrections due to spin orbit coupling in spin-dipolar term existand were also implemented [58,59]. In this line, 1H and 17O hyper-fine Coupling Constant (HFCC) values were chosen as the parame-ter to evaluate the effect of the number of selected structures fromthe MD simulation, because Aiso is more sensitive than other geo-metrical parameters [21]. It is important to mention that confor-mations from a MD simulation were selected from statisticalinefficiency calculations, which are able to determine uncorrelatedconfigurations of the studied system. It is well-known that a fewuncorrelated configurations represent the statistical average ofall configurations in a large MD simulation [46]. For the complex[MnH3buea(OH)]2�, 80 uncorrelated structures were selected.Turning to iron oxide, 208 uncorrelated structures of d-FeOOH withwater were used for HFCC calculations.

In gases and liquids, the isotropic contribution is oneof the main parameters for the hyperfine coupling tensor [50].Initially, the HFCC calculations were carried out for the[MnH3buea(OH)]2� complex. In the structure in equilibrium(Aeq

iso(PBE1PBE(H2O)//PBE1PBE(H2O))) without relativistic effects,the HFCC values with the program Gaussian 09, at thePBE1PBE/EPR-III level, were 0.1 and 1.11 MHz for 1H and 17O and0.12 and 0.95 MHz at the PBE1PBE/TZP level with the programADF for 1H and 17O, respectively. The relativistic calculations withspin–orbit corrections (SO) had no significant difference for 1H,which also was expected, spin–orbit underlies the theory thatmade it possible to find the ways of overcoming spin prohibitionsin the case of weak intermolecular interactions and in the course ofchemical reactions, normally associated with heavy atoms. Theobtained values were 0.15 MHz for 1H and 1.22 MHz for 17O, a dif-ference of only 0.05 MHz for the 1H and 0.11 MHz for the 17O. For[MnH3buea(OH)]2�, thus, it is possible to conclude that the rela-tivistic effects have no significant influence on the 1H HFFC valuesfor this kind of complex. On the other hand, oxygen is more sensi-tive than hydrogen to relativistic effects. With the explicit solventand implicit in the system (Aeq

iso(PBE1PBE (H2O)/PCM//PBE1PBE(H2O))), the calculations showed that no significant difference

100 M.A. Gonçalves et al. / Computational and Theoretical Chemistry 1069 (2015) 96–104

was observed, in fact, the HFCC results were 0.10 MHz for the 1Hand 1.18 MHz for the 17O, a difference of 0.01 MHz for the 1Hand 0.07 MHz for the 17O, these values are shown in Table 2. Ourfindings point out, then, that our system with the implicit solventis a good model for the Aiso calculation. These values can beexplained by the strong hydrogen bond (confirmed by the QTAIMcalculations) between the hydrogen of the water molecules withthe oxygen atoms of the complex (Fig. 3a). As expected, oxygenis more sensitive than hydrogen to Aiso parameters. It is importantto notice that the PCM methodology has been widely used since1981 for studying chemical phenomena in solution [35,36].

The theoretical Aiso values for Mn2+ atoms are close to theexperimental results, as seen in Table 2. In fact, AFC (absence of rel-ativistic effect) and APC (presence of relativistic effects) values are194.40 and 206.50 MHz, respectively. The relativistic effectscorrespond to an increase of about 12.1 MHz. When the thermalcorrection for the non-relativistic effects are included in thecalculation, this difference decreases to 4.50 MHz.

Compare Aeqiso(PBE1PBE(H2O)//PBE1PBE(H2O)) and A300K

iso (MD(H2O)//MD(H2O)) in Table 2. The only available experimental value for[MnH3buea(OH)]2� is the Aiso value for the Mn2+ atom. In this line,this information is crucial to evaluate the theoretical strategy usedfor Aiso calculations.

Furthermore, in order to validate the theoretical strategy for 1Hand 17O hyperfine coupling constants calculations, the complexes[Mn(EDTA)(H2O)]2��5H2O and [Mn(H2O)6]2+, which had beenwidely used as a contrast agent in MRI, were also investigated[60,61]. In this line, a good agreement between theoretical andexperimental data was observed for both complexes as reportedin Table 1. For [Mn(EDTA)(H2O)]2��5H2O, according to Table 1,the Aiso values for the 17O HFCC values were of 5.00 and

Table 1Aiso values for [Mn(EDTA)(H2O)]2��5H2O and [Mn(H2O)6]2+ at the PBE1PBE/EPR-IIIlevel.

Compounds 1H (MHz) 17O (MHz)

AFC AFC + APC AFC AFC + APC

[Mn(EDTA)(H2O)]2��5H2O 2.07 – 5.22 –1.87a 2.85b 5.00a 5.23b

Experimental [60] – 6.45[Mn(H2O)6]2+ 0.87 – 5.32 –

0.81a 0.93b 5.38a 5.43b

Experimental [61] 0.86 5.40

a Results at the non-relativistic PBE1PBE/TZP level.b Results at the ZORA-SO-PBE1PBE/TZP level.

Table 2Aiso values for [MnH3buea(OH)]2� and d-FeOOH at the PBE1PBE/EPR-III level.

1H (MHz)

AFC AFC + APC

Water in the presence of [MnH3buea(OH)]�2

Aeqiso(PBE1PBE(H2O)//PBE1PBE(H2O)a) 0.10 –

0.12b 0.15c

Aeqiso PBE1PBE (H2O)/PCM//PBE1PBE(H2O) 0.11 –

A300Kiso (MD(H2O)//MD(H2O)) 0.22 –

Experimental –

Water in the presence of d-FeOOHAeq

iso (PBE1PBE(H2O)//PBE1PBE(H2O)a) 2.76 –

2.22b 2.04c

Aeqiso PBE1PBE (H2O)/PCM//PBE1PBE(H2O) 2.78 –

A300Kiso (MD(H2O)//MD(H2O)) 2.88 –

a Notation ‘level of HFCC computation//level of geometry optimization or MD simulatb Results at the non-relativistic PBE1PBE/TZP level.c Results at the ZORA-SO-PBE1PBE/TZP level.

5.23 MHz with and without relativistic effects, respectively. It isimportant to notice that the experimental result for the same com-plex is 6.45 MHz. Turning now to the complex [Mn(H2O)6]2+, thenon-relativistic 1H HFCC value was 0.81 MHz. However, for thesame complex, the computed value including the relativisticeffects with spin–orbit corrections (SO) was 0.93 MHz. On goingfrom the AFC values to relativistic calculations, the concomitantchanges are 5.38 and 5.43 MHz for the 17O HFCC values. Thus,the agreement between theoretical and experimental results isclear, because the experimental 17O HFCC value is 5.40 MHz.

In fact, we can realize that the theoretical results corroboratethe experimental values. The good agreement with the experimen-tal can be confirmed by theoretical calculations of hyperfine cou-pling constants (A) [59]. Thus, the calculations are consistent andthe methodology used is in good agreement with experimentalresults for 1H, 17O and 55Mn hyperfine coupling constants.Therefore, from our findings, HFCC values with and without rela-tivistic effects are in good agreement with experimental data, indi-cating that the theoretical strategy used was fairly consistent.

As discussed by Iglesias and coworkers [51], geometricalparameters, such as the dihedral angle (N–Mn–O–H) and theMn–O bond length are important features that modulate HFFC val-ues. Table 3 shows that the Mn–O bond length is shorter than thatof Mn–Ow, as expected, because the Mn–OH bond has a lowersteric hindrance compared to the Mn–OH2 bond, both in the com-plex [Mn(EDTA)(H2O)]2� as well as [Mn(MeNO2A)(H2O)], as speci-fied in Table 3. In the complex studied, [MnH3buea(OH)]2�, theMn–O bond length obtained was 1.95 Å. It should keep in mindthat the N–Mn–O–H dihedral angle also modifies the HFCC values,which varied considerably during our simulations [22].

Tables 3 and 4 show bound lengths in Ångstrøm for the com-plex [Mn(EDTA)(H2O)]2�, for instance, the bond Mn–OH has alength of 1.95 Å, as reported in Table 3. The Mn–NC bond, whereNC is the nitrogen atom bonded directly to a carbon atom, featuresa bond length of 1.95 Å. The Mn–NCO bond, where the NCO atom isthe nitrogen atom bonded directly to a carbon atom making a dou-ble bond with oxygen, has a length of 2.06 Å. The Mn–NCO bondfeatures a larger bond length than the Mn NC bond. For thed-FeOOH, the Fe–O bond has a length 2.04 Å, and the Fe–Fe,2.28 Å. The Fe–Fe chemical bond is longer than the Fe–O bond,which is quite common for complexes and iron oxides [62].

Turning now to the d-FeOOH structure in the equilibrium struc-ture (Aeq

iso(PBE1PBE(H2O)//PBE1PBE(H2O))) without relativisticeffects, the 1H and 17O HFCC values were, at the PBE1PBE/EPR-IIIlevel, 2.76 and 2.80 MHz obtained from the program Gaussian09, and 2.22 and 2.51 MHz with the program ADF at the

17O (MHz) 55Mn2+ (MHz)

AFC AFC + APC AFC AFC + APC

1.11 – 194.40 –

0.98b 1.22c 170.08b 206.50c

1.18 – 170.75 –

2.36 – 202.00 –

– 250.00

2.80 – – –

2.51b 2.60c – –3.10 – – –

3.02 – – –

ion’.

Fig. 3. Typical snapshot from a MD simulation of (a) [MnH3buea(OH)]�2 with water and (b) d-FeOOH with water.

Table 3Bond length values of Mn–O for [MnH3buea(OH)]�2.

Complex Bond Bond length (Å)

[MnH3buea(OH)]�2 Mn–OH 1.95[Mn(EDTA)(H2O)]�2 Mn–Ow 2.43[Mn(MeNO2A)(H2O)] Mn–Ow 2.23

Table 4Selected bond length values for [MnH3buea(OH)]�2 and d-FeOOH.

Structure Bond Bond length (Å)

Mn–OH 1.95[MnH3buea(OH)]�2 Mn–NC 1.95

Mn–NCO 2.06

d-FeOOH Fe–O 2.04Fe–Fe 2.28

Table 5Additional atomic properties obtained by QTAIM calculations for hydrogen bondedatoms (in au) of the [MnH3buea(OH)]�2.

Structure q(H) M1(H) V(H) E(H)

1H(OH) +0.491 +0.298 +28.825 �0.3872H(a). . .O(a) +0.632 +0.180 +14.922 �0.323

Table 6Additional atomic properties obtained by QTAIM for hydrogen bonded atoms (in au)of the d-FeOOH.

Structure q(H) M1(H) V(H) E(H)

1H(OH) +0.148 +0.298 +54.554 �0.5632H(a). . .O(a) +0.454 +0.197 +24.281 �0.440

M.A. Gonçalves et al. / Computational and Theoretical Chemistry 1069 (2015) 96–104 101

PBE1PBE/TZP level for 1H and 17O, respectively. Taking into accountthe relativistic effects (spin–orbit), the 1H and 17O HFCC resultswere 2.04 for 1H and 2.60 MHz for 17O HFCC. The calculation withboth explicit and implicit solvents (PCM) in the system(Aeq

iso(PBE1PBE(H2O)/PCM//PBE1PBE (H2O))) point out values of2.78 MHz for the 1H and 3.10 MHz for the 17O. This means only adifference of 0.02 MHz for the 1H and 0.30 MHz for the 17Obetween (Aeq

iso(PBE1PBE(H2O)//PBE1PBE(H2O))) and (Aeqiso(PBE1PBE

(H2O)/PCM//PBE1PBE(H2O))), thus, the Aiso values do not differ sig-nificantly in the system. The number of water molecules with theexplicit solvent is adequate for the Aiso calculations. This approachhas provided very similar thermal effects, when the effect ofimplicit solvent was introduced into the system. On going from

the static equilibrium values to the thermal averages (A300Kiso

(MD(H2O)//MD(H2O))), the concomitant changes are 2.88 and3.02 MHz for the 1H and 17O HFCC values. We have, then, observedthat the 1H and the 17O are quite sensitive to parameter Aiso. Thesevalues can be explained by the strong interaction between nuclearspins of water molecules in the proximity and the electron spin ofthe Fe ions, which can be seen in Fig. 3b, where the water mole-cules interact with iron and oxygen atoms from the d-FeOOH struc-ture, as well as among the water molecules themselves.

According to Table 2, 1H and 17O of d-FeOOH are more sensitiveto the hyperfine constant parameters than the complex[MnH3buea(OH)]2�, for instance 0.10 and 1.11 MHz versus 3.74and 2.80 MHz for Aeq

iso(PBE1PBE(H2O)//PBE1PBE(H2O)) in[MnH3buea(OH)]2� and d-FeOOH, respectively. The same behavioris also observed for [Mn(H2O)6]2+, whose the experimental 1H

HFCC value is 0.86 MHz. Whereas both compounds are capable ofincreasing the Aiso values of the water molecules, d-FeOOH showsa higher influence. In spite of [Mn(EDTA)(H2O)]2��5H2O and[Mn(H2O)6]2+ are commonly used contrast agents, surprisingly,the 1H hyperfine coupling constants for those compounds arelower or similar in terms of magnitude in relation to d-FeOOH.This feature could, in principle, put in evidence the use ofd-FeOOH as a promising contrast agent for MRI.

Eqs. ((1) and (2)) are able to associate the Aiso values with therelaxation times T1 and T2, which indicate longer relaxation timesfor d-FeOOH. Actually, our findings suggest that both compounds,d-FeOOH and [MnH3buea(OH)]2�, can act as contrast agents inMRI, since d-FeOOH possesses longer relaxation times (T1 and T2),thus pointing out d-FeOOH as a promising alternative to be usedas a contrast agent.

3.3. Quantum theory of atoms in molecules (QTAIM) and natural bondorbitals (NBO) analysis

In order to evaluate the influence of hydrogen bonds on thehyperfine constants as well as electronic and spectroscopic proper-ties of the molecular aggregates (d-FeOOH and [MnH3buea(OH)]2�)with water molecules, QTAIM and NBO calculations were carriedout. In fact, the electron distribution analysis of a molecule is apromising starting point to obtain chemical insight into a moleculeor an aggregate of molecules [63]. Among all known electron den-sity methods, an appealing theory that takes advantage of thisobservation is the ‘‘Atoms in Molecules’’ model (AIM) [64]. Thus,the QTAIM and NBO calculations are very important in an attemptto understand the nature of the chemical bond (for example, if thebond is covalent, partially covalent or noncovalent).

Table 7QTAIM parameters obtained at the hydrogen bond BCPs for the structures of 1–2 (au) (Structures:1: [MnH3buea(OH)]�2 with water and 2: d-FeOOH with water).

Structure q(r) r2q(r) e V(r) G(r) H(r)

1a(Oa. . .Ha) +0.026054 +0.075588 +0.083473 �0.019435 +0.019166 �0.0002691b(Ob. . .Hb) +0.023328 +0.057532 +0.148430 �0.017510 +0.015946 �0.0015642a(Oa. . .Ha) +0.018195 +0.075304 +0.353814 �0.013814 +0.016320 �0.0025062b(Ob. . .Hb) +0.019287 +0.052765 +0.878977 �0.019241 +0.003025 �0.0162162c(Fea. . .Oc) +0.018886 +0.025838 +0.810782 �0.008555 +0.007508 +0.001048

Fig. 4. Orbitals of d-FeOOH.

102 M.A. Gonçalves et al. / Computational and Theoretical Chemistry 1069 (2015) 96–104

From those calculations, it is possible to characterize hydrogenbonds between the atoms involved and to investigate orbitals thatare participating in this interaction with their respective energyvalues.

The QTAIM calculations significantly corroborate the HFCC val-ues for both cases d-FeOOH and [MnH3buea(OH)]2�. On analyzingthe complex [MnH3buea(OH)]2�, Table 5 shows atomic charge (q),first dipole moment (M1), atomic volume (V) and atomic energy (E)values. From our calculations, the studied structures are capable offorming hydrogen bonds according to the criteria proposed byKoch and Popeliers. Strong hydrogen bonds are characterized bya decrease of the M1(H) and V(H) values as well as an increase ofq(H) and E(H). Table 7 shows the value for 1a and 1b (the atomsare specified in Fig. 3). The atoms in 1a and 1b have partially cova-lent interaction according to the parameters r2q(r) > 0 andH(r) < 0 [65]. The results showed that the solvent water molecules

Fig. 5. Electronic density, (a) d-FeOOH and water molecules and

and the oxygen of the complex can form strong hydrogen bonds.NBO analysis stresses the role of intermolecular orbital interac-tions in the complex, particularly charge transfer. This is carriedout by considering all possible interactions between filled donorand empty acceptor NBOs and estimating their energetic impor-tance by second-order perturbation theory [66]. The results revealthat the electronic relocation starting from the free electron pairsof the oxygen atom (LP1 + LP2) to the antibonding orbital O–H,(nO ? r⁄OH) may contribute significantly to the increase of thehyperfine constant (Aiso). According to our calculations, this interac-tion nO ? r⁄OH has an energy of 0.95 kcal mol�1 which contributes tosystem stabilization.

By evaluating Table 6, which reports the values of atomic charge(q), first dipole moment (M1), atomic volume (V) and atomic energy(E) for d-FeOOH, we can notice that the structures are capable offorming hydrogen bonds according to the criteria already specifiedabove. Table 7 shows the analyzed parameter values for 2a, 2b and2c (the atoms are specified in Fig. 3b) are the atoms selected in thed-FeOOH structure. According to the Koch and Popeliers parame-ters, the atoms in 2a and 2b possess r2q(r) > 0 and H(r) < 0, whichindicate partly covalent interactions. On the other hand, the atomsin 2c have weak interaction parameters, as discussed by Koch andPopelier,r2q(r) > 0 and H(r) > 0, and suggest non-covalent interac-tions. In this case, the electrostatic interaction is the dominant,thus, the energy coefficient is low. The NBO calculation resultsare in agreement with the AIM data [67–70]. From our findings,in the interaction nO ? dFe, the pair of electrons in the orbital pof oxygen is donating to the empty orbital d of iron (Fig. 4) andcontributes significantly to the increase of the hyperfine constant(Aiso), (Fig. 4). The OH� � �H interaction, as shown in Fig. 4, representsa type of relatively strong hydrogen bond, the existence ofnO ? r⁄OH contributes to stabilizing the system. According to thecalculations, the Fe� � �O interaction is able to strongly influencethe hyperfine constant data with an interaction energy of

(b) [MnH3buea(OH)]�2 in the presence of water molecules.

M.A. Gonçalves et al. / Computational and Theoretical Chemistry 1069 (2015) 96–104 103

1.16 kcal mol�1, while the OH� � �H hydrogen bond has an energyvalue of 0.12 kcal mol�1.

Fig. 5a displays the electronic density map of[MnH3buea(OH)]2�, which reinforces a higher electronic densityaround the water molecules, the molecules form hydrogen bondswith oxygen in the complex, thus increasing the electron density.Thus, a transfer charge to the iron atom from the water moleculecan take place; which could in principle, rationalize the Aiso

increase.

4. Conclusions

From our results, the calculations showed that no significantdifference was observed between implicit and explicit solvent inthe system. The theoretical findings also highlight that both[MnH3buea(OH)]2� and the d-FeOOH significantly alter the Aiso val-ues. Our results for [MnH3buea(OH)]2� indicate that 17O is moresensitive than 1H hyperfine coupling constants (HFCCs) to solventand thermal effects, while for the d-FeOOH both the 1H and 17OHFCCs values are sensitive to solvent and thermal effects. NBOand QTAIM calculations were carried out to study the nature ofthe chemical bond and verify its influence on the increase of Aiso.

The theoretical description of the solute–solvent interaction aswell as the thermal effects and their influence on spectroscopyproperties of solute is a crucial concern in theoretical chemistry.Currently, little attention has been given to the spectroscopic stud-ies of the NMR relaxation parameters. In this line, the present workwas devoted to the theoretical study of [MnH3buea(OH)]2� andd-FeOOH (100). From our findings, d-FeOOH possesses longerrelaxation times (T1 and T2) due to both higher changes of Aiso aswell as a longer correlation time for water molecules around theFe atom in relation to the Mn atom. Therefore, our findings suggestthat polymorphs of iron oxyhydroxides, such as d-FeOOH, can be apromising alternative to be used as a contrast agent. Thus, westrongly feel that this study could be helpful for the design andselection of new MRI CAs.

Acknowledgements

The authors thank the Brazilian agencies FAPEMIG, CAPES, andCNPq for the financial support of this research and UFLA for infras-tructure and encouragement in this work. T.C.R. thanks also theinvited professor position at the Czech Republic Center for Basicand Applied research.

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