Jana Kopřivová
email: koprivova@pcp.lf3.cuni.cz

Marco Congedo

Jiří Horáček

Ján Praško

Michal Raszka

Martin Brunovský

Barbora Kohútová

Cyril Höschl

EEG source analysis in obsessive

Keywords: compulsive disorder obsessive-compulsive disorder (OCD), standardized low-resolution electromagnetic tomography (sLORETA), independent component analysis (ICA), medial frontal cortex

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INTRODUCTION

Obsessive-compulsive disorder (OCD) is a common neuropsychiatric disorder marked by recurrent intrusive thoughts (obsessions) and repetitive behaviours (compulsions) with a prevalence of 2-3% [START_REF] Karno | The epidemiology of obsessive-compulsive disorder in five US communities[END_REF]. Neuroimaging studies provide evidence for the involvement of cortico-striatal circuits in OCD pathophysiology [START_REF] Aouizerate | Pathophysiology of obsessive-compulsive disorder: a necessary link between phenomenology, neuropsychology, imagery and physiology[END_REF]. The traditional and most widely accepted model, supported by a large body of scientific evidence, postulates a hyperactive orbitofronto-striatal circuit including orbitofrontal and cingulate cortex, ventral striatum, ventral pallidum, mediodorsal thalamus, hippocampus and amygdala (Menzies et al., 2008a). However, accumulating evidence from various methodological approaches suggests that OCD is mediated by more widely distributed neural networks including also dorsal brain regions such as dorsolateral prefrontal cortex [START_REF] Gu | Neural correlates of cognitive inflexibility during taskswitching in obsessive-compulsive disorder[END_REF][START_REF] Remijnse | Reduced orbitofrontal-striatal activity on a reversal learning task in obsessive-compulsive disorder[END_REF][START_REF] Van Den Heuvel | Frontal-striatal dysfunction during planning in obsessive-compulsive disorder[END_REF], parietal cortex (Menzies et al., 2008b) or cerebellum [START_REF] Nabeyama | Functional MRI study of brain activation alterations in patients with obsessive-compulsive disorder after symptom improvement[END_REF][START_REF] Van Den Heuvel | The major symptom dimensions of obsessive-compulsive disorder are mediated by partially distinct neural systems[END_REF]. A recent multimodal review and meta-analytic study by Menzies et al. (2008a) proposed a more comprehensive OCD model including two relatively segregated fronto-striatal networks: affective orbitofronto-striatal loop and dorsolateral prefrontostriatal loop which also includes parietal and lateral prefrontal cortex and subserves spatial and attentional functions. Aberrant functioning and imbalanced interactions between frontostriatal networks might explain clinical OCD symptoms and neuropsychological deficits such as excessive perception of error [START_REF] Ullsperger | The role of intact frontostriatal circuits in error processing[END_REF], abnormal reward processing [START_REF] Remijnse | Reduced orbitofrontal-striatal activity on a reversal learning task in obsessive-compulsive disorder[END_REF], cognitive and behavioural inflexibility [START_REF] Gu | Neural correlates of cognitive inflexibility during taskswitching in obsessive-compulsive disorder[END_REF] and difficulty to inhibit prepotent responses [START_REF] Roth | Event-related functional magnetic resonance imaging of response inhibition in obsessive-compulsive disorder[END_REF]. Electroencephalographic (EEG) studies based on quantitative analysis reported abnormalities registered at frontal or frontotemporal electrode sites in OCD (e.g. [START_REF] Karadag | Quantitative EEG analysis in obsessive compulsive disorder[END_REF][START_REF] Pogarell | Symptom-specific EEG power correlations in patients with obsessive-compulsive disorder[END_REF][START_REF] Prichep | Quantitative electroencephalographic subtyping of obsessive-compulsive disorder[END_REF]. However, only limited attention has been paid to the localization of generators of the aberrant EEG activity in OCD. EEG sources have been investigated in relation to treatment response [START_REF] Bolwig | Toward a better understanding of the pathophysiology of OCD SSRI responders: QEEG source localization[END_REF][START_REF] Fontenelle | Low-resolution electromagnetic tomography and treatment response in obsessive-compulsive disorder[END_REF] and in subjects with obsessive-compulsive symptoms [START_REF] Sherlin | Obsessive-compulsive dimension localized using low-resolution brain electromagnetic tomography (LORETA)[END_REF] and recently also in drug naïve obsessive-compulsive patients [START_REF] Velikova | Dysfunctional brain circuitry in obsessive-compulsive disorder: source and coherence analysis of EEG rhythms[END_REF]. All studies using low-resolution electromagnetic tomography in OCD [START_REF] Fontenelle | Low-resolution electromagnetic tomography and treatment response in obsessive-compulsive disorder[END_REF][START_REF] Sherlin | Obsessive-compulsive dimension localized using low-resolution brain electromagnetic tomography (LORETA)[END_REF][START_REF] Velikova | Dysfunctional brain circuitry in obsessive-compulsive disorder: source and coherence analysis of EEG rhythms[END_REF] reported significant results in anterior cingulate (ACC). In addition, abnormal ACC functioning in OCD has been supported by evoked-potential EEG research that revealed an enhanced error-related negativity (ERN) in OCD patients. ERN is generated after erroneous response or in conflict situations and reflects activity of the performance monitoring system in OCD [START_REF] Endrass | Overactive performance monitoring in obsessive-compulsive disorder: ERP evidence from correct and erroneous reactions[END_REF]. Its source has been localized near to dorsal ACC [START_REF] Dehaene | Localization of a neural system for error detection and compensation[END_REF] using electrophysiological inverse solution methods as well as simultaneous EEG and fMRI recording [START_REF] Debener | Trial-by-trial coupling of concurrent electroencephalogram and functional magnetic resonance imaging identifies the dynamics of performance monitoring[END_REF]. Functional magnetic resonance studies confirmed the overactivity of the performance monitoring system in OCD and its link with ACC and medial frontal cortex hyperactivation [START_REF] Fitzgerald | Error-related hyperactivity of the anterior cingulate cortex in obsessive-compulsive disorder[END_REF][START_REF] Ursu | Overactive action monitoring in obsessive-compulsive disorder: evidence from functional magnetic resonance imaging[END_REF]. It has been hypothesized that an overactive performance monitoring system generates a feeling that something is wrong or not just right and triggers compulsive behaviour, thus providing a possible explanation how brain abnormalities translate in clinical symptoms of OCD [START_REF] Maltby | Dysfunctional action monitoring hyperactivates frontal-striatal circuits in obsessive-compulsive disorder: an event-related fMRI study[END_REF]. Our study aimed to compare resting state current density power in intracortical sources between OCD patients and control subjects as well as between unmedicated patients and patients medicated with selective serotonin reuptake inhibitors (SSRIs). To address this issue we used two different methods of EEG analysis: standardized low-resolution electromagnetic tomography (sLORETA) and normative independent component analysis (NICA) recently described by [START_REF] Congedo | Group Independent Component Analysis of Resting-State EEG in Large Normative Samples[END_REF]. sLORETA [START_REF] Rd | Standardized low-resolution brain electromagnetic tomography (sLORETA): technical details[END_REF]) is a widely used inverse solution technique that estimates the intracranial distribution of electrical activity in the cortex based on a head model. ICA is a data-driven (i.e. model-free) technique widely used to decompose the multivariate EEG signal into sources as independent as possible [START_REF] Congedo | On the blind source separation of human electroencephalogram by approximate joint diagonalization of second order statistics[END_REF][START_REF] Onton | Imaging human EEG dynamics using independent component analysis[END_REF]. The assumption of EEG source independence is consistent with the fact that the cortex is organized into functionally distinct areas and that neighbouring and highly connected regions (e.g. via corpus callosum) are likely to fire in synchrony [START_REF] Onton | Imaging human EEG dynamics using independent component analysis[END_REF]. Physical and statistical principles supporting the use of decomposition methods based on secondorder statistics for EEG data have been reviewed in [START_REF] Congedo | On the blind source separation of human electroencephalogram by approximate joint diagonalization of second order statistics[END_REF]. Whereas sLORETA focuses on voxel by voxel analysis without searching for relationships between them, ICA separates the signal based on its intrinsic relationships. For example, sLORETA may identify abnormal power in a cluster containing a number of independent sources that ICA would split into several components. On the other hand ICA would group correlated sources into the same components, even if they are distant in space from each other. The two methods provide complementary information and their application on the same data may provide a more comprehensive and consistent view, especially considering a high sample size as in this study.

METHODS

Subjects

Fifty in-patients diagnosed with OCD according to ICD-10 (World Health Organisation, 2009) and DSM-IV (American Psychiatric Association, 1994) criteria and 50 healthy controls matched for age, sex and handedness were included in the study (Table 1). Exclusion criteria involved concurrent severe or chronic medical disease, substance abuse, mental retardation, organic mental disorder, lifetime history of psychosis, mood disorders, severe head injury and neurosurgery. In addition, controls were required to have no history of any mental disorder. At the time of EEG recording, 20 patients were drug-free and 30 were using SSRIs medication. The medication status was stable for at least four weeks prior to the study. Besides the diagnosis of OCD, the rationale to include both SSRIs medicated and drug-free patients was the presence of marked clinical symptoms that could possibly be reflected in EEG. At the same time, the drug-free subgroup served as a reference group allowing a control of the effect of the SSRIs medication. Clinical data in the patient group included age of OCD onset, illness duration and symptom severity (Table 1). Symptom severity was assessed using the Yale-Brown Obsessive Compulsive Scale (Y-BOCS) [START_REF] Goodman | The Yale-Brown Obsessive Compulsive Scale. I. Development, use, and reliability[END_REF]. The level of general anxiety was measured with the Hamilton Anxiety Rating Scale (HAMA) [START_REF] Hamilton | The assessment of anxiety states by rating[END_REF]. The study was carried out in accordance with the Declaration of Helsinki and written informed consent was obtained from all subjects.

EEG recording and data preprocessing

EEG was recorded during eyes-closed resting state on a BrainScope differential amplifier (Unimedis, Ltd., Czech Republic) against the AFz, FCz or Cz reference. The signal was obtained from 19 scalp locations according to the international 10-20 system using an ECI electro-cap (Electro-Cap International, Inc., Eaton, USA). The EEG recording system acquired the data with a 16-bit depth and a 7.63 nV/bit resolution (i.e. approx. 130 bit/ µV) and a dynamic range of ± 250 µV. The data were sampled at a rate of 250 or 256 Hz and filtered with a 0.15 -70 Hz band-pass filter.

Data were imported to EureKa software (NovaTechEEG, Inc., Mesa, Arizona, USA) to remove episodic artefacts. If necessary, continuous muscle artefacts were removed as independent components using ICoN software (http://sites.google.com/site/marcocongedo/software/nica). This procedure was done by a trained clinician with a special attention to K-complexes and was equal in both groups. At least 60 s of artefact-free data were analyzed in subsequent analysis. Before analysis, all data filtered between 2 -45 Hz were re-referenced against the average reference montage and re-sampled at 128 Hz. Several comparisons of subgroups recorded with different references and re-referenced against the average reference montage were performed by means of sLORETA and normative group ICA confirming that there was no systematic effect due to different recording references. Mean normalized absolute power at all electrodes for both groups of subjects is shown in Figure 1.

sLORETA analysis

Average Fourier cross-spectral matrices were computed for each frequency in the range of 2 -45 Hz with 1 Hz resolution as well as for 11 frequency bands defined analogous to the previous LORETA study in obsessivecompulsive subjects [START_REF] Sherlin | Obsessive-compulsive dimension localized using low-resolution brain electromagnetic tomography (LORETA)[END_REF]: delta (2 -3.5 Hz), theta (4 -7.5 Hz), alpha1 (8 -10 Hz), alpha2 (10 -12 Hz), beta1 (12 -16 Hz), beta2 (16 -20 Hz), beta3 (20 -24 Hz), beta4 (24 -28 Hz), beta5 (28 -32 Hz), gamma (32 -45 Hz) and total band (2 -45 Hz). Subsequently, absolute and relative current density power were computed in 2394 cortical voxels using sLORETA and the three-shell spherical head model coregistered with the Talairach atlas as implemented in the LORETA-Key software (Key Institute for Brain-Mind Research, Zurich, Switzerland). Current density power was normalized in the solution volume. Absolute and relative current density data were log transformed, smoothed with a 14 mm spatial moving average filter and compared between groups (drug-free vs. medicated patients, all patients vs. controls, drug-free patients vs. controls and medicated patients vs. controls) by means of randomization-permutation statistics (100 000 permutations) using MHyT software (NovaTechEEG, Inc.). All bands were treated simultaneously in the tbetween two-sided max-statistics test guaranteeing that the family-wise type I error (FWE) did not exceed the nominal level (0.05). Mean current densities in the significant regions of interest (ROIs) were extracted and a correlation analysis was performed to investigate their relationships with clinical symptoms as assessed with Y-BOCS, the level of general anxiety measured with HAMA, age of onset and illness duration. A partial correlation analysis was used to eliminate the potential confounding effect of age. Before the analysis, all data were tested for severe departures from gaussianity.

Group ICA and group comparison

We employed the blind source separation approach described in [START_REF] Congedo | On the blind source separation of human electroencephalogram by approximate joint diagonalization of second order statistics[END_REF] that can separate uncorrelated sources provided they have non-proportional power spectrum. For normal brain we have reasons to suppose that a great majority of healthy individuals share the same resting-state components (discussed in [START_REF] Congedo | Group Independent Component Analysis of Resting-State EEG in Large Normative Samples[END_REF] which ensures that the group components are meaningful. However, the same may not be true for the clinical sample, which is in general much more heterogeneous in terms of EEG features. Therefore, in this research, we have focused on the identification of normal EEG features that deviate significantly in the OCD population. The procedure used in this study is fully explained in [START_REF] Congedo | Group Independent Component Analysis of Resting-State EEG in Large Normative Samples[END_REF]. In brief, we estimated Fourier cospectral matrices for each subject in the control group and each frequency. Group ICA was performed as the approximate joint diagonalization of the grand-average Fourier cospectral matrices. We diagonalized cospectra in the range of 2 -26 Hz. Based on the previous study by [START_REF] Congedo | Group Independent Component Analysis of Resting-State EEG in Large Normative Samples[END_REF] on large samples of normal individuals we extracted the seven most energetic components (normative components). The resulting demixing matrix was used to extract the power of the same components from the OCD group as well as to compute the mixing matrix which contains in columns scalp spatial pattern associated with each components and thus can serve as an input for sLORETA to estimate their cortical location. For each component, absolute, relative and normal power (normal power indicates for each frequency the proportion of power expressed by each component compared to the all of them) were computed with 1 Hz resolution and compared to normative data obtained from the control group using the randomization-permutation multiple-comparison approach as in sLORETA. The individual power values were used for correlation analyses as described above.

RESULTS

Demographic data

All groups were equivalent for age, sex and handedness. Drug-free and SSRIs medicated OCD patients did not differ in clinical characteristics with the exception of higher compulsion score in medicated patients (Table 1). The mean Y-BOCS scores 19.4 indicates marked severity of obsessive-compulsive symptoms. sLORETA Drug-free and SSRIs medicated patients did not differ from each other in absolute or in relative power, therefore they were further tested as a unitary group. Compared with controls, OCD patients had higher normalized absolute current density power at low frequencies (2 -6 Hz) in the medial frontal cortex (anterior cingulate, medial frontal gyrus, medial orbitofrontal cortex) and at 2 and 3 Hz frequencies in the left parahippocampal gyrus and uncus (Table 2). The highest t-values were localized in the dorsal anterior cingulate (t max = 4.24, p < 0.05, FWE corrected, Figure 2). A comparison of the SSRIs and control groups yielded the same results (t max = 4.39, p < 0.05, FWE corrected). A comparison of drug-free patients and controls was not significant at p < 0.05, however, moving the t-value threshold down the same pattern of increased low frequencies in the medial frontal cortex was seen also in drug-free OCD patients (local t-value maxima 2.44, 2.58, 3.07, 3.32, 3.33 were found at 2, 3, 4, 5 and 6 Hz respectively, Figure 3). In a broader band comparison, delta and theta absolute current density power were higher in OCD (t max = 4.39, p < 0.05, FWE corrected). Relative power also tended to be higher in OCD patients in the same region and frequencies as absolute power, however, the significance threshold was exceeded only at 5 Hz and was localized in the dorsal ACC. Additionally, an increase in relative current density at 18 and 19 Hz was found in a very small cluster (7 and 3 voxels, respectively) in the right superior and middle temporal gyrus (t max = 3.77, p < 0.05, FWE corrected). In broader band testing, OCD patients had higher relative power in the beta2 band in a small area of the right superior and middle temporal gyrus (t max = 3.57, p < 0.05, FWE corrected). Correlation analysis did not reveal any relationship between low-frequency current density power and obsessive-compulsive symptoms, anxiety, age of onset and illness duration.

Group ICA

The 7 components separated through the group independent component analysis performed on the whole control sample are shown in Figure 4. Only component 5 differed in power between OCD patients and controls (p < 0.05, corrected). Relative power was higher in OCD at low frequencies (3 -6 Hz) and normal power was elevated at 2 -6 Hz and at 20 Hz (Figure 5). The local maxima of this component were localized in subgenual anterior cingulate (BA 25), subcallosal gyrus (BA 34), rectal gyrus (BA 11), insula (BA 13), superior temporal and parahippocampal gyrus (BA 38), midcingulate (BA 24) and marginally in lateral frontal lobe (BA 6,8,9). The component was bilateral and more pronounced on the left side. When comparing separately, neither drug-free nor medicated patients showed any difference compared with controls at the adopted threshold (p < 0.05, corrected). However, both groups displayed the same pattern of difference from controls at lower significance level (p < 0.1, corrected). Correlation analysis did not reveal any relationship between component 5 power at frequencies that were significant in the inter-group analysis and obsessive-compulsive (Y-BOCS) or anxiety (HAMA) rating scale scores. Age of onset showed a trend towards a positive correlation with normal power in component 5 at 4 and 5 Hz (r = 0.27, p = 0.078, resp. r = 0.27, p = 0.082).

DISCUSSION

Both methods, sLORETA and group ICA, indicated abnormal functioning of medial frontal cortex in OCD. The results converge with the leading orbitofronto-striatal model of OCD as well as with the performance monitoring hypothesis. The orbitofronto-striatal model postulating hyperactivation of the medial frontal cortex has been reported using a variety of methodological approaches [START_REF] Rotge | Provocation of obsessive-compulsive symptoms: a quantitative voxel-based meta-analysis of functional neuroimaging studies[END_REF]Yucel et al., 2007). Low frequencies generated in the frontal midline cortex have been connected with mental activity [START_REF] Onton | Frontal midline EEG dynamics during working memory[END_REF] and higher cerebral glucose metabolism [START_REF] Leuchter | Relationship between brain electrical activity and cortical perfusion in normal subjects[END_REF][START_REF] Pizzagalli | Coupling of theta activity and glucose metabolism in the human rostral anterior cingulate cortex: an EEG/PET study of normal and depressed subjects[END_REF]. Thus, our findings are in agreement with medial frontal hyperactivation in OCD. In line with performance monitoring hypothesis and ERN findings in OCD, sLORETA revealed an excess in absolute power at slow frequencies peaking at 4 and 5 Hz and reaching maximal t-values in dorsal ACC. Studies show that ERN arises at least in part from ongoing theta activity of 4 -7 Hz [START_REF] Luu | Electrophysiological responses to errors and feedback in the process of action regulation[END_REF][START_REF] Luu | Frontal midline theta and the error-related negativity: neurophysiological mechanisms of action regulation[END_REF][START_REF] Luu | Regulating action: alternating activation of midline frontal and motor cortical networks[END_REF][START_REF] Trujillo | Theta EEG dynamics of the error-related negativity[END_REF]. Although the main role in performance monitoring has been attributed to dorsal medial frontal cortex, it has been shown that other medial frontal and limbic structures [START_REF] Luu | Electrophysiological responses to errors and feedback in the process of action regulation[END_REF] are necessary for the generation of ERN. Accordingly, the low-frequency excess revealed by sLORETA in our study was not confined to dorsal ACC but included the entire ACC, medial orbitofrontal cortex and part of the left parahippocampal gyrus. The independent component that differentiated patients and controls received the strongest signal from the subgenual part of anterior cingulate. This structure is an important gateway in the regulation of neural circuits involved in mood and anxiety disorders ( [START_REF] Van Laere | Metabolic imaging of anterior capsular stimulation in refractory obsessive-compulsive disorder: a key role for the subgenual anterior cingulate and ventral striatum[END_REF]. It has been shown that metabolic activity in subgenual ACC predicts therapeutic response to anterior capsular electrostimulation in patients with OCD and comorbid depression and decreases post-treatment ( [START_REF] Van Laere | Metabolic imaging of anterior capsular stimulation in refractory obsessive-compulsive disorder: a key role for the subgenual anterior cingulate and ventral striatum[END_REF]. Interestingly, the most promising targets of deep brain stimulation in OCD and depression focus on fronto-striatal pathways, especially on fibres connecting the subgenual anterior cingulate and orbital cortex with basal ganglia, thalamus, and amygdala [START_REF] Haber | Cognitive and limbic circuits that are affected by deep brain stimulation[END_REF]. In the context of the enhancing effect of negative affect on ERN [START_REF] Luu | Medial frontal cortex in action monitoring[END_REF], we hypothesize that the hyperactive neural circuit of subgenual ACC represented by the component which is abnormal in OCD might impact on possibly vulnerable dorsal ACC and thus lead to generation of obsessive-compulsive symptoms as suggested by [START_REF] Pitman | A cybernetic model of obsessive-compulsive psychopathology[END_REF]. The component that was abnormal in OCD in our study was localized more on the left side and included the insula, parahippocampal gyrus, midcingulate and lateral frontal cortex. The increasing body of evidence indicates that lateral frontal cortex is necessary for the performance monitoring system [START_REF] Maltby | Dysfunctional action monitoring hyperactivates frontal-striatal circuits in obsessive-compulsive disorder: an event-related fMRI study[END_REF][START_REF] Ridderinkhof | The role of the medial frontal cortex in cognitive control[END_REF] and there is also support for the insular contribution in error detection [START_REF] Menon | Error-related brain activation during a Go/NoGo response inhibition task[END_REF]. Moreover, insula is connected with ACC and midcingulate [START_REF] Taylor | Two systems of resting state connectivity between the insula and cingulate cortex[END_REF], other parts of the neural circuit represented by the component. It has been suggested that the performance monitoring network communicates via transient synchronous oscillations in the theta range [START_REF] Cavanagh | Prelude to and resolution of an error: EEG phase synchrony reveals cognitive control dynamics during action monitoring[END_REF]. Interestingly, already [START_REF] Gevins | Event-related covariances during a bimanual visuomotor task. II. Preparation and feedback[END_REF] revealed that theta activity over the frontal midline sites was related to theta recorded at the left lateral frontal electrodes during error feedback signal. Our findings involve the classic theta (4 -8 Hz) as well as delta bands encompassing even lower frequencies. However, given that the abnormalities in both bands concerned the same location and component, we suggest that the low frequency increases at 2 -6 Hz reflect the same pathophysiological process. Interestingly, a recent factor analysis indicated similarities between low frequencies and proposed a broader low frequency band ranging from 1.5 Hz to 7 Hz [START_REF] Pascual-Marqui | sLORETA-based functional segmentation of the human cortex during REST[END_REF]. Moreover, it has been found that at low frequencies, the highest correlation with cerebral perfusion as measured by positron emission tomography was in the 2 -6 Hz frequency band [START_REF] Leuchter | Relationship between brain electrical activity and cortical perfusion in normal subjects[END_REF] which corresponds with our findings. Although most ERP studies used a 4 Hz high-pass filter and thus a priori excluded lower frequencies [START_REF] Luu | Electrophysiological responses to errors and feedback in the process of action regulation[END_REF][START_REF] Luu | Frontal midline theta and the error-related negativity: neurophysiological mechanisms of action regulation[END_REF][START_REF] Luu | Regulating action: alternating activation of midline frontal and motor cortical networks[END_REF], delta activity has also been related to performance monitoring processes [START_REF] Yordanova | Parallel systems of error processing in the brain[END_REF]. Another approach that might explain our findings is based on the concept of thalamocortical dysrhythmia [START_REF] Llinás | Thalamocortical dysrhythmia: A neurological and neuropsychiatric syndrome characterized by magnetoencephalography[END_REF]. Thalamocortical dysrhythmia is a disrupted dynamic between thalamus and cortex arising due to changes in the behavior of thalamic cells caused by their hyperpolarization. This leads to pathological theta oscialtion in the cortex. In neuropsychiatric symptoms the areas where we expect to see maximal lowfrequency activity include the cingulate, medial prefrontal, and orbitofrontal cortices [START_REF] Llinás | Thalamocortical dysrhythmia: A neurological and neuropsychiatric syndrome characterized by magnetoencephalography[END_REF] which corresponds with our findings. Our results indicate that medial frontal low-frequency excess was present in both the drug-free and SSRIs medicated group and in sLORETA it was even more pronounced in the SSRIs group. This suggests that the increased low-frequency power was not due to medication and, moreover, that SSRIs did not normalize this EEG pattern. Previous studies in OCD show that treatment response to serotonin reuptake inhibitors is linked with a decrease in alpha power which is enhanced pre-treatment in responding patients [START_REF] Hansen | Quantitative electroencephalography in OCD patients treated with paroxetine[END_REF][START_REF] Prichep | Quantitative electroencephalographic subtyping of obsessive-compulsive disorder[END_REF]. On the other hand, pre-treatment EEG analysis in patients who did not respond to serotonin reuptake inhibitors showed an excess in the theta frequency band [START_REF] Prichep | Quantitative electroencephalographic subtyping of obsessive-compulsive disorder[END_REF]. On average, our patients had marked obsessive-compulsive symptoms and had been suffering from OCD for more than twelve years despite previous treatment. Therefore, it is plausible that our sample included a high percentage of SSRIs non-responders. In our opinion, this is the main reason why our results differ from those reported by [START_REF] Velikova | Dysfunctional brain circuitry in obsessive-compulsive disorder: source and coherence analysis of EEG rhythms[END_REF]. Although in the context of the electrophysiological effect of serotonin reuptake inhibitors in OCD and the presence of low-frequency excess in both medicated and drug-free patients (a trend in sLORETA and a significant finding in group ICA analysis) it does not seem likely that the results would be due to poor treatment adherence in medicated patients, it should be acknowledged that EEG was recorded at the beginning of hospitalization and that we do not have data about prior treatment adherence. An interesting view of these results would be provided by extending the study to clinical control groups that would allow us to resolve the question of whether our findings are specific for OCD or whether they represent a more general characteristic of a broader diagnostic category. The fact that low-frequency power excess did not correlate with clinical data may have several reasons. Firstly, clinical rating scales evaluate symptom severity experienced up to one week before, whereas EEG recording comprises only a few minutes. Secondly, inter-individual differences in expectations and anxiety during EEG examination might have confounded the results. Finally, similarly to anatomical and functional abnormalities [START_REF] Chamberlain | Orbitofrontal dysfunction in patients with obsessive-compulsive disorder and their unaffected relatives[END_REF][START_REF] Menzies | Neurocognitive endophenotypes of obsessive-compulsive disorder[END_REF] our findings may represent a neurobiological substrate for the disorder rather than a correlate of symptom severity.

Several limitations of this study should be mentioned. First, the identified regional activity cannot be assumed to measure neuronal activity at those sites. It is instead used to infer an activity that is consistent with the sLORETA model. Source localization is susceptible to errors and it is less accurate than direct measurements from anatomical regions. The spatial resolution of the sLORETA method is low and a confounding effect comes also from the use of a standard head model that was applied in our study as individual MRI anatomical data were not available. Second, the seven separated components were only partially identical with those reported in [START_REF] Congedo | Group Independent Component Analysis of Resting-State EEG in Large Normative Samples[END_REF]. The components 1, 3 and 5 in our sample correspond with those described in [START_REF] Congedo | Group Independent Component Analysis of Resting-State EEG in Large Normative Samples[END_REF] in terms of both, spatial and spectral distribution. The component 4 has a similar spatial distribution as the corresponding component in [START_REF] Congedo | Group Independent Component Analysis of Resting-State EEG in Large Normative Samples[END_REF], however it does not have low normal alpha power. On the other hand, the components 2 and 6 correspond with their counterparts in the power distribution but their localization is only partially identical. We did not find the anterior cingulate component (component 5 in [START_REF] Congedo | Group Independent Component Analysis of Resting-State EEG in Large Normative Samples[END_REF] and found instead an extra component localized in BA 6 and the adjacent regions (component 7). There are several reasons for this discrepancy. First, the mean age of our sample was higher than the age of subjects in both databases used in [START_REF] Congedo | Group Independent Component Analysis of Resting-State EEG in Large Normative Samples[END_REF]. Second, the sample size in all databases might not be high enough. Third, our data were re-referenced to average reference montage before the analysis which we believe to be the major factor explaining the divergence of the result. However, despite the different settings and machines used in the three samples, the overall similarities are substantial. We are aware of a special attention that should be paid to ocular artifacts because the main result of our study is at low frequencies. Although we did not record electrooculogram, we are confident that the main result is not due to eye movement artifacts because 1) the samples are large, 2) the peak effect was observed at 4 and 5 Hz, whereas the effect due to eye movements would peak at very low frequencies, 3) there were visible lowfrequency abnormalities in the raw EEG in the OCD group described by a certified neurologist as focal 4 -5 Hz theta with highest amplitude at electrodes F7, Fz, F3 or T3 without simultaneous amplitude increase (or any sign of propagation) at Fp1 or Fp2. Another potential confounding factor at low frequencies may be the presence of K-complexes. Although the artefact-free segments in our study were selected with a special attention to K-complexes, we asked a certified neurologist to independently review the data. He confirmed that OCD subjects did not present enhanced K-complexes during resting state EEG and, therefore, that the results are not due to K-complexes. A long research tradition has shown the importance to consider individually-defined frequency bands for EEG analysis. For example, Klimesch and colleagues described three narrow alpha sub-bands that can be defined in each individual based on the alpha peak frequency and showed their different physiological meaning [START_REF] Klimesch | EEG alpha and theta oscillations reflect cognitive and memory performance: a review and analysis[END_REF][START_REF] Klimesch | Brain oscillations and human memory performance: EEG correlates in the upper alpha and theta bands[END_REF]. According to [START_REF] Klimesch | EEG alpha and theta oscillations reflect cognitive and memory performance: a review and analysis[END_REF] the individual alpha frequency should be used as a reference point not only for adjusting different alpha frequency sub-bands but also for theta range definition [START_REF] Klimesch | EEG alpha and theta oscillations reflect cognitive and memory performance: a review and analysis[END_REF]. Because our results are also within the theta band, we tested if there are differences in the alpha peak between OCD patients and healthy controls. We extracted the alpha peak frequency with 0.5 Hz resolution for each individual and compared the groups. The mean alpha peak in the patient group was 10.54±1.059 Hz and the mean alpha peak in the control group was 10.36±0.969 Hz. The groups did not differ in the alpha peak frequency (p=0.370). Therefore, on these samples it is not necessary to individualize the band definition.

In summary, our study presents the largest set of results concerning resting state EEG in OCD patients. Consistently with previous EEG studies it confirms a differential EEG pattern between OCD patients and healthy controls. Although this study was not conceived to distinguish between SSRIs responders and non-responders, it supports previous findings on theta excess in non-responding patients. In addition, it provides information about the sources of enhanced low-frequency activity in OCD. Their localization in the medial frontal cortex and mainly in ACC is congruent with neuroimaging findings on medial frontal hyperactivation in OCD as well as with the performance monitoring hypothesis. Both the sLORETA and group ICA methods deserve further investigation as diagnostic tools. Our results are of practical interest for potential nonpharmacological treatment such a neurofeedback intervention aimed at normalizing EEG patterns. Figures show only the most significant voxels (the darker the red colour, the higher the t-value). For all significant voxels see Table 2.

Tables:

Figures:Figure 1 :

 1 Figures:

Figure 2 :

 2 Figure2: Sagittal view (left of the picture is front of the head) of absolute current density increase in OCD patients compared with controls at 2 -6 Hz. Each figure is sliced to its own t-value maximum (t max2Hz = 5.36, t max3Hz = 5.46, t max4Hz = 5.87, t max5Hz = 5.82, t max6Hz = 5.56). Figures show only the most significant voxels (the darker the red colour, the higher the t-value). For all significant voxels see Table2.

Figure 3 :

 3 Figure 3: Mean absolute current density at low frequencies (2 -6 Hz) in controls (circles), drug-free (triangles) and medicated OCD (diamonds) patients. The filled elements indicate the mean current density value in each group.

Figure 4 :

 4 Figure 4: Seven independent components separated in the control group. The components are sorted according to explained variance and the images are sliced to their own maxima. From left to right, the inserts 1 to 7 show the axial (top of the picture is front of the head), sagittal (left of the picture is front of the head) and coronal (top of the picture is top of the head) view. The intensity of the red colour indicates the intensity of the signal contributing to the component (arbitrary unit and scaled to its own maximum for each component). Component 5 is also displayed on a three-dimensional cortical template.

Figure 5 :

 5 Figure 5: Absolute, relative and normal power (arbitrary units) of the 5 th component along frequencies in the range 2 -45 Hz. Comparison between OCD patients and controls (a), drug-free patients and controls (b) and medicated patients and controls (c). In each insert the solid and dotted lines indicate the mean and 95% confidence interval for the normal group, whereas the disks indicate the mean of the OCD group, with violet disks flagging significant power increase (p < 0.05, corrected).

Table 1 :

 1 Demographic and clinical characteristics of the groups of subjects. Yale-Brown Obsessive-Compulsive scale, SD -standard deviation, DF -drug-free, SSRIs -selective serotonin reuptake inhibitors, NA -not applied/not applicable

		OCD		controls	OCD -DF	OCD -SSRIs	OCD vs.	OCD -DF	OCD -SSRIs	OCD-DF vs.
		(N = 50)	(N = 50)	(N = 20)	(N = 30)	controls	vs. controls	vs. controls	OCD-SSRIs
	Sample characteristics	mean SD mean SD mean SD mean SD stat. test	p	p	p	p
	Demographic
	age (years)	29.2 5.0 28.4 5.6 28.4 4.7	29.1	5.3 Wilcoxon	0.319	0.303	0.533	0.781
	sex (men:women)	20:30 NA 23:27 NA 7:13 NA 13:17 NA chi-square	0.545	0.401	0.816	0.556
	handedness (right:left)	48:2 NA 48:2 NA 19:1 NA	29:1	NA chi-square	1.000	0.852	0.879	0.768
	Clinical
	Y-BOCS (n = 38)	19.4 8.0	NA	NA 16.4 7.6	21.0	7.9 t-test	NA	NA	NA	0.092
	obsessions	9.8	3.4	NA	NA	9.4	3.6	10.0	3.3 t-test	NA	NA	NA	0.576
	compulsions	9.8	5.0	NA	NA	7.5	4.4	11.0	5.0 t-test	NA	NA	NA	0.040
	HAMA (n = 35)	12.7 6.0	NA	NA	12.7 5.0	12.7	6.5 t-test	NA	NA	NA	0.979
	age of onset (years)	16.9 7.2	NA	NA 18.1 6.9	16.1	7.4 t-test	NA	NA	NA	0.406
	illness duration (years)	12.5 7.9	NA	NA 11.2 8.8	13.3	7.4 t-test	NA	NA	NA	0.402
	Abbreviations: Y-BOCS -

Table 2 :

 2 Number and localization of voxels with excessive absolute current density in OCD compared with controls (p < 0.05). The structures are reported in their mean t-value order.

	2 Hz	3 Hz	4 Hz	5 Hz	6

Hz Brain structure and Brodmann area

  mean t voxels mean t voxels mean t voxels mean t voxels mean t voxels Anterior cingulate(BA 24, 25, 32, 33)

		4.86	45	4.91	49	5.26	55	5.26	58	5.04	55
	Cingulate gyrus (BA 24, 32)	4.65	21	4.76	27	4.82	38	4.83	31	4.60	17
	Subcallosal gyrus (BA 25, 34)	4.70	15	4.65	14	4.77	14	4.78	10	4.62	8
	Medial frontal gyrus (BA 9, 10, 11, 25)	4.58	22	4.55	29	4.71	45	4.79	51	4.62	47
	Rectal gyrus (BA 11)	4.57	14	4.59	14	4.62	15	4.57	17	4.40	12
	Left parahippocampal gyrus (BA 28, 34, 35, 37)	4.48	16	4.39	9	4.42	5	4.71	1	n.s.	0
	Inferior frontal gyrus (BA 47)	4.42	8	4.40	5	4.38	6	4.34	3	n.s.	0
	Left uncus (BA 28, 36)	4.40	10	4.33	3	n.s.	0	n.s.	0	n.s.	0
	total		151		150		178		171		139

This work was supported by the grant IGA NS 9751-3/2008 provided by the Ministry of Health of the Czech Republic.


M Deschamps

S Cadars

E Gilbert

P Azaïs

Encarnacion Raymundo-Pinero

F Béguin

D Massiot

Michaëldeschamps

Sylviancadars

Edouardgilbert

Philippeazaïs

Françoisbéguin

Dominiquemassiot

AsolidstateNMRstudyofC 70 :amodelmolecule foramorphouscarbons

published or not. The documents may come     A solid-state NMR study of C70: a model molecule for amorphous carbons

Introduction

Electrochemical double-layer capacitors are made of porous carbon electrodes containing an electrolyte. Upon charging, the electronic charges are stored on the carbon electrode surface while the electrolyte structure is reorganized to maintain local electroneutrality. The carbon materials used for the electrodes, including materials originating from biomass, such as coconutshells,havebeenshowntohave alargeimpactontheenergyandpower densities, which can be obtained in supercapacitors. Recent research using more sophisticated materials such as curved graphene sheets [START_REF] Liu | Graphene-Based Supercapacitor with an Ultrahigh Energy Density[END_REF][START_REF] Zhu | Carbon-Based Supercapacitors Produced by Activation of Graphene[END_REF][START_REF] Yoo | UltrathinPlanarGrapheneSupercapacitors[END_REF][START_REF] Miller | Graphene Double-Layer Capacitor with ac Line-Filtering Performance[END_REF] or nanotubes [START_REF] Niu | High power electrochemical capacitors based on carbon nanotubeelectrodes[END_REF][START_REF] Frackowiak | Supercapacitor electrodes from multiwalled carbon nanotubes[END_REF][START_REF] Futaba | Shape-engineerable and highly densely packed single-walled carbon nanotubes and their applicationassupercapacitorelectrodes[END_REF][START_REF] Izadi-Najafabadi | Extracting the Full Potential of Single-Walled Carbon Nanotubes as Durable Supercapacitor Electrodes Operableat4VwithHighPowerandEnergyDensity[END_REF] have shown that these carbon structures can be used as electrode materials and provide very promising strategies for the electrochemicalstorageofenergy.

However,littleisknownconcerningthe interplay between the carbon atomic structure and the repartition of electronic charges on the carbon surface. The molecules of the fullerenes familymaybeinterestingmodelsforthe understanding of more complicated carbon structures. First, it has been shown that the charge distribution in C70 6-is not uniform and is concentrated near the poles of the C70 molecule (Figure 1A) and the presence of electronic charges mainly affects fivemembers rings. [START_REF] Sternfeld | Fullereneanions:Unusualchargedistributionin C70 6[END_REF] Second, the [START_REF] Johnson | 2DNuclearMagneticResonanceStudyoftheStructure oftheFullereneC70[END_REF] C chemical shifts have been shown to depend upon the local curvature of the fullerene molecule [START_REF] Taylor | Isolation, Separation and Characterisation of the FullerenesC60andC70:TheThirdFormofCarbon[END_REF][START_REF] Haddon | Chemistry of the Fullerenes: The Manifestation of Strain in a Class of Continuous AromaticMolecules[END_REF] and upon the local charge density when anions [START_REF] Sternfeld | Fullereneanions:Unusualchargedistributionin C70 6[END_REF] or cations [START_REF] Reed | TamingSuperacids:StabilizationoftheFullereneCations HC60 + andC60 .+[END_REF] areconsidered. In order to assign the [START_REF] Johnson | 2DNuclearMagneticResonanceStudyoftheStructure oftheFullereneC70[END_REF] C NMR resonances of fullerenes, INADEQUATE spectra have been recorded using [START_REF] Johnson | 2DNuclearMagneticResonanceStudyoftheStructure oftheFullereneC70[END_REF] Cenriched samples since the low [START_REF] Johnson | 2DNuclearMagneticResonanceStudyoftheStructure oftheFullereneC70[END_REF] C natural abundance (1.07%) makes the probability of finding naturally occurring [START_REF] Johnson | 2DNuclearMagneticResonanceStudyoftheStructure oftheFullereneC70[END_REF] C- [START_REF] Johnson | 2DNuclearMagneticResonanceStudyoftheStructure oftheFullereneC70[END_REF] C pairs quite low. [START_REF] Johnson | 2DNuclearMagneticResonanceStudyoftheStructure oftheFullereneC70[END_REF][START_REF] Sternfeld | Fullereneanions:Unusualchargedistributionin C70 6[END_REF] Otherwise, ab initio calculations have been performed to assign the observed linesin [START_REF] Johnson | 2DNuclearMagneticResonanceStudyoftheStructure oftheFullereneC70[END_REF] C, 3 Heor 7 LiNMR. [START_REF] Bühl | Helium and Lithium NMR ChemicalShiftsofEndohedralFullereneCompounds:AnabInitioStudy[END_REF][START_REF] Meier | A 13 C INADEQUATE and HF-GIAO Study of C60H2 and C60H6 Identification of Ring Currents in a 1,2-Dihydrofullerene[END_REF] NMRhas also been used for the characterization of more complicated molecules of the same family such as C80. [START_REF] Hennrich | Isolation and Characterization of C80[END_REF] To probe the magnetic properties of fullerene molecules, [START_REF] Yoo | UltrathinPlanarGrapheneSupercapacitors[END_REF] He NMR on He@C70 complexes where the He atoms are located inside the C70 [START_REF] Saunders | Probing the interioroffullerenesby 3 HeNMRspectroscopyofendohedral 3 He@C60and 3 He@C70[END_REF][START_REF] Sternfeld | The Inside Story of Fullerene Anions: A 3 He NMR AromaticityProbe[END_REF] has been successfully used, while the surface properties have been characterized using [START_REF] Liu | Graphene-Based Supercapacitor with an Ultrahigh Energy Density[END_REF] Hand [START_REF] Johnson | 2DNuclearMagneticResonanceStudyoftheStructure oftheFullereneC70[END_REF] CNMRofsurfacegroups graftedonreducedC70molecules. [START_REF] Sternfeld | ReductionofFulleroidsC71H2:Probing theMagneticPropertiesofC70 6[END_REF] CrystallizedsolvatedC70moleculeshave also been studied by solid-state NMR using 1 H- [START_REF] Johnson | 2DNuclearMagneticResonanceStudyoftheStructure oftheFullereneC70[END_REF] C cross-polarization to enhance the [START_REF] Johnson | 2DNuclearMagneticResonanceStudyoftheStructure oftheFullereneC70[END_REF] C signal. [START_REF] Kolodziejski | 13 C-1 H and 1 H-13 C cross-polarization NMR in toluene-solvated fullerene-70[END_REF] In the solidstate, pure C70 molecules have been shown to rotate freely around their symmetry axis at room temperature using longitudinal relaxation (T1) and Chemical Shift Anisotropy (CSA) considerations. [START_REF] Firtej | MolecularMotioninSolidC70by 13 CHigh-ResolutionNMR[END_REF] Inthispaper,weshowforthefirsttime that naturalabundance [START_REF] Johnson | 2DNuclearMagneticResonanceStudyoftheStructure oftheFullereneC70[END_REF] C INADEQUATE solid-state NMR spectra can be recorded for C70 samples, using the J-couplings between naturally occurring [START_REF] Johnson | 2DNuclearMagneticResonanceStudyoftheStructure oftheFullereneC70[END_REF] C- [START_REF] Johnson | 2DNuclearMagneticResonanceStudyoftheStructure oftheFullereneC70[END_REF] C pairs for magnetization transfer. The 2D INADEQUATE can be recorded at "low" magneticfields(7Tor300MHzfor 1 H) where the line widths are narrower (in Hz)andtheJ-splittingscanberesolved. However,theT1valuesarelongeratlow fields, and the strong Jcoupling effect between two close resonances additionally leads to vanishing crosspeaks. [START_REF] Bax | Investigationof 13 C-13 CCouplingsinNaturalAbundanceSamples:TheStrong CouplingCase[END_REF] Athigher magneticfields (20 T or 850 MHz for 1 H), the Boltzmann population difference is enhanced, the longitudinalrelaxationisfaster,andthe strong Jcoupling effects are lessened even if the broader line widths (in Hz) preclude the direct observation of Jsplittings. The [START_REF] Johnson | 2DNuclearMagneticResonanceStudyoftheStructure oftheFullereneC70[END_REF] Cchemicalshiftscanbecalculated using a DFT approach. The calculated values show an excellent agreement with the experimental measurements. The [START_REF] Johnson | 2DNuclearMagneticResonanceStudyoftheStructure oftheFullereneC70[END_REF] Cchemicalshiftsofthesecarbons (experimental and calculated) are shown to correlate with the average bond angles with the three neighboring carbons. The presence of a broad contributionbetween140and160ppm in the [START_REF] Johnson | 2DNuclearMagneticResonanceStudyoftheStructure oftheFullereneC70[END_REF] C NMR spectra of nanoporous amorphous activated carbons can be explained by the presence of carbon atoms with smaller CCC angles in regions of higher carbon surface curvatures.

ExperimentalNMR

The solid C70 powder have been purchasedfromSigma-Aldrichandused as is, without further purification. The supercapacitor electrode was provided by Batscap and was obtained from carbonized and activated coconut shell, with a PVDF binder and carbon black additive for conductivity. The carbon powders have been placed in a 4 mm Bruker ZrO2 rotor. The NMR spectra have been obtained with Bruker NMR spectrometers operating at 7 and 20 T, correspondingtoLarmorfrequenciesof 75.5 and 213.8 MHz for [START_REF] Johnson | 2DNuclearMagneticResonanceStudyoftheStructure oftheFullereneC70[END_REF] C (300 and 850 MHz for 1 H), using Magic Angle Spinning (MAS) rates of 10.000 and 14.286kHzinBrukerdoubleresonance MAS-NMR probes. The 13 C chemical shifts are referenced to TMS at 0 ppm. ThelongitudinalrelaxationtimesforC70 have been found to range between 2.6 and 2.9 s at 7 T, and 1.6 to 2 s at 20 T. The recovery delays have been set to 5xT1forthequantitative1Dspectraand 3 and 2.4 s to obtain the best signal-to-noiseratiointheINADEQUATEspectra. The 1D [START_REF] Johnson | 2DNuclearMagneticResonanceStudyoftheStructure oftheFullereneC70[END_REF] C MAS-NMR spectrum of the supercapacitor electrode was recorded witharecoverydelayof60s(duetothe slower longitudinal relaxation of PVDF, comparedtoT1≤5sforthedisordered nanoporous carbon). The 90° excitation pulseshavebeenperformedusingB1RF fieldsof68and50kHzrespectively,and trains of eight 90° pulses 20 ms apart were used for presaturation. The INADEQUATE spectra were recorded using a refocused INADEQUATE sequence,followedbya20msZ-filterto obtain a pure phase spectrum. 23 2048 transients have been recorded for each natural-abundance [START_REF] Johnson | 2DNuclearMagneticResonanceStudyoftheStructure oftheFullereneC70[END_REF] C INADEQUATE, using conversion and reconversion delaysof8.2ms(≈1/2J)toallowforthe build-up of antiphase magnetization considering that 2 J( 13 C-13 C) ≈ 60 Hz. In the indirect dimension, spectral widths of 2000 and 7143 Hz have been recorded using 100 and 50 increments at 7 and 20 T, respectively. The experiments lasted 7 and 3 days, respectively. Single component baseline corrections and exponential broadeningsof20and100Hzhavebeen applied on the INADEQUATE spectra in both dimensions. The 1D spectra and theINADEQUATEsliceshavebeenfitted and/or extracted using the dmfit software. [START_REF] Massiot | Modellingoneandtwo-dimensionalsolid-stateNMRspectra[END_REF] Thesimulationsshowingthe strongJcouplingeffectswereperformed usingSPINEVOLUTION. [START_REF] Veshtort | SPINEVOLUTION:Apowerfultoolforthesimulationofsolidandliquidstate NMRexperiments[END_REF] DFT First principles calculations with periodic boundary conditions were achieved using the CASTEP code, [START_REF] Segall | First-principlessimulation:ideas,illustrationsandtheCASTEPcode[END_REF][START_REF] Clark | Firstprinciplesmethods usingCASTEP[END_REF] which relies on a plane-wave-based density functional theory (DFT) approach. The electron correlation effects are modeled using the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA). [START_REF] Perdew | GeneralizedGradientApproximationMadeSimple[END_REF] For geometry optimizations we employed a planewavecut-offenergyof450eVand the default "ultrasoft" 29 pseudo-potentials of CASTEP 5.5 (described in Supporting Information, Table S1). Convergencethresholdsweresetto10 -5 eV/atom for the total energy, 3.10 -2 eV/Å for the maximum ionic force, and 10 -3 Å for the maximum ionic displacement.Weaknon-bondingforces, which are generally absent in DFT calculations and yet crucial in the description of π-π interactions, for example,wereaccountedforherebythe damped atom-pairwise semi-empirical dispersion corrections of Tkatchenko and Scheffler. [START_REF] Tkatchenko | Accurate Molecular Van Der Waals Interactions from Ground-State ElectronDensityandFree-AtomReferenceData[END_REF] The NMR calculations were performed using the Gauge Including Projector Augmented Wave approach (GIPAW), [START_REF] Pickard | All-electron magnetic response with pseudopotentials: NMR chemical shifts[END_REF][START_REF] Yates | CalculationofNMRchemicalshiftsforextendedsystemsusingultrasoft pseudopotentials[END_REF] at the same cut-offenergyof450eV. The crystal structure of C70 was previously determined by diffraction. [START_REF] Vansmaalen | Low-temperaturestructureof solidC70[END_REF] For gas-phase calculations on isolated C70, one of the four C70 molecules was put in a cell of 15x15x15 Å 3 to avoid inter-molecular interactions, with a 2x2x2 Monkhorst-Pack (MP) grid [START_REF] Monkhorst | Special points for Brillouin-zone integrations[END_REF] to sample the Brillouin zone. The solidstate calculations were conducted with and without the symmetries of the Pbmn (#62) space group, with unit cell parametersa=10.016Å,b=17.349Å,c =18.530Å,andα=β=γ=90°keptfixed during geometry optimizations, and a 2x1x1 MP grid. An internal reference was used to calculate chemical shifts using the expression δcalc = σref -σcalc + δref, where σref is the average of all calculated shieldings for a given calculation, and δref the corresponding average of all experimental [START_REF] Johnson | 2DNuclearMagneticResonanceStudyoftheStructure oftheFullereneC70[END_REF] C shifts of C70 (weighed by populations) with respecttoTMS.

Resultsanddiscussion

Although the low-temperature XRD structure of crystallized C70 shows 40 inequivalent sites, [START_REF] Vansmaalen | Low-temperaturestructureof solidC70[END_REF] rotation about the polar axis [START_REF] Firtej | MolecularMotioninSolidC70by 13 CHigh-ResolutionNMR[END_REF] at room temperature reducesthenumberofinequivalentsites to five, with populations in a 1:1:2:2:1 ratio.Thesesitesarelabeledfromatoe and the lines were first assigned using the local curvature and the population ratio. [START_REF] Taylor | Isolation, Separation and Characterisation of the FullerenesC60andC70:TheThirdFormofCarbon[END_REF] The assignment has been confirmed with a 13 C liquid-state NMR 2DrefocusedINADEQUATErecordedon isotopically enriched C70. [START_REF] Johnson | 2DNuclearMagneticResonanceStudyoftheStructure oftheFullereneC70[END_REF] The C70 molecule with the a-e sites and the quantitative1D [START_REF] Johnson | 2DNuclearMagneticResonanceStudyoftheStructure oftheFullereneC70[END_REF] CMAS-NMRspectrum areshowninFigure1.Theresultsfrom the fits are provided in Table S2. The longitudinal relaxation time constants (T1) are rather small for these compounds (between 1.5 and 3s) and become smaller with increasing B0 strength.Thisisexpectedgiventhelarge chemical shift anisotropies (CSA) calculated by DFT (190 ppm) for the (static) low-temperature Pbmn structure and the comparatively small values (30-50 ppm) measured at room temperature, where C70 molecules undergo free rotation around the polar axis. [START_REF] Firtej | MolecularMotioninSolidC70by 13 CHigh-ResolutionNMR[END_REF] CSA fluctuations are thus expected to be the main source of relaxation, [START_REF] Firtej | MolecularMotioninSolidC70by 13 CHigh-ResolutionNMR[END_REF] which are consequently more efficient at higher magnetic fields. It is possible as a result to directly record a natural-abundance [START_REF] Johnson | 2DNuclearMagneticResonanceStudyoftheStructure oftheFullereneC70[END_REF] C spectruminashorttimewithoutcross-polarizationforC70.

No [START_REF] Liu | Graphene-Based Supercapacitor with an Ultrahigh Energy Density[END_REF] Horparamagneticdefectisfoundin the crystallized C70 samples. The loss of coherence is consequently slow (long T2), no decoupling is needed, and MAS easilyremovestheCSAsidebandsandis expectedtoquenchanyundesiredcrossterm. [START_REF] Fayon | Through-space contributionstotwo-dimensionaldouble-quantumJcorrelationNMRspectraofmagic-angle-spinning solids[END_REF] TheJ-couplingbetweenadjacent [START_REF] Johnson | 2DNuclearMagneticResonanceStudyoftheStructure oftheFullereneC70[END_REF] C spins, around 60 Hz, [START_REF] Johnson | 2DNuclearMagneticResonanceStudyoftheStructure oftheFullereneC70[END_REF] is then sufficient to mediate the creation of antiphase coherences between chemically bound [START_REF] Johnson | 2DNuclearMagneticResonanceStudyoftheStructure oftheFullereneC70[END_REF] C pairs and thus to allow acquisition of J-mediated correlation experiments. The optimum refocused INADEQUATE signal was found for conversion and reconversion delays of 8.2 ms before and after the double-quantum evolution time, which is equal to the theoretical optimum of 1/(2J), as expected for comparatively longT2. The2DrefocusedINADEQUATEspectra recorded at 7 and 20 T are shown in Figure1CandD.Forthefirsttime,these spectra were recorded using nonenriched C70 samples. Whereas a few examples of [START_REF] Johnson | 2DNuclearMagneticResonanceStudyoftheStructure oftheFullereneC70[END_REF] C- [START_REF] Johnson | 2DNuclearMagneticResonanceStudyoftheStructure oftheFullereneC70[END_REF] C correlation spectra collected at natural abundance in the solid state have been reported 36 (most of which with the refocused INADEQUATE experiment), this is also the first example using direct [START_REF] Johnson | 2DNuclearMagneticResonanceStudyoftheStructure oftheFullereneC70[END_REF] C excitationratherthanthe [START_REF] Johnson | 2DNuclearMagneticResonanceStudyoftheStructure oftheFullereneC70[END_REF] C{ 1 H}crosspolarization(CP)classicallyemployedin organicsolids.Thespectrumobtainedat 7Tshowsthreepairsofcross-peaks,ab, c-d and d-e. The b-c pair of crosspeaks is missing because the frequency separation of b and c (40 Hz) remains too small as compared to the J-coupling (60 Hz) inducing strong Jcoupling effects, i.e. the J-coupling Hamiltonian (2πJIS)cannotbereducedto2πJIzSz. [START_REF] Bax | Investigationof 13 C-13 CCouplingsinNaturalAbundanceSamples:TheStrong CouplingCase[END_REF][START_REF] Levitt | SpinDynamics.BasicsofNuclearMagneticResonance[END_REF] In such a case, antiphase terms are not created,andsimulationsperformedwith SPINEVOLUTION confirm this result. [START_REF] Veshtort | SPINEVOLUTION:Apowerfultoolforthesimulationofsolidandliquidstate NMRexperiments[END_REF] Thelinewidths(≈40Hz)ofthe [START_REF] Johnson | 2DNuclearMagneticResonanceStudyoftheStructure oftheFullereneC70[END_REF] Clines are small enough to allow direct observation of the 2 J( 13 C-13 C) splitting, asillustratedinthecorrespondingslices (Figure 2). The SPINEVOLUTION simulations accurately reproduce the distortion of the multiplets stemming from the strong Jcoupling effect ("roof" effect,showninFigure2). To observe the missingb-c cross-peaks, thefrequencyseparationbetweenband clines(inHz)mustbeincreased,which iseasilyachievedbyusingastrongerB0 field. At 20 T, the frequency separation betweenbandc(113Hz)becomeslarge enoughtoobservetheb-ccross-peaksin the 2D INADEQUATE spectrum (Figure 1D).However,thelinewidths(resulting from the interplay of J-splitting and chemical shift distribution stemming fromstructuraldisorder)becomelarger (≈ 150 Hz full width at half maximum, FWHM) and the multiplets cannot be observed directly anymore. Correlated disorder effects can even be distinguishedfromtheelongatedshapes ofthecross-peaks. [START_REF] Cadars | ChemicalShiftCorrelationsinDisorderedSolids[END_REF] Figure2.1Dslicesoftherefocused [START_REF] Johnson | 2DNuclearMagneticResonanceStudyoftheStructure oftheFullereneC70[END_REF] CINADEQUATE spectrum of C70 obtained at 7T (blue), for each observedpairofcross-peaks(a-b,c-dandd-e).Thebc pair is not observed because of the strong coupling effect as the spectral separation between b and c (40Hz) becomes small and interferes with the Jcoupling (≈ 60 Hz). The theoretical spectra with no strong J-coupling effect are shown in red (obtained with dmfit24) and the simulated spectra obtained with SPINEVOLUTION [START_REF] Veshtort | SPINEVOLUTION:Apowerfultoolforthesimulationofsolidandliquidstate NMRexperiments[END_REF] are shown in purple to illustratethe"roof"effectresultingfromthestrongJcoupling.

The main interest behind studying C70 lies in its ability to mimic on a small scale the expected structure of nanoporous carbons. [START_REF] Harris | NewPerspectivesontheStructureofGraphiticCarbons[END_REF][START_REF] Kumar | PorousamorphouscarbonmodelsfromperiodicGaussianchainsof amorphouspolymers[END_REF] The 13 C MAS-NMR spectrum of a supercapacitor electrode made with a nanoporous carboniscomparedtotheC70MAS-NMR spectrum in Figure 3. The expected chemical shifts of commonly found moieties are also represented. In the nanoporous carbon, the signals appearing between 140-160 ppm does not correspond to commonly found chemical groups and therefore may indicate sp 2 carbons with stronger curvatures, as seen in the C70 NMR spectrum. To understand the origins in terms of local structure of the chemical shift variations in C70, the chemical shifts have also been calculated with DFT. Three cases have been considered: isolated C70 molecules and crystalline C70 with and without the symmetries of the original Pbmn space group of the low-temperature structure. Although the solid-state calculations provide slightly better agreement with the experimental values, the three calculationsmethodsprovidedchemical shifts with strong linear correlation to the experimental values. Systematic deviations from the perfect 1:1 correlation are not unusual for DFT calculations of NMR parameters. They are most probably accounted for by approximations of the exchangecorrelation functional and, in the presence case, by the comparison of a static model and a strongly dynamic experimental system. The results are provided in the supplementary materialssection(TableS3).Thevalues obtained with the immobile C70 molecules in the Pbmn structure have beenaveragedtoreproducetheeffectof the molecular rotation about the polar axis. The resulting values are shown in Figure3,andthestandarddeviationsof thecalculatedshiftsforeachtypeof [START_REF] Johnson | 2DNuclearMagneticResonanceStudyoftheStructure oftheFullereneC70[END_REF] C site are plotted as error bars thus reflecting the spread in chemical shifts expected when the C70 rotation is stopped. One can see that the linear correlation is excellent, with R=0.9990, showing that the DFT calculations are perfectly able to offer an alternate way to assign the 13 C resonances. Interestingly, the average shifts calculated for each type of site do not significantly differ when the C70 molecule is considered in isolation (see Supplementary Material, Table S3). The spread of calculated values for each [START_REF] Johnson | 2DNuclearMagneticResonanceStudyoftheStructure oftheFullereneC70[END_REF] C site, in contrast, varies considerably between the isolated molecule and the solid-statemodel.Specifically,calculated shifts are virtually identical of every atom of a given type in isolated C70 (standard deviations of 0.01 to 0.03 ppm,seeTableS3)andaresubstantially distributed for crystalline C70 with and without symmetry (standard deviations of 0.8 to 2.0 ppm). This result clearly indicates that the spread of calculated [START_REF] Johnson | 2DNuclearMagneticResonanceStudyoftheStructure oftheFullereneC70[END_REF] C shifts for static crystalline C70 is entirely due to inter-molecular effects due to ring currents induced by the magneticfieldinadjacentC70molecules. Atambienttemperature,fastrotationof the molecules is expected to reduce theseeffectstozero. Translating the observed chemical shift values into simple geometric considerations is more difficult, but important trends can nevertheless be obtained based on the combination of experimental NMR and diffraction data andDFTcalculations.AsshowninFigure 3E,foreachcarboninC70,thethreeCCC bond angles (obtained from the DFToptimizedstructure)canbedividedinto twogroups:twolargeangleswithvalues close to 120°, which correspond to the typical angles observed for sp 2 carbons, and one smaller angle, close to 109°, whichisclosetotheCCCangleobserved for sp [START_REF] Yoo | UltrathinPlanarGrapheneSupercapacitors[END_REF] carbons. Therefore, we may expectactivatedcarbonstohavesimilar behaviors for the CCC bond angles, wherethecurvatureofgraphenelayeris achieved with similar bond angles variations by including five-members ringsamongthenetworkof6-members rings. The best linear correlation we found was between the average of the three CCCanglesandthe [START_REF] Johnson | 2DNuclearMagneticResonanceStudyoftheStructure oftheFullereneC70[END_REF] Cchemicalshiftof the carbon atom in the center. The correlation obtained between the experimental shifts and the CCC angles obtainedfromXRD,CCC=131.0-0.100 δ, is quite good (R = 0.916, see Figure S4AfromtheSupplementaryMaterials). Furthermore, this correlation improves with the angles obtained from the DFToptimized structure: CCC = 131.95 -0.1065δ,withR=0.936(Figure3E).It is a common finding that, for crystal structures obtained with powder diffractionratherthanonsinglecrystals, theprecisionofatomicpositions,and-as a result-of calculated NMR parameters, can be significantly improved by a DFT minimization with fixed unit cell parameters [START_REF] Harris | Chemicalshiftcomputationsona crystallographicbasis:somereflectionsandcomments[END_REF] .Inthiscasethevariations inatomicpositionsbetweenthepowder XRD and the DFT-optimized structure are small (RMSD of 0.051 Å), but nevertheless sufficient to improve the trend between experimental NMR results and structural features. Finally, further improvement of the correlation isobtainedwhenconsideringcalculated ratherthanexperimentalchemicalshifts and the average CCC angles from the DFT-optimized structure: CCC = 129.4 -0.087δ,withR=0.946(FigureS4Bfrom the Supplementary Materials). This improvementmaybeprimarilyduetoa compensation of small residual errors ontheatomicpositionsasminimizedby DFT. In the three cases, some discrepancies are observed and must resultfromothereffectswhichhavenot been accounted for. Nonetheless, using this linear correlation, one can assume that the chemical shift range between 120 and 160 ppm corresponds to average CCC angles between 119.2 and 114.9°. It is also interesting to notice that the deviation from the planar sp 2 carbons found in C70 remains quite small, with only one angle expected to deviatesignificantlyfrom120°.

Conclusion

Carbon materials are now used in supercapacitors, graphite electrodes in batteries, and hybrid systems, "supercapattery", try to take advantage ofthebestofthetwoworlds.Therefore, with nanotubes, graphene and graphite oxide, elaborated carbon compounds haveabrightfutureaheadinthesearch for better energy storage strategies. In this paper, we show that natural abundance [START_REF] Johnson | 2DNuclearMagneticResonanceStudyoftheStructure oftheFullereneC70[END_REF] C correlation spectra can be recorded owing to the short longitudinal relaxation times of [START_REF] Johnson | 2DNuclearMagneticResonanceStudyoftheStructure oftheFullereneC70[END_REF] C in C70. A similar effect may be expected in some of the more complex carbon materials, either because of the CSA induced relaxation, or due to the presence of paramagnetic centers. Moreover, experimental chemical shifts can be reproduced with a reasonable accuracy using DFT, and the [START_REF] Johnson | 2DNuclearMagneticResonanceStudyoftheStructure oftheFullereneC70[END_REF] C chemical shift may be translated in terms of average CCC bond angles, offeringaplausibleinterpretationofthe [START_REF] Johnson | 2DNuclearMagneticResonanceStudyoftheStructure oftheFullereneC70[END_REF] C MAS-NMR spectra of activated carbons in terms of deviations of graphenelayersfromplanarity.

Supplementarymaterials

Figure 1 .

 1 Figure 1. A: C70 molecule showing the five classes of equivalent carbon atoms in the room-temperature structure where C70 rotates along one of the symmetryaxis.B:1Dquantitative 13 Csolid-stateNMR spectrum of C70 (blue), recorded at 7 T, with the 5 corresponding resonances (green) and the resulting model(red).TheresultsofthefitareshowninTable S2 of the Supplementary Material section. C: Double-Quantum/Single-Quantum natural abundance 13 C refocused INADEQUATE spectrum recorded at 7T, showing the expected pairs of cross-peaks (red) and the missing pair b-c, which vanishes because of the strongcouplingeffect(theJ-couplingandthechemical shift difference between the coupled spins are of the sameorder).Thestar(*)indicateszero-quantum(ZQ) artifacts. D: the same spectrum, recorded at 20 T, showing all the expected pairs of cross-peaks,

Figure 3 .

 3 Figure3.[START_REF] Johnson | 2DNuclearMagneticResonanceStudyoftheStructure oftheFullereneC70[END_REF] C MAS-NMR spectra of a supercapacitor electrode(A)andsolid-stateC70(B)withtheexpected chemical shift ranges for the commonly found chemical entities (C). , D: Plot of the[START_REF] Johnson | 2DNuclearMagneticResonanceStudyoftheStructure oftheFullereneC70[END_REF] C chemical shifts calculated by DFT (obtained with the lowtemperature Pbmn structure, in which the C70 molecules do not rotate, as opposed to the roomtemperature behavior[START_REF] Firtej | MolecularMotioninSolidC70by 13 CHigh-ResolutionNMR[END_REF] ) vs the experimentally measured[START_REF] Johnson | 2DNuclearMagneticResonanceStudyoftheStructure oftheFullereneC70[END_REF] Cshifts.WeassumedthattheC70rotation averaged the chemical shifts in each class of a-e atoms, and the error bars represent the standard deviations observed for each set of calculated chemical shifts. E: Plot of the three CCC angles obtained from the DFT-optimized structure and their averageasafunctionoftheexperimental[START_REF] Johnson | 2DNuclearMagneticResonanceStudyoftheStructure oftheFullereneC70[END_REF] Cchemical shiftsmeasuredforC70.Theerrorbarscorrespondto the standard deviations for each set of angles. The

  Figure S4. A: Plot of the three CCC angles obtained from the XRD structure and their average as a function of the experimental 13 C chemical shifts measured for C70. The green lines indicate the CCC bond angles obtained for sp 2 carbons (120°) and sp 3 carbons (109.5°). B: Same graph with the 13 C chemical shifts calculated with the DFT. Thehorizontalerrorbarscorrespondtothestandarddeviationsforeachsetofchemical shiftsfromthea-esites.Theverticalbarsareverysmallandcorrespondtothestandard deviationsobtainedforeachsetofCCCangles.

Table S1 . Description of pseudopotential used for planewavebased DFT calculations.

 S1 Where rloc is the pseudisation radius for the local component of the pseudopotential, rnonloc is the pseudisation radius for the non-local components of the pseudopotential, andraugisthepseudisationradiusforthechargeaugmentationfunctions. Thecorrespondingcastepon-the-flystringusedtogeneratethesepotentialsis:

	Atom Corestates	Local channel	rloc (a.u.)	rnonloc (a.u.)	raug (a.u.)	Pseudopotential projectors	PAWprojectors
	C	1s		D		1.4	1.4	1.3	2x2s,2x2p	2x2s,2x2p
	C2|1.4|1.4|1.3|6|10|12|20:21(qc=6)
	TableS2.Resultsfromthefitofthe1DNMRspectra.
	Site δ(ppm)	Width(Hz) @850MHz	Width(Hz) @300MHz	Area (%)
		a 151.1	137		39	14%
		b 148.1	135		40	31%
		c 148.7	135		41	15%
		d 146.1	137		42	28%
		e 131.6	124		40	12%
	TableS3.

ChemicalshiftsobtainedbyDFT. Site Averageδ (ppm) IsolatedC70 StDev (ppm) Isolated C70 Averageδ (ppm) P1C 70 StDev (ppm) P1C 70 Averageδ (ppm) PbmnC 70 StDev (ppm) PbmnC 70

								Multiplicity
	a	151.58	0.02	151.64	0.87	151.65	0.89	10
	b	146.61	0.01	147.85	0.86	147.85	0.86	10
	c	148.25	0.02	147.93	0.74	147.92	0.75	20
	d	145.13	0.03	144.52	1.26	144.52	1.25	20
	e	126.79	0.02	127.31	2.02	127.32	2.03

Acknowledgements

For DFT calculations, we thank the "Centre de Calcul Scientifique en region Centre"(Orléans,France).