Géraldine Vitellius

Marc Lombes
email: marc.lombes@u-psud.fr.

Dr Marc Lombès

Partial glucocorticoid resistance in the pathophysiology of adrenal cortex hyperplasia

Keywords: NR3C1, glucocorticoid signaling, adrenal incidentalomas, glucocorticoid resistance

The pathophysiology of Bilateral Adrenal Hyperplasia (BAH) remains obscure. Even though several genetic causes have been associated with this disease, often related to overactivation of the cAMP signaling pathway, cortisol regulation by autocrine adrenal ACTH production has also been proposed to enhance corticosteroidogenesis, cortisol secretion and adrenal cortex growth. Recently, heterozygous glucocorticoid receptor (GR) loss-of-function mutations have been discovered in patients with BAH, highlighting a potential new genetic cause of adrenal hyperplasia, as previously reported in a mouse model of GR haploinsufficiency. However, the molecular mechanisms linking adrenal hyperplasia and GR haploinsufficiency need to be further elucidated.

Introduction

Morphological criteria to define adrenal hyperplasia remain scarce. Even though the prevalence of adrenal mass incidentally discovered during imaging or adrenal incidentaloma (AI), varies between 1-8% following autopsy studies, it seems to increase with age [START_REF] Bourdeau | MANAGEMENT OF ENDOCRINE DISEASE: Differential diagnosis, investigation and therapy of bilateral adrenal incidentalomas[END_REF]. A large number of AI are nowadays discovered and frequently referred to a clinical endocrinologist. Recent guidelines (2) define benign AI with strict radiological criteria (3).

Among AI, 15% are bilateral but mainly non-functional [START_REF] Bourdeau | MANAGEMENT OF ENDOCRINE DISEASE: Differential diagnosis, investigation and therapy of bilateral adrenal incidentalomas[END_REF]. Diagnosis of Bilateral Adrenal Hyperplasia (BAH) may be considered easy. However, the definition of normal adrenal glands is still controversial. Initially, normal adrenal glands were defined as a right lateral and medial limb measurement at 2.8 cm, with the left medial limb at 3.3 cm and lateral at 3.0 cm [START_REF] Vincent | The size of normal adrenal glands on computed tomography[END_REF]. More recently, adrenal volume assessed by computerized tomography (CT) was used to define normality [START_REF] Carsin-Vu | MDCT Linear and Volumetric Analysis of Adrenal Glands: Normative Data and Multiparametric Assessment[END_REF]. Left adrenal gland volume was estimated at 4.5 ± 1.6 cm 3 while the volume of the right adrenal gland was 3.8 ± 1.3 cm 3 . Volume measurements appear to be more reproducible among investigators compared with linear measurements. The association between BAH and steroid excess facilitates diagnosis and is important to recognize given the potential increased morbidity and mortality. Hypercortisolism occurs in 12% of AI, while hyperaldosteronism or catecholamine excess is observed in 2.5% and in 7% of cases, respectively [START_REF] Fassnacht | Management of adrenal incidentalomas: European Society of Endocrinology Clinical Practice Guideline in collaboration with the European Network for the Study of Adrenal Tumors[END_REF]. Metabolic disorders (glucose intolerance, diabetes, hypertension, dyslipidemia and osteoporosis) can be associated with AI and subclinical hypercortisolism [START_REF] Fassnacht | Management of adrenal incidentalomas: European Society of Endocrinology Clinical Practice Guideline in collaboration with the European Network for the Study of Adrenal Tumors[END_REF]. Malignancy was described in 3% of cases [START_REF] Bourdeau | MANAGEMENT OF ENDOCRINE DISEASE: Differential diagnosis, investigation and therapy of bilateral adrenal incidentalomas[END_REF] and congenital adrenal hyperplasia in 21% [START_REF] Patócs | Hormonal evaluation and mutation screening for steroid 21-hydroxylase deficiency in patients with unilateral and bilateral adrenal incidentalomas[END_REF]. A new nomenclature of BAH associated with Cushing' syndrome was recently published [START_REF] Stratakis | Genetics of adrenal tumors associated with Cushing's syndrome: a new classification for bilateral adrenocortical hyperplasias[END_REF]. When the nodule size is <1cm, thus referring to micronodular adrenals, the main cause is primary pigmented nodular adrenal disease (PPNAD). However, if their size exceeds 1 cm, primary bilateral macronodular adrenal hyperplasia (PBMAH) should be considered [START_REF] Bonnet-Serrano | Genetics of tumors of the adrenal cortex[END_REF].

In this review, we will discuss the pathogenesis of BAH in the context of subclinical hypercortisolism, highlighting the recently discovered NR3C1 mutations as recently discussed by Nicolaides & Chrousos [START_REF] Nicolaides | Bilateral adrenal hyperplasia and NR3C1 mutations causing glucocorticoid resistance: Is there an association?[END_REF]. Adrenal pheochromocytomas or hyperaldosteronism, carcinoma, metastasis or etiologies of unilateral AI were excluded.

Adrenal hyperplasia.

Physiology of adrenal cortex

Cortisol release is under the control of hypothalamic corticotropin releasing hormone (CRH).

As illustrated in Fig. 1, CRH stimulates corticotrope cells of the anterior pituitary, which secrete adrenocorticotropic hormone (ACTH). ACTH is one of the most potent physiological modulators of steroidogenesis and binds to its 7-transmembrane G protein-coupled receptor (GPCR) MC2R, expressed in all zones of the adrenal cortex. ACTH binding to MC2R, in association with melanocortin-2 receptors accessory proteins (MRAP), activated Gs protein, followed by activation of adenylyl cyclase, enhancing intracellular cAMP concentration (Fig. 2), thus stimulating Protein Kinase A (PKA) signaling. PKA is a hetero-tetramer composed of 2 catalytic subunits, encoded by three different catalytic subunits of which Cα predominates in the adrenal gland plus 2 regulatory subunits, encoded by four genes (R1α, R1β, R2α and R2β) [START_REF] Weigand | Differential expression of the protein kinase A subunits in normal adrenal glands and adrenocortical adenomas[END_REF]. Binding of 4 cAMP molecules to PKA regulatory subunit dimers allows release and activation of the 2 PKA catalytic subunits, which phosphorylate several targets, such as cAMP response element (CRE) binding protein (CREB), or steroidogenic factor 1 (SF1), regulating StAR function. Phosphodiesterase, involved in cAMP degradation, act as negative regulators of this pathway.

StAR is the first step of steroidogenesis, involved in cholesterol flux into the inner mitochondrial membrane [START_REF] Miller | MECHANISMS IN ENDOCRINOLOGY: Rare defects in adrenal steroidogenesis[END_REF]. Cortisol, the final steroidogenic compound, exerts a negative feedback loop on hypothalamic CRH and pituitary ACTH (Fig. 1). ACTH also plays a major role in the vasculature development via local synthesis of VEGF and in adrenal tissue growth. ACTH may be locally produced by medullary chromaffin cells, thus playing a major autocrine/paracrine role in the adrenal gland [START_REF] Lefebvre | Role of ACTH in the Interactive/Paracrine Regulation of Adrenal Steroid Secretion in Physiological and Pathophysiological Conditions[END_REF]. Activation of cAMP/PKA signaling pathway may lead to hypercortisolism [START_REF] Gallo-Payet | 60 YEARS OF POMC: Adrenal and extra-adrenal functions of ACTH[END_REF]. A functional link between PKA and Wnt pathways was reported, as demonstrated by a cell-specific PKA-activated downregulation of β-catenin phosphorylation in H295R cells [START_REF] Drelon | PKA inhibits WNT signalling in adrenal cortex zonation and prevents malignant tumour development[END_REF].

Genetic abnormalities

Every enzyme or protein involved in these pathways could be mutated and responsible for overactivation of signaling cascades resulting in hypercortisolism and adrenal hyperplasia.

(summarized in Table 1).

PPNAD

PPNAD, an autosomal dominant manner disorder, is often observed in patients with Carney's complex. Seventy percent of index cases are familial, while the remaining cases are de novo germline mutations [START_REF] Tirosh | Genetics of micronodular adrenal hyperplasia and Carney complex[END_REF]. One hundred and thirty-five pathogenic mutations have been reported to date. PPNAD is mainly related to germline inactivating mutations of the PRKAR1A gene, associated with constitutive activation of PKA ( 16), or phosphodiesterases PDE11A and PDE8B mutations [START_REF] Horvath | A genome-wide scan identifies mutations in the gene encoding phosphodiesterase 11A4 (PDE11A) in individuals with adrenocortical hyperplasia[END_REF]. PPNAD can be associated with hypercortisolism leading to ACTH-independent Cushing syndrome. Of note, the glucocorticoid receptor (GR) was shown to be overexpressed in PPNAD nodules, underlying paradoxical dexamethasone (DXM) induction of cortisol secretion [START_REF] Bourdeau | Primary pigmented nodular adrenocortical disease: paradoxical responses of cortisol secretion to dexamethasone occur in vitro and are associated with increased expression of the glucocorticoid receptor[END_REF].

PBMAH

Expression of illicit receptors in the adrenal glands (GIP, LH/HCG, vasopressin, catecholamines, serotonin 5 HT, angiotensin II or glucagon) was first identified as a leading cause of regulatory mechanism of cortisol production in PBMAH. The prevalence of these illegitimate membrane receptors is rather high (up to 77-87% of cases), leading to cAMP/PKA pathway activation and enhanced corticosteroidogenesis [START_REF] Barisson | Genetics of primary macronodular adrenal hyperplasia[END_REF]. Intra-adrenal ACTH secretion responsible for an autocrine/paracrine regulation in cortisol production, was recently reported in PBMAH (20). Activating MC2R mutations [START_REF] Barisson | Genetics of primary macronodular adrenal hyperplasia[END_REF], or point mutations of the α subunit types of G proteins responsible for altered GTPase activity

Mutations of steroidogenesis players

Mutations of important players, either transporters (StAR) or enzymes (CYP11A1, HSD3B2, CYP17A1, POR, CYP11B1 and CYP21A2) involved in steroidogenesis, are responsible for adrenal hyperplasia associated with a cortisol secretion defect and high levels of ACTH.

Glucocorticoid resistance

Definition

Glucocorticoid hormones (including Cortisol) regulate various biological functions involved in development, metabolism, inflammatory processes and stress. Their actions are mediated mainly by GR, a member of the nuclear receptor superfamily, which is an intracellular receptor protein acting as a ligand-activated transcription factor. Human GR (hGR) is encoded by the NR3C1 gene (MIM#138040). GR may exist in multiple isoforms generated by alternative splicing: hGRα, hGRβ, hGRγ, hGR-A and hGR-P. Eight alternative initiation sites into hGRα have been previously described [START_REF] Miller | MECHANISMS IN ENDOCRINOLOGY: Rare defects in adrenal steroidogenesis[END_REF][START_REF] Lefebvre | Role of ACTH in the Interactive/Paracrine Regulation of Adrenal Steroid Secretion in Physiological and Pathophysiological Conditions[END_REF], leading to distinct GR protein variants (GRα-A to D3). GRα-A results from translation of GRα mRNA from the first AUG codon (Met 1 ) while the shorter GRα-B results from translation beginning from the second AUG codon (Met 27 ). Even though numerous GR variants have been discovered by next generation sequencing (NGS) methods [START_REF] Foussier | Functional Characterization of Glucocorticoid Receptor Variants Is Required to Avoid Misinterpretation of NGS Data[END_REF], only twenty-eight NR3C1 loss-of-function mutations have been clearly associated with a glucocorticoid resistance syndrome (MIM#615962) [START_REF] Vitellius | Pathophysiology of Glucocorticoid Signaling[END_REF][START_REF] Al Argan | Glucocorticoid resistance syndrome caused by a novel NR3C1 point mutation[END_REF][START_REF] Molnár | Polymorphisms of the GR and HSD11B1 genes influence body mass index and weight gain during hormone replacement treatment in patients with Addison's disease[END_REF] while 30 index cases were studied [START_REF] Vitellius | Pathophysiology of Glucocorticoid Signaling[END_REF][START_REF] Al Argan | Glucocorticoid resistance syndrome caused by a novel NR3C1 point mutation[END_REF][START_REF] Molnár | Polymorphisms of the GR and HSD11B1 genes influence body mass index and weight gain during hormone replacement treatment in patients with Addison's disease[END_REF]. Eight patients out of 12 in whom an adrenal CT examination was performed, presented with BAH, bringing into question the role played by GR mutations and on the involvement of glucocorticoid resistance in the pathophysiology of adrenal hyperplasia.

Role of GR in adrenal cortex

The presence of GR in the normal adrenal gland remains controversial. Several authors reported a significant contribution of GR in the pathogenesis of hyperplastic glands [START_REF] Bourdeau | Primary pigmented nodular adrenocortical disease: paradoxical responses of cortisol secretion to dexamethasone occur in vitro and are associated with increased expression of the glucocorticoid receptor[END_REF][START_REF] Louiset | The paradoxical increase in cortisol secretion induced by dexamethasone in primary pigmented nodular adrenocortical disease involves a glucocorticoid receptor-mediated effect of dexamethasone on protein kinase A catalytic subunits[END_REF].

Bourdeau et al [START_REF] Bourdeau | Primary pigmented nodular adrenocortical disease: paradoxical responses of cortisol secretion to dexamethasone occur in vitro and are associated with increased expression of the glucocorticoid receptor[END_REF] demonstrated, by RT-qPCR and immunohistochemistry, that PPNAD cells and some PBMAH cells overexpress endogenous GR. Later on, Louiset et al [START_REF] Louiset | The paradoxical increase in cortisol secretion induced by dexamethasone in primary pigmented nodular adrenocortical disease involves a glucocorticoid receptor-mediated effect of dexamethasone on protein kinase A catalytic subunits[END_REF] showed, using PPNAD cells, the involvement of GR in a paradoxical response to cortisol by measuring cortisol release by RIA in culture supernatants [START_REF] Louiset | The paradoxical increase in cortisol secretion induced by dexamethasone in primary pigmented nodular adrenocortical disease involves a glucocorticoid receptor-mediated effect of dexamethasone on protein kinase A catalytic subunits[END_REF]. They demonstrated that DXM decreased cortisol production using a PKA inhibitor, indicating that DXM stimulates PKA catalytic subunits. The GR antagonist RU486 was found to decrease basal glucocorticoid production, suggesting that cortisol exerts an ultrashort positive feedback on its own production in PPNAD, via GR and supporting GR dependent up-regulation of PKA catalytic subunit genes [START_REF] Bourdeau | Primary pigmented nodular adrenocortical disease: paradoxical responses of cortisol secretion to dexamethasone occur in vitro and are associated with increased expression of the glucocorticoid receptor[END_REF].

More recently, our group demonstrated that GR directly impacts human adrenocortical H295R cell function by increasing key factors of steroidogenesis, including MC2R expression, as shown by pharmacological GR inhibition or RNA interference strategy (32).

Finally, the presence of GR was confirmed in human normal adrenal tissue by RT-PCR and WB [START_REF] Paust | Expression of the glucocorticoid receptor in the human adrenal cortex[END_REF], while the GRα-D isoform, that had a reduced transcriptional activity compared to GRα-B, was reported in normal and adrenal cortex tumors [START_REF] Damjanovic | Glucocorticoid receptor and molecular chaperones in the pathogenesis of adrenal incidentalomas: potential role of reduced sensitivity to glucocorticoids[END_REF]. Later, it was also demonstrated that an overexpression of GR variant: A3669G and BclI polymorphism, can be associated with AI. The BclI polymorphism was also overrepresented in patients with BAH (35). To conclude, the involvement of GR in adrenal cortex and in the pathogenesis of different diseases with adrenal hyperplasia remains unclear, but its link with different signaling pathways in the adrenal cortex needs to be further elucidated. To address this issue, we recently used CRISPR/Cas 9 technology to introduce a GR loss-of-function mutation, previously functionally characterized [START_REF] Vitellius | Three Novel Heterozygous Point Mutations of NR3C1 causing Glucocorticoid Resistance[END_REF], in human H295R cells.

BAH in patients with NR3C1 mutations

The French National Hospital Clinical Research Program (PHRC), Muta-GR, was launched to determine the prevalence of NR3C1 mutations in a cohort of one hundred patients presenting with BAH, associated with high blood pressure (HBP) and/or biological hypercortisolism without Cushing features. Forty patients had abnormal DXM suppression tests (plasma cortisol concentration remains >50 nmol/L) and high urinary free cortisol levels sometimes associated with unsuppressed ACTH levels. Five novel heterozygous NR3C1 mutations were discovered, among which three have been already functionally characterized [START_REF] Vitellius | Three Novel Heterozygous Point Mutations of NR3C1 causing Glucocorticoid Resistance[END_REF][START_REF] Bouligand | Familial glucocorticoid receptor haploinsufficiency by non-sense mediated mRNA decay, adrenal hyperplasia and apparent mineralocorticoid excess[END_REF], leading to the 5% prevalence of GR mutations. The phenotype of glucocorticoid resistant patients was much milder than the initial description (Table 2) [START_REF] Vingerhoeds | Spontaneous hypercortisolism without Cushing's syndrome[END_REF]. We recently unraveled the molecular mechanisms of defective GR-dependent regulation of 11β-HSD2 in patients carrying GR loss-of-function mutations, associated with pseudohypermineralocorticism (39). These findings emphasize the importance of GR genetic screening in selected patients enabling their appropriate management and optimized followup. Primary fibroblast cultures were obtained after skin biopsy in four mutated patients (R469X, R477S, R491X, Q501H GR mutations) and GR haploinsufficiency was further demonstrated by a reduced DXM induction of FKBP5 mRNA levels, consistent with glucocorticoid resistance observed in the mutated patients.

The study of the first heterozygous GR stop mutation, R469X, was very informative [START_REF] Bouligand | Familial glucocorticoid receptor haploinsufficiency by non-sense mediated mRNA decay, adrenal hyperplasia and apparent mineralocorticoid excess[END_REF].

Indeed, among 8 mutated family members spanning three generations, four had BAH, among them a 9-y-old child, suggesting the involvement of GR haploinsufficiency in the pathogenesis of BAH.

However, the exact mechanisms by which GR haploinsufficiency could modulate adrenal hyperplasia remain unknown. Up to now, it was proposed that ACTH overstimulation of the adrenal gland accounts for BAH in the context of GR loss-of-function mutations, supported by several human studies, including three heterozygous GR mutations associated with BAH and high ACTH levels [START_REF] Al Argan | Glucocorticoid resistance syndrome caused by a novel NR3C1 point mutation[END_REF]35,[START_REF] Charmandari | A novel point mutation in helix 11 of the ligand-binding domain of the human glucocorticoid receptor gene causing generalized glucocorticoid resistance[END_REF]. This was also reminiscent of the homozygous Nr3c1 gene inactivation in mouse models [START_REF] Cole | Targeted disruption of the glucocorticoid receptor[END_REF] in which 90% of these mice died 1-2 h postnatally, while an aberrant GR binding site was recovered in different tissues of the 10% of mouse survivors despite overt glucocorticoid resistance (42). An enlarged adrenal gland size and disorganized adrenocortical cells were reported in homozygous GRKO mice that presented with high corticosterone and ACTH levels, consistent with altered HPA regulation [START_REF] Cole | Targeted disruption of the glucocorticoid receptor[END_REF].

However, a heterozygous GR mouse model was recently published in which one functional GR allele, responsible for GR haploinsufficiency, also had enlarged adrenal glands (29) but normal ACTH levels, precluding an exclusive role of high circulating ACTH levels in the pathogenesis of adrenal hyperplasia.

Conclusion

Adrenal hyperplasia is often associated with overactivation of cAMP signaling pathways, related to well-characterized GPCR or other genetic alterations. Given that GR is expressed in the adrenal cortex and owing to the recent discovery of heterozygous GR mutations in BAH patients, it is likely that GR haploinsufficiency might affect adrenal function and proliferation. The molecular mechanisms involved remain to be elucidated.

  (21) leading to constitutive activation of the cAMP/PKA pathway, have been also described less frequently in PMBAH. Recently, a new tumor suppressor gene, inactivation of Armadillo Repeat Containing Familly (ARMC5), was discovered after whole genome sequencing of 26 patients with corticotropin-independent macronodular hyperplasia (22). ARMC5 was described in familial and sporadic forms of PBMAH, but the mechanism by which ARMC5 was responsible for hypercortisolism and adrenal hyperplasia remains unknown (23). Recently, Lecoq et al (24), identified somatic duplications in the 19q13.32 chromosome region in three patients. These genetic rearrangements lead to a new genomic environment in which cisregulatory regions, containing glucocorticoid response elements of the ZMYND8 gene, drive ectopic expression of glucose-dependent insulinotropic polypeptide receptor (GIPR) in two GIP-dependent cortisol secreting adenomas and one adrenal tumor with PBMAH. PBMAH was also described in genetic syndromes, as multiple endocrine neoplasia type 1, or APC syndrome (1).

Figure 1 :

 1 Figure 1: Hypothalamus-Pituitary-Adrenal gland axisCortisol release is under the control of hypothalamic corticotropin releasing hormone (CRH). CRH stimulates secretion of pituitary adrenocorticotropic hormone (ACTH) which is responsible the production of cortisol by adrenal cortex. Paracrine/autocrine regulation of cortisol and ACTH secretion in adrenal glands has also been described(20,[START_REF] Paust | Expression of the glucocorticoid receptor in the human adrenal cortex[END_REF]. Cortisol exerts a negative feedback loop on hypothalamic and pituitary cells.

Figure 2 :

 2 Figure 2: Steroidogenesis in adrenal cells ACTH binds its MC2R receptor and activates a cAMP pathway leading to PKA activation through release and activation of the 2 PKA catalytic subunits. Subsequent phosphorylation of several targets allows StAR activation.

Figure 3 :

 3 Figure 3: Bilateral adrenal hyperplasia in mutated GR patients Examples of CT images in BAH patients; (A) left and right, lateral and medial limb >5mm without nodules;(B) nodules and right and left lateral and medial limb >5 mm; (C) Adrenal macronodules >10 mm.

Fig. 2

 2 Fig. 2

Fig. 3

 3 Fig. 3

This article reports the unique murine model of GR haploinsufficiency.

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	42. Cole TJ, Myles K, Purton JF, Brereton PS, Solomon NM, Godfrey DI, & Funder JW.
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	(doi:10.1096/fj.08-111914)
	Genome editing
	technology may help unravel these issues.

Table 1 :Genetic alteration involved in adrenal hyperplasia

 1

		Gene	Bilateral adrenal hyperplasia
		PRKAR1A	PPNAD
		PDE11A	PPNAD
		PDE8B	PPNAD and BAH
	ACTH pathways	MC2R GNAS	PBMAH PBMAH
		ARMC5	PBMAH
		NEM 1	PBMAH
		FH	PBMAH
		StAR	lipoid CAH
		CYP11A1 (P450scc)	lipoid CAH
		HSD3B2	CAH
	Steroidogenesis enzyme	CYP17A1	CAH
		POR	CAH
		CYP11B1	CAH
		CYP21A2	CAH
	GR pathways	NR3C1 chromosome 19q13 microduplication	BAH BAH
	Wnt/β catenin pathway	CTNNB1 APC	PBMAH PBMAH

Genes involved in adrenal hyperplasia and corresponding altered signaling pathways. ACTH, adrenocorticotropic hormone; BAH, bilateral adrenal hyperplasia; CAH, congenital adrenal hyperplasia; GR, Glucocorticoid receptor; PBMAH, primary bilateral macronodular adrenal hyperplasia; PPNAD, primary pigmented nodular adrenal disease.

Table 2 : Phenotype comparison between mutated GR patients described in Muta-GR study (35) and the first mutated GR patient (38)

 2 BMI: Body mass index; SBP / Systolic Blood Pressure; DBP: Diastolic Blood Pressure; UFC: Urinary Free Cortisol, DST: 1 mg DXM suppresion test , _ : negative.

		Mutated patients Muta-GR study First described patient Normal range
	Type of Mutation	Heterozygous	Homozygous
	Age (Years)	53.2 ± 7.7	58
	BMI (kg/m 2 )	30.7 ± 9.5	24.01	<25
	SBP (mmHg)	123 ± 4.5	190	<140
	DBP (mmHg)	72 ± 4.5	130	<90
	Kalemia (mmol/L)	3.6 ± 0.2	↘	3.5-5
	Aldosterone (pg/mL)	17.3 ± 9.9	↘	19-117
	Renin (pg/mL)	47.2 ± 92.6	Normal	3-16
	Adrenal Hyperplasia	Yes	No
	8-AM ACTH (pg/mL)	N	2.1N	<1
	UFC (ULN)	1.7 ± 0.65	30-40	<1
	DST	─	─

Acknowledgments

The authors would like to thank Pr. Brigitte Delemer (CHU Reims) who was co-principal investigator of the Muta-GR study. We thank Dr. Jérôme Bouligand and Dr Severine Trabado (Department of Molecular Genetics, Pharmacogenetics and Hormonology, CHU Bicêtre, France) for their implication in this project. GV is the recipient of a doctoral fellowship from the "Fondation pour la Recherche Médicale" (FRM). We are also indebted to the clinical endocrinologists who refereed the patients to our laboratory. We would like to address a very special thanks to the patients and their family and to Pr Michael DuBow (Institute for Integrative Biology of the Cell (I2BC), Université Paris Sud) for his careful English editing of the manuscript.

Fundings

GV is the recipient of a doctoral fellowship from the Fondation pour la Recherche Médicale (FRM). This work was supported by grants from Institut National de la Santé et de la Recherche Médicale (Inserm), and Paris-Sud University.

Disclosure

The authors declare that there is no conflict of interest that could be perceived as prejudicing the impartiality of this study.

Abbreviations:

cAMP, cyclic adenosine monophosphate; ACTH, adrenocorticotropic hormone; AI, adrenal incidentaloma; BAH, bilateral adrenal hyperplasia; CAH, congenital adrenal hyperplasia; CRH, corticotropin releasing hormone; DXM, dexamethasone; DST, DXM suppression test; GIP, glucose-dependent insulinotropic polypeptide; GR, Glucocorticoid receptor; PBMAH, primary bilateral macronodular adrenal hyperplasia; PHRC, Hospital Clinical Research Program; PPNAD, primary pigmented nodular adrenal disease; PKA, protein kinase A; UFC, Urinary-free Cortisol.


Yun-Lai Zhu

Jun-Hui Yuan

Ya-Qian Song

Kan-Hao Xue

Sheng Wang

Chen Lian

Zhao-Nan Li

Ming Xu

Xiao-Min Cheng
email: xmcheng@hust.edu.cn

Xiang-Shui Miao

Promising photocatalysts with high carrier mobility for water splitting in monolayer Ge2P4S2 and Ge2As4S2

Keywords: 2D Materials, Photocatalysts, Direct band gap, Carrier mobility, Water splitting

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Photocatalytic water splitting to produce hydrogen and oxygen has been considered as a potential means for resolving the serious energy and environment problems [1][2][3][4][5][START_REF] Pulipaka | Tin disulfide based ternary composites for visible light driven photoelectrochemical water splitting[END_REF]. Thus far, enormous works have been performed since the discovery of TiO 2 as an effective photocatalyst for water splitting [START_REF] Ehrmaier | Mechanism of photocatalytic water splitting with triazine-based carbon nitrides: insights from ab initio calculations for the triazine-water complex[END_REF][START_REF] Ehrmaier | Mechanism of Photocatalytic Water Splitting with Graphitic Carbon Nitride: Photochemistry of the Heptazine-Water Complex[END_REF][START_REF] Fujishima | Electrochemical Photolysis of Water at a Semiconductor Electrode[END_REF][START_REF] Tabata | Modified Ta 3 N 5 Powder as a Photocatalyst for O 2 Evolution in a Two-Step Water Splitting System with an Iodate/Iodide Shuttle Redox Mediator under Visible Light[END_REF][START_REF] Ding | Hierarchical spheres assembled from large ultrathin anatase TiO 2 nanosheets for photocatalytic hydrogen evolution from water splitting[END_REF][START_REF] Lin | In-situ photo-deposition CuO1-cluster on TiO2 for enhanced photocatalytic H2-production activity[END_REF][START_REF] Liu | Design of cocatalyst loading position for photocatalytic water splitting into hydrogen in electrolyte solutions[END_REF][START_REF] Wang | Branched hydrogenated TiO 2 nanorod arrays for improving photocatalytic hydrogen evolution performance under simulated solar light[END_REF][START_REF] Yang | A facile fabrication of hierarchical Ag nanoparticles-decorated N-TiO 2 with enhanced photocatalytic hydrogen production under solar light[END_REF]. A primary requirement for such photocatalyst is that the conduction band minimum (CBM) should stay above the hydrogen reduction potential (H + /H 2 ), while the valence band maximum (VBM) should lie below the water oxidation potential (H 2 O/O 2 ) [START_REF] Kudo | Heterogeneous photocatalyst materials for water splitting[END_REF][START_REF] Phoon | Recent developments of strontium titanate for photocatalytic water splitting application[END_REF].

Consequently, its band gap must be larger than the 1.23 eV threshold, but nevertheless lower than 3.00 eV for the purpose of efficient solar energy harvesting [START_REF] Ni | A review and recent developments in photocatalytic water-splitting using TiO2 for hydrogen production[END_REF][START_REF] Cook | Solar Energy Supply and Storage for the Legacy and Nonlegacy Worlds[END_REF]. Therefore, an intermediate band gap around 1.8 eV is considered ideal for visible-light photocatalytic water splitting [START_REF] Guo | MXene: a promising photocatalyst for water splitting[END_REF][START_REF] Ran | Earth-abundant cocatalysts for semiconductor-based photocatalytic water splitting[END_REF][START_REF] Singh | Computational Screening of 2D Materials for Photocatalysis[END_REF][START_REF] Chen | Increasing Solar Absorption for Photocatalysis with Black Hydrogenated Titanium Dioxide Nanocrystals[END_REF].

Two-dimensional (2D) materials have been extensively investigated for photocatalytic water splitting, due to their distinct properties such as high specific surface areas, high photon-harvesting efficiency in the visible light region, and small charge transport distances [START_REF] Ni | A review and recent developments in photocatalytic water-splitting using TiO2 for hydrogen production[END_REF][START_REF] Li | Review of two-dimensional materials for photocatalytic water splitting from a theoretical perspective[END_REF][START_REF] Qiao | PdSeO 3 Monolayer: Promising Inorganic 2D Photocatalyst for Direct Overall Water Splitting Without Using Sacrificial Reagents and Cocatalysts[END_REF][START_REF] Su | Role of Interfaces in Two-Dimensional Photocatalyst for Water Splitting[END_REF]. All these reduce the probability of electron-hole recombination, bringing about enhanced photocatalytic performance. For example, monolayer ZnSe exhibits a great photocurrent density up to 2.14 mA cm -2 , which is about materials have been synthesized experimentally or predicated theoretically for photocatalyst application, such as transition metal dichalcogenides [START_REF] Liao | Design of High-Efficiency Visible-Light Photocatalysts for Water Splitting: MoS 2 /AlN(GaN) Heterostructures[END_REF], g-C 3 N 4 [START_REF] Wang | A metal-free polymeric photocatalyst for hydrogen production from water under visible light[END_REF][START_REF] Mishra | Graphitic carbon nitride (g-C3N4)-based metal-free photocatalysts for water splitting: A review[END_REF][START_REF] Reddy | Polymeric graphitic carbon nitride (g-C3N4)-based semiconducting nanostructured materials: Synthesis methods, properties and photocatalytic applications[END_REF], group-III mono-chalcogenides [START_REF] Zhuang | Single-Layer Group-III Monochalcogenide Photocatalysts for Water Splitting[END_REF], and so forth. However, achieving both fast carrier migration and effective separation of photo-generated electrons and holes in these 2D materials remains challenging.

Recently, Jing et al. proposed 2D GeP 3 with the buckling blue phosphorene-type honeycomb structure, showing strong interlayer quantum confinement and high carrier mobility up to 8.84 × 10 3 cm 2 V -1 s -1 for the bilayer [START_REF] Jing | GeP 3 : A Small Indirect Band Gap 2D Crystal with High Carrier Mobility and Strong Interlayer Quantum Confinement[END_REF]. Thereafter, a series of monolayer metal phosphides such as GaP 3 [START_REF] Yao | 2D Triphosphides: SbP3 and GaP3 monolayer as promising photocatalysts for water splitting[END_REF], InP 3 [START_REF] Miao | Tunable Magnetism and Extraordinary Sunlight Absorbance in Indium Triphosphide Monolayer[END_REF], SnP 3 [START_REF] Sun | Novel two-dimensional semiconductor SnP 3 : high stability, tunable bandgaps and high carrier mobility explored using first-principles calculations[END_REF] and TlP 5 [START_REF] Yuan | TlP 5 : an unexplored direct band gap 2D semiconductor with ultra-high carrier mobility[END_REF], with high carrier mobilities have been theoretically predicted, which are candidates for optoelectronic applications. However, these 2D materials are not suitable for photocatalytic water splitting, because of their small band gap values or improper CBM/VBM positions. For example, monolayer SnP 3 only has an indirect band gap of 0.83 eV, albeit possessing very high carrier mobilities in the range of 3000-7000 cm 2 V -1 s -1 [START_REF] Ghosh | SnP 3 : A Previously Unexplored Two-Dimensional Material[END_REF]. On the other hand, through proper element substitution, certain ternary compounds can be designed to fulfill the desired electronic properties. Typical examples involve Si 2 BN [START_REF] Andriotis | Prediction of a new graphenelike Si 2 BN solid[END_REF], P 2 SiS [START_REF] Xie | Prediction of new group IV-V-VI monolayer semiconductors based on first principle calculation[END_REF] and BNBe 3 [START_REF] Ding | Tunable electronic and magnetic properties of graphene-like XYBe 3 (XY = BN, AlN, SiC, GeC) nanosheets with carrier doping: a first-principles study[END_REF]. Hence, it is expected that the band gap of monolayer GeP 3 can be intentionally adjusted by neighboring elements substitution.

In this work, two isoelectric monolayer compounds based on GeP 3 and GeAs 3 are designed, where part of the P/As atoms are replaced by S atoms. The resulting monolayer Ge 2 P 4 S 2 and Ge 2 As 4 S 2 well meet the desired band gap value and band edge positions required by water redox potentials. Through thermodynamic and kinetic stability as well as carrier mobility studies, we shall show the great potential of monolayer Ge 2 P 4 S 2 and Ge 2 As 4 S 2 in photocatalytic water splitting.

Computational methods

All calculations were based on density functional theory (DFT) as implemented in the Vienna Ab initio Simulation Package (VASP) [START_REF] Kresse | Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[END_REF].

The electrons considered as valence were 3d, 4s and 4p for Ge; 3s and 3p for P; 3s and 3p for S; 4s and 4p for As; 2s and 2p for O; 1s for H. Core electrons were replaced by projector augmented-wave (PAW) pseudopotentials [START_REF] Kresse | From ultrasoft pseudopotentials to the projector augmented-wave method[END_REF]. The generalized gradient approximation (GGA) within the Perdew-Burke-Ernzerhof (PBE) functional form [START_REF] Perdew | Generalized Gradient Approximation Made Simple[END_REF] was adopted for the exchange-correlation energy. The plane-wave kinetic energy cutoff was fixed to be 500 eV. The geometric structures were fully relaxed with the force convergence criterion set to 0.001 eV Å -1 , while all self-consistent electronic loops were regarded as convergent when the energy difference between two consecutive steps became less than 10 -7 eV.

A vacuum space of ~20 Å along the z direction was used to minimize the undesired interaction between the atomic layer and its periodic images.

The Brillouin zone sampling was carried out using equal spacing Γ-centered 11×11×1 k-point mesh for structural relaxation. The Heyd-Scuseria-Ernzerhof (HSE06) screened exchange hybrid functional [START_REF] Heyd | Hybrid functionals based on a screened Coulomb potential[END_REF] was also adopted to characterize the electronic and optical properties more precisely. The phonon dispersion relations were calculated with the density functional perturbation theory as implemented in the PHONOPY code [START_REF] Chaput | Phonon-phonon interactions in transition metals[END_REF][START_REF] Togo | First-principles calculations of the ferroelastic transition between rutile-type and ${\text{CaCl}}_{2}$-type ${\text{SiO}}_{2}$ at high pressures[END_REF]. In addition, ab initio molecular dynamics (AIMD) simulations were performed to assess the thermodynamic stability of the structures, where canonical ensembles (NVT) were used [START_REF] Martyna | Nosé-Hoover chains: The canonical ensemble via continuous dynamics[END_REF].

Results and discussion

Atomic structures and stability analysis

As shown in Figs. 1a and1b, the optimized structure of Ge 2 P 4 S 2 (Ge 2 As 4 S 2 ) monolayer is similar to the recently investigated GeP 3 [START_REF] Jing | GeP 3 : A Small Indirect Band Gap 2D Crystal with High Carrier Mobility and Strong Interlayer Quantum Confinement[END_REF],

where only two P atoms in the hexagonal unit cell of GeP 3 are replaced by S atoms. Detailed geometric data are further listed in Table 1. The optimized lattice constant of Ge 2 P 4 S 2 is 6.77 Å with a buckling height of 1.91 Å, while the lattice constant of Ge 2 As 4 S 2 increases to 7.10 Å, accompanied by a corresponding 1.85 Å buckling height. The visualization of the electron localization function (ELF) [START_REF] Silvi | Classification of chemical bonds based on topological analysis of electron localization functions[END_REF] is conducted to investigate the nature of the chemical bonding in Ge 2 P 4 S 2 (see Fig. 1c).

The ELF values of 1, 0.5 and 0 correspond to fully localized electrons, free electron gas and the absence of electrons, respectively. A substantial concentration of electrons is found to reside along the Ge-P and Ge-S bonds, while the difference in the ELF values of various atoms exists, indicating the coexistence of covalent bond and ionic bond for Ge-P and Ge-S. The Bader charge analysis [START_REF] Henkelman | A fast and robust algorithm for Bader decomposition of charge density[END_REF] further reveals that in Ge 2 P 4 S 2 the Ge/P atom has lost 0.54/0.02 e, while the S atom has gained 0.57 e; in Ge 2 As 4 S 2 the amount of electron loss is 0.43/0.12 e for the Ge/As atom and the amount of electron gain is 0.66e for the S atom. Subsequently, we calculated the cohesive energy E C , which is defined by (Ge 2 As 4 S 2 ) mainly stems from S 3p, P 3p (As 4p) and Ge 4p states. In our electronic structure calculations, the spin-orbit coupling (SOC) effect was neglected, since we observed little impact on the band diagrams through turning on SOC, as confirmed by the band diagram comparison in Fig.

S1.

Strain engineering is a feasible method to tune the band structure of 2D materials [START_REF] Hu | Strain induced new phase and indirect-direct band gap transition of monolayer InSe[END_REF][START_REF] Kamal | Arsenene: Two-dimensional buckled and puckered honeycomb arsenic systems[END_REF][START_REF] Lü | Tuning the indirect-direct band gap transition of SiC, GeC and SnC monolayer in a graphene-like honeycomb structure by strain engineering: a quasiparticle GW study[END_REF][START_REF] Yuan | Ideal strength and elastic instability in single-layer 8-Pmmn borophene[END_REF][START_REF] Zhang | Atomically Thin Arsenene and Antimonene: Semimetal-Semiconductor and Indirect-Direct Band-Gap Transitions[END_REF]. Hence, we further studied the evolution of band gap values upon the application of biaxial strain, using the PBE functional.

Notwithstanding the issue of band gap underestimation, the consequence of strain on the band structure can be well described by PBE-calculations.

Figure 4 shows that the band gap increases gradually and then drops slowly upon varying the applied strain from -6% to 6%. Notably, the Ge 2 P 4 S 2 monolayer turns into a direct gap semiconductor by adding an extra 3% compressive strain (Fig. 4a), while the Ge 2 As 4 S 2 monolayer becomes indirect band gap with an applied tensile strain of 1% (Fig. 4b).

Moreover, the calculated strain energy as a function of the biaxial strain is also given in these figures. The band structure evolution upon applying biaxial strain is reasonable (Figs. 4c and4d), thus applying strain is an effective way to delicately tune the electronic properties of Ge 2 P(As) 4 S 2 monolayers.

Band alignments and optical properties

As the Ge 2 P 4 S 2 and Ge 2 As 4 S 2 monolayers possess suitable band gaps (>1.23 eV), it is worthwhile to explore their application potential as visible light photocatalysts. Yet, certain criteria of suitable band edges should be complied with, namely the position of CBM must be higher than the hydrogen reduction potential H + /H 2 (-4.44 eV) while the VBM must be lower than the water oxidation potential of H 2 O/O 2 (-5.67 eV).

Our calculation results shown in Fig. 5a verify that the band edges of Ge 2 P 4 S 2 and Ge 2 As 4 S 2 monolayers perfectly cover the redox potentials of water, fulfilling the thermodynamic requirements for water splitting.

Moreover, the Ge 2 P 4 S 2 monolayer with 3% compressive strain also has favorable band edge positions for water splitting, and the direct gap feature would make it more beneficial over the strain-free counterpart. To efficiently harvest solar energy is another important requirement for photocatalysts. Hence, we further explored the optical properties of

1 1 2 2 2 2 1 2 1 2 ( ) ( ) ( ) ( ) c ω α ω ε ω ε ω ε ω     = + -      
. As shown in Fig. 5b, the absorption coefficients of monolayer Ge 2 P(As) 4 S 2 reach the order of 10 5 cm -1 , which is comparable to that of the crystalline silicon for solar cells [START_REF] Green | Optical properties of intrinsic silicon at 300 K[END_REF].

Out-of-plane absorption is larger than in-plane absorption in the invisible light region from 100 nm to 160 nm, while smaller than the latter in the wavelength region from 160 nm to ~600 nm. Overall, the Ge 2 P(As) 4 S 2 monolayers have considerable absorption in both ultraviolet and visible light regions.

Carrier mobility

Subsequently, we systematically calculated the carrier mobility (electrons and holes) based on the deformation potential (DP) theory proposed by Bardeen and Shockley [START_REF] Bardeen | Deformation Potentials and Mobilities in Non-Polar Crystals[END_REF]. The acoustic phonon-limited carrier mobility of homogeneous 2D materials can be evaluated by the following equation , where E is the total energy of the 2D structure, and 0 S is the lattice area of the equilibrium supercell. The deformation potential constant l i E is defined as l 0 = / ( / )

i i E E l l ∆ ∆
.

Here i E ∆ is the energy change of the i th band under proper cell compression and dilatation (calculated using a step of 0.5%), l 0 is the lattice constant in the transport direction and ∆l is the deformation of l 0 .

As summarized in Table 2, the effective masses of electrons and holes for semiconductors [START_REF] Lang | Mobility anisotropy of two-dimensional semiconductors[END_REF]. The carrier mobility along the a-axis of anisotropic 2D materials can be calculated using the following equation [65]

2 2 3 3 1 2 2 2 l l l l 2 2 B 5 +3 8 9 +7 4 ( ) ( ) ( ) 20 D D a b a a a b b a b C C e E E E E k T m m µ       = + h .
Through this formula, one can take into the account the anisotropic elastic constants or deformation potential constants, which in general tends to reduce the strong anisotropy stemming from the Bardeen-Shockley formula [START_REF] Zhou | Widely tunable and anisotropic charge carrier mobility in monolayer tin( II ) selenide using biaxial strain: a first-principles study[END_REF][START_REF] Song | KTlO: a metal shrouded 2D semiconductor with high carrier mobility and tunable magnetism[END_REF]. For monolayer Ge 2 P 4 S 2 , Lang et al.'s formula yields electron mobilities of 1.61×10 4 cm 2 V -1 s -1 and 1.02×10 4 cm 2 V -1 s -1 along the a and b directions, respectively. For holes, the large anisotropy is greatly diminished, yielding 150 cm 2 V -1 s -1 and 280 cm 2 V -1 s -1 along the a and b directions, respectively. Compared with monolayer Ge 2 P 4 S 2 , however, the hole mobilities of monolayer Ge 2 As 4 S 2 are homogenized to 1.24×10 3 cm 2 V -1 s -1 and 760 cm 2 V -1 s -1 along the a and b directions, respectively. And for electrons, the mobilities are 3.42×10 3 cm 2 V -1 s -1 and 1.37×10 3 cm 2 V -1 s -1 cm 2 V -1 s -1 along the a and b directions, where the a-direction now becomes the fast-transport direction. After fixing the treatment of carrier mobility anisotropy, the generally high carrier mobilities are still confirmed in Ge 2 P(As) 4 S 2 monolayers. (unit: eV), elastic modulus C2D (unit: N m -1 ), carrier mobility µ2D (unit: 10 3 cm 2 V -1 s -1 )

for monolayer Ge2P4S2/Ge2As4S2 along the a and b directions. For mobility, two distinct values are listed in the format of α/β, where α was obtained directly from the Bardeen-Shockley formula while β (underlined) was obtained using the new theory proposed by Lang et al. [START_REF] Lang | Mobility anisotropy of two-dimensional semiconductors[END_REF].

Materials Carrier type * a m * b m l | | a E l | | b E 2 D a C 2 D b C 2 D a µ 2 D b µ Ge2P4S2 Ge2As4S2

Water adsorption and decomposition on the surface of 2D

Ge2As4S2

Last but not least, we have investigated the stability of Ge 2 P(As) 4 S 2 monolayers in liquid water, which is essential for their practical implementation as photocatalysts. To this end, AIMD simulations were performed at room temperature (300 K) with a time scale of 6 ps. Owing to the structural similarity, monolayer Ge 2 As 4 S 2 was chosen to be the representative model system for both materials. Our results in Fig. S2 demonstrate that monolayer Ge 2 As 4 S 2 is still thermodynamically stable in liquid water at room temperature. The redox reactions of water on monolayer Ge 2 As 4 S 2 were also investigated to further reveal the mechanism of photocatalytic hydrogen evolution. The adsorption energy of a species or functional group X on a 2D surface can be defined as . The first scheme is consistent with several previously published works [START_REF] Guo | MXene: a promising photocatalyst for water splitting[END_REF][START_REF] Peng | Computational mining of photocatalysts for water splitting hydrogen production: two-dimensional InSe-family monolayers[END_REF][START_REF] Lv | Two-dimensional germanium monochalcogenides for photocatalytic water splitting with high carrier mobility[END_REF][START_REF] Meng | Two dimensional XAs (X = Si, Ge, Sn) monolayers as promising photocatalysts for water splitting hydrogen production with high carrier mobility[END_REF][START_REF] Chowdhury | Monolayer Group IV-VI Monochalcogenides: Low-Dimensional Materials for Photocatalytic Water Splitting[END_REF], but the second scheme considers that the source of surface -H and -OH is mainly water molecules.

According [START_REF] Guo | MXene: a promising photocatalyst for water splitting[END_REF] and GeS [START_REF] Lv | Two-dimensional germanium monochalcogenides for photocatalytic water splitting with high carrier mobility[END_REF]. These encouraging results list monolayer Ge 2 As 4 S 2 as an excellent candidate for photocatalytic water splitting.

Conclusion

To summarize, the structural, electronic and optical properties of

Fig. 1

 1 Fig. 1 (a) Top view and (b) side view of Ge2P(As)4S2 monolayers in a 2×2×1 supercell. (c) Visualization of the electron localization function for monolayer Ge2P4S2.

Fig. 2

 2 Fig. 2 Phonon band structures of (a) Ge2P4S2, and (b) Ge2As4S2 monolayers. The total energy fluctuations during AIMD simulations are shown for (c) Ge2P4S2, and (d)

Fig. 3

 3 Fig. 3 Electronic band structure and projected density of states (PDOS) of (a) Ge2P4S2 and (b) Ge2As4S2 monolayers, calculated with the screened exchange HSE06 hybrid functional (solid line) and the PBE functional (dotted line). The pentagram points refer to VBM (blue) and CBM (red) locations, respectively.

Fig. 4

 4 Fig. 4 Effect of strain effects on band gap and total energy (in energy variation ∆E) of (a) monolayer Ge2P4S2, and (b) monolayer Ge2As4S2. (c) The electronic band structure of Ge2P4S2 with 3% compressive strain. (d) The electronic band structure of Ge2As4S2 with 1% tensile strain using the screened exchange HSE06 hybrid functional (solid line) and the PBE functional (dotted line). The Fermi level is set to zero energy and the pentagram points indicate the VBM (blue) and CBM (red) locations, respectively.

Fig. 5

 5 Fig. 5 (a) VBM and CBM locations of Ge2P4S2 and Ge2As4S2 monolayers with respect to the vacuum level (labeled as zero energy). The positions of the reduction potential of H + to H2 and the oxidation potential of H2O to O2 are indicated by the blue dashed lines. (b) The calculated optical absorption coefficients of Ge2P4S2/Ge2As4S2 monolayers using the screened exchange HSE06 hybrid functional.

Ge 2 P

 2 (As) 4 S 2 monolayers by calculating the in-and out-of-plane absorption spectra using the HSE06 functional. describe the optical properties of materials, where ω is the photon frequency, 1 ( ) ε ω and 2 ( ) ε ω are the real and imaginary parts of the dielectric function, respectively. The absorption coefficient can be evaluated according to the expression[START_REF] Yuan | First-Principles Calculations of the Electronic Structure and Optical Properties of Y-Cu Co-Doped ZnO[END_REF]

[ 62 ,*

 62 where h is the reduced Planck constant, B k is the Boltzmann constant, m* is the effective mass in the direction of transport, m d is the average effective mass determined by and T is the temperature (T = 300 K). The elastic modulus 2D C of the longitudinal strain in the propagation direction is derived from

Ge 2 P 4 S 2 /

 242 Ge 2 As 4 S 2 monolayers along the a direction are 0.202/0.209 m e and 1.669/0.123 m e (m e is the free electron mass), while those for the b direction are 0.395/0.836 m e (for electrons) and 1.656/0.418 m e (for holes), respectively. The elastic moduli are slightly anisotropic with the value of 54.14/48.46 N m -1 and 43.72/42.55 N m -1 for Ge 2 P 4 S 2 and Ge 2 As 4 S 2 monolayers along the a/b directions, respectively. The deformation potential constants E l are small for Ge 2 P(As) 4 S 2 , except for the hole of Ge 2 As 4 S 2 along the a direction (7.54 eV). Based on the values of m * , C 2D and E l , we estimated the carrier mobilities of Ge 2 P(As) 4 S 2 monolayers according to the Bardeen-Shockley formula. The electron mobilities of monolayer Ge 2 P 4 S 2 are as high as 1.22/1.56×10 4 cm 2 V -1 s -1along a/b directions. In contrast to the high electron mobilities, the hole mobilities are relatively low with the value of 0.08/4.20×10 3 cm 2 V -1 s -1 along a/b directions, respectively. The low hole mobilities mainly stem from their large effective masses. For monolayer Ge 2 As 4 S 2 , the electron and hole mobilities are 2.03/4.45 and 0.59/45.68×10 3 cm 2 V -1 s -1 along a/b directions, respectively. Note that for both materials the hole mobilities show great anisotropy, which implies that the homogeneous approximation is questionable, rendering the application of Bardeen-Shockley formula improper. Therefore, we re-calculated the acoustic phonon-limited mobilities of Ge 2 P(As) 4 S 2 monolayers using a new formula proposed byLang et al., which considers the scattering from the other direction in 2D

E

  are the total energies of the 2D material with and without the adsorbed X, respectively; µ X is the chemical potential of X. We specify the chemical potential of water as the total energy of an isolated H 2 O molecule. Yet, the chemical potentials of -H and -OH suffer from uncertainties. Here, two schemes are proposed:(1) their chemical potentials equal the total energies of isolated neutral H and OH function groups; (2) H µ is chosen as a half of the H 2 molecule energy, while OH µ satisfies OH H water µ µ µ + =

Fig. 6

 6 Fig. 6 (a) Adsorption configurations of H, OH, and H2O, and decomposition mechanism of H2O on monolayer Ge2As4S2. (b) Interaction between two hydrogen adatoms, showing the formation and releasing of hydrogen molecules on/from monolayer Ge2As4S2.

Fig. S1

 S1 Fig. S1 The band structures of monolayer (a) Ge 2 P 4 S 2 ; and (b) Ge 2 As 4 S 2 with/without spin-orbit coupling (SOC) effects using HSE06 functional.

Fig. S2

 S2 Fig. S2 The vibration of the total energies for Ge 2 As 4 S 2 monolayers during ab initio molecular dynamics (AIMD) simulations in the water environment at 300K. The insets show snapshots of the structures after the 6 ps simulation time with 3 × 3 supercell with six water molecule.

Fig. S5

 S5 Fig. S5 (a) Electronic band structure of Ge 2 As 4 S 2 monolayer in an

  Ge 2 P 4 S 2 and 3.15 eV/atom for Ge 2 As 4 S 2 , which are comparable with blue phosphorene (3.29 eV/atom) [52]. Hence, it is possible to experimentally synthesize monolayer Ge 2 P 4 S 2 and Ge 2 As 4 S 2 from an energetic point of view.

	C E	[ = -	total E	-	1 n E (Ge)	-	2 n E (P/As)	-	3 n E (S)]/ ( n n n 1 2 3 + +	)	[51]. Here E total
	stands for the energy of Ge 2 P 4 S 2 (Ge 2 As 4 S 2 ) per unit cell, E(Ge), E(P/As),
	and E(S) are the energies of free Ge, P(As) and S atoms, and n 1 , n 2 and n 3
	are the numbers of Ge, P(As) and S atoms per unit cell. We find E C to be
	3.40 eV/ atom for

Table . 1

 . CalculatedIn addition, the phonon spectra of Ge 2 P 4 S 2 and Ge 2 As 4 S 2 monolayers were calculated to examine their kinetic stability, as shown in Figs.2a and 2b. No appreciable imaginary vibrational frequency modes are observed in the entire Brillouin zone for both Ge 2 P 4 S 2 and Ge 2 As 4 S 2 Ge 2 P 4 S 2 and Ge 2 As 4 S 2 monolayers up to 500 K. The mechanical stability of Ge 2 P 4 S 2 /Ge 2 As 4 S 2 monolayers was further verified by calculating their linear elastic constants. As listed in TableS1, the elastic constants satisfy the corresponding mechanical stability conditions based on the Born

	criteria [53]: 11 C	0,	44 C	0,	11 C C 12	0
		a(Å)	h(Å)		Ec		TB(e)	Eg (eV)
						(eV/atom)	Ge	S	P(As)	PBE HSE06
	Ge2P4S2	6.77	1.91		3.40	-0.54 +0.57 -0.02	1.12	1.86
	Ge2As4S2	7.10	1.85		3.15	-0.43 +0.66 -0.12	1.21	1.89

lattice constant a, buckling height h, cohesive energy Ec, amount of charge transfer TB between different atoms, band gaps Eg (at both PBE and HSE06 levels) of Ge2P4S2 and Ge2As4S2 monolayers. monolayers, proving that both two monolayers are kinetically stable. The thermal stability, however, can be tested by AIMD simulations at finite temperatures, where in our case the simulations were carried out at 500 K for 6 ps, with a time step of 1 fs. As shown in Figs.

2c and 2d

, no obvious disruption of the geometries is found and the total energies fluctuate in a narrow range, suggesting robust thermodynamic stability of > > -> . The kinetic, thermodynamic and mechanical stabilities pave the way for experimental realization of Ge 2 P 4 S 2 and Ge 2 As 4 S 2 monolayers.

3.2 Electronic structures and the strain effect Figures 3a and 3b

  Unlike the Ge 2 P 4 S 2 monolayer, however, the Ge 2 As 4 S 2 and valence bands involve contributions from all atoms in both materials. The VBM of Ge 2 P 4 S 2 (Ge 2 As 4 S 2 ) mainly consists of P 3p (As 4p), Ge 4p, S 3p and Ge 4s states, while the CBM of Ge 2 P 4 S 2

demonstrate the electronic band structures as well as the projected density of states (PDOS) of Ge 2 P 4 S 2 /Ge 2 As 4 S 2 monolayers. Monolayer Ge 2 P 4 S 2 is a semiconductor with an indirect band gap of 1.85 eV according to our HSE06 calculation. The PBE-predicted gap value is 1.12 eV, which is also indirect, though with the well-known band gap underestimation. The VBM lies at the K point whereas the CBM is at the Γ point. monolayer presents direct band gap feature with VBM/CBM both located at Γ. The band gap value is 1.89 eV based on the HSE06 calculation (1.21 eV for PBE). A PDOS analysis (the right column of Fig.

3

) reveals that the conduction

Table 2 .

 2 Calculated

effective mass m* (unit: me), deformation potential constant l | | i E

  to Scheme 1, the adsorption energies of H, OH and H 2 O on As 4 S 2 is only 0.05 eV, facilitating the release of produced H 2 from the surface, which is similar to the case of Zr 2 CO 2

	monolayer Ge 2 As 4 S 2 are -1.71 eV, -2.58 eV and -0.30 eV, respectively,
	favoring their surface adsorption. Using Scheme 2, we find the
	corresponding adsorption energies of H and OH become 0.56 eV and 0.52
	eV, while the adsorption energy of H 2 O is the same (-0.30 eV) by
	definition. It should be noted that the reaction energy of subsequent water
	decomposition on monolayer Ge 2 As 4 S 2 is from -0.30 eV to 0.71 eV,
	indicating an endothermic reaction, which is similar to the water
	decomposition reaction on anatase TiO 2 surface [72]. In addition, the
	remotely separated hydrogen adatoms prefer to migrate close to each
	other, forming hydrogen molecules, when the photo-generated hydrogen
	atoms are adsorbed on monolayer Ge 2 As 4 S 2 (Fig. 6b). It is beneficial that
	the endothermic reaction energy required for removing one H 2 molecule
	from monolayer Ge 2

  Ge 2 P 4 S 2 /Ge 2 As 4 S 2 monolayers were investigated systematically through density functional theory calculations. The cohesive energy, phonon dispersions as well as AIMD simulation results demonstrate the high stability of Ge 2 P 4 S 2 and Ge 2 As 4 S 2 monolayers. Monolayer Ge 2 As 4 S 2 has a direct Γ-Γ band gap of 1.89 eV, while monolayer Ge 2 P 4 S 2 is an indirect band gap semiconductor with 1.85 eV gap value, which can become direct band gap by applying 3% compressive strain. Attractively, the band edge positions of Ge 2 P(As) 4 S 2 monolayers perfectly meet the requirement of the reduction and oxidation levels for water splitting. Moreover, the Ge 2 P 4 S 2 and Ge 2 As 4 S 2 monolayers show great anisotropy, and the highest It can be observed that E x and E y are very close both for the Ge 2 P 4 S 2 and Ge 2 As 4 S 2 monolayers, indicating the weak structural anisotropy. The Young's modulus of Ge 2 P 4 S 2 monolayer along the x and y direction are 46.89 and 49.84 N m -1 , while that is 42.12 (x direction) and 43.45 N m -1 (y direction) for Ge 2 As 4 S 2 monolayer, respectively. Compared to other 2D materials, the Young's modulus of Ge 2 P 4 S 2 and Ge 2 As 4 S 2 monolayers are smaller than that of graphene (344.2 N m -1 )4 and MoS 2 (130N m -1 )5 monolayers, indicating that the Ge 2 P 4 S 2 and Ge 2 As 4 S 2 monolayers are rather flexible material. Table S1 Effective independent elastic constants (C ij , in N m -1 ), and Young's moduli (E x , E y , in N m -1 ) of Ge 2 P 4 S 2 and Ge 2 As 4 S 2 monolayers. Ge 2 P 4 S 2 47.59 5.94 50.48 21.48 46.89 49.84 Ge 2 As 4 S 2 43.37 7.48 44.74 18.20 42.12 43.45

	acoustic phonon-limited electron mobilities are 1.606 × 10 4 cm 2 V -1 s -1
	and 3.42 × 10 3 cm 2 V -1 s -1 , respectively. Their high carrier mobilities and
	moderate optical absorption in the visible-light wavelengths add to their
	application potential in photocatalytic water splitting.
	0, elastic constants stratify above mentioned conditions, suggesting that the 0, 0 C C C C > > -> . 2 Obviously, the Ge 2 P 4 S 2 and Ge 2 As 4 S 2 monolayers are mechanically stable. Furthermore, the Young's modulus E x (E y ) is defined as 2 2 12 12 11 22 22 11 , x y C C E C E C C C = -= -. 3 C 11 C 12 C 22 C 44 E x E y

Acknowledgement

This work was supported by the National Natural Science Foundation of China under Grant No. 11704134, and the Hubei "Chu-Tian Young Scholar" program. K.-H. Xue received support the China Scholarship Council (No. 201806165012).

Appendix A. Supplementary data

Supplementary data to this article can be found online.

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Promising photocatalysts with high carrier mobility for water splitting in monolayer Ge2P4S2 and Ge2As4S2

Yun-Lai Zhu, a+ Jun-Hui Yuan, a+ Ya-Qian Song, a Kan-Hao Xue, a,b* Sheng Wang, a Chen Lian, a Zhao-Nan Li, a Ming Xu, a Xiao-Min Cheng, a* Xiang-Shui Miao

Corresponding Authors

*E-mail: xmcheng@hust.edu.cn (X.-M. Cheng) xkh@hust.edu.cn (K.-H. Xue)

The 2D elastic constants matrix components C 11 , C 12 , C 22 and C 44 of Ge 2 P 4 S 2 and Ge 2 As 4 S 2 monolayers are calculated, as listed in Table S1.

For 2D materials, the corresponding mechanical stability conditions based on the Born criteria 1 are 11 [START_REF] Perdew | Generalized Gradient Approximation Made Simple[END_REF] 11 12