Pierre Hennebert

Flore Rebischung

P Langeron

Eu waste hazardousness assessment -proposition of methods

The European waste hazardousness classification is currently under revision by the DG ENV of the European Commission and the Member States. This paper proposes some methods for measuring or calculating some Hazard Properties (HP). Laboratory test batteries for assessing HP 1 'Explosive', HP 2 'Oxidising', HP 3 'Flammable' and HP 14 'Ecotoxic' are proposed. For calculations of HP 3 to 8, 10, 11 and 13 to 14, a general analytical protocol for the determination of elements and substances in waste has been developed in France and is submitted to CEN TC292 "Characterisation of waste" for standardization. All the organic substances, mineral elements and main anions are identified and quantified if their concentration is greater than > 0.1% or a lower threshold. For mineral elements, a stepwise approach for the difficult speciation of elements in mineral substances in waste is proposed. In a first "worst case" approach, for the different HPs, tables with concentration limits triggering the classification control are presented. For HP 14, two additional "worst case" methods are proposed, as well as an approach based on leachate concentration, taking into account the aquatic bioavailability of potential pollutants of waste. Detailed proposition of methods with tables of EC 50 , NOEC and M factors for hundreds of organic and mineral substances for calculation of HP 14 are provided in

INTRODUCTION

The European Waste Framework Directive (2008/98/EC) and the List of Wastes Decision (2000/532/EC) are under revision. The DG Environment of the EU has proposed new definitions for the waste hazardousness assessment (DG ENV 2012a and b). This paper proposes methods to apply the classification rules where no methods are available or defined yet.

A tiered approach is recommended for waste assessment:

-1 st tier: Classification according to the European List of Waste (LoW) as "hazardous", "non-hazardous", or as "mirror entry". In this latter case:

-2 nd tier: Some HP can be assessed as "hazardous" or "non-hazardous" by expert judgment;

-3 rd tier: The remaining HP can be assessed as "hazardous" or "non-hazardous" from organic content and "worst case" hypothesis from total elemental content. If the "worst case" approach is unsatisfactory (unrealistic, not in accordance with what is known of the waste), perform 4 th tier;

-4 th tier: For some HP, perform specialized total analysis, leachate analysis or speciation of mineral content, or tests. An example of tiered approach can be found in [START_REF] Lewin | Assessment of Hazard Classification of UK IBA -Report for the January-June 2011 IBA dataset[END_REF].

It is remembered that landfill acceptance criteria cannot replace the waste hazardousness assessment.

The classification approach and the propositions of this paper are summarized in Figure 1.

Figure 1: Method for classification of waste from chemical composition and tests

An analytical package allows the detection and the semi-quantification of all the organic substances and all the mineral elements present in a liquid or solid waste sample. New parameters are defined and a mass balance is used as quality control. Results can be used for calculations of HP 3 to 8, 10, 11 and 13 to 14.

Stepwise surrogates methods are proposed for the speciation of the elements in mineral substances, from the "worst case" approach: if the element concentration, expressed in substance, is below the concentration limit of the most hazardous substance of that element for that HP, the waste is not hazardous by that element. This rule is refined when sum of substances are to be accounted for.

Battery of laboratory tests are proposed for HP 1 'Explosive', HP 2 'Oxidising' and HP 3 'Flammable'. They are more convenient than the detection of substances with corresponding hazard statement codes (R or H), as it is proposed by DG ENV. A battery of ecotoxicological test is proposed for HP 14 'Ecotoxic'.

A useful concept is the hazard index. A hazard index of a rule of a hazard property is the ratio of the relevant concentrations (for some HPs the sum or the weighted sum) by the concentration limit of this rule of this HP. If it is ≥ 1 [the (sum of) (weighted) concentration(s) is/are above the concentration limit(s)], the waste is hazardous for this HP. If it is <1, the waste is considered as non-hazardous.

Those methods are explained in detail in a guide [START_REF] Hennebert | Waste Hazardousness Assessment -Proposition of methods[END_REF].

PROPOSITION OF ANALYTICAL PACKAGE

A method for the exhaustive determination of elements and substances in liquid and solid waste has been developed in France (AFNOR 2013). It is proposed for standardization at European level to CEN TC 292 « Characterization of waste ».

New parameters taking into account unresolved chromatographically mass of volatile extracts, semi-volatile extracts, and non extractible pool, are proposed. This latter is assumed to be high molecular weight insoluble compounds -polymers, cellulose, lignin, etc…), without hazard. An analytical mass balance between 90% and 110% is reached for most waste. The analytical laboratory will provide tabular mass balance, the list of elements and substances, CAS number, concentrations, and limits of quantification. Concentrations in solid waste are expressed in mg/kg dry matter at 105 °C (some analyses are performed on raw waste or pretreated at 40 °C, the water content of raw and pretreated are measured on a separate aliquot and the results are expressed on a dry matter at 105 °C) and in mg/kg of raw material. Concentrations of liquid waste are expressed in mg/kg of raw material. The method and results with 32 waste can be found in Hennebert et al, 2013.

PROPOSITION OF ELEMENT SPECIATION SURROGATES

The elemental analyses performed in the laboratory do not speciate the chemical form of minerals present in the waste. Since classification rules are based on substances, it is necessary to reconstruct a mineralogical set from available information, or to bypass the problem. Different methods are presented below. A tiered approach is proposed.

3.1

Cases for which speciation is not neseccary: "worst case calculations", generic entries

3.1.1"Worst case" calculation

For each HP (and for some HP for each different rule), a hypothetical mineralogical set can be developed from stoichiometric calculation focusing on the most toxic substances (i.e. classifying substances with lowest limit concentration). This method is called "worst case". This approach is used in the document of the German Federal Ministry of the Environment (BAM 2002) and by the consulting firm POLDEN in 2004 (Abdelghafour et al, 2002).

It can be used for HP 4 'Irritant -Skin irritation and eye damage', HP 5 'Specific Target Organ Toxicity (STOT)/Aspiration', HP 6 'Acute Toxicity', HP 7 'Carcinogenic', HP 8 'Corrosive', HP 10 'Toxic for reproduction', HP 11 'Mutagenic', HP 13 'Sensitising'. Tables are available for each HP in Hennebert and Rebischung 2013. An example is given for HP 4 in Table 1.

The method is the following:

calculate for each element the ratio between the element concentration in the waste and the calculated element concentration limit supplied in the Table compare the sum or the maximum of these ratios to 1:

o Sum for HP 4, HP 6, HP 8 and HP 14. This sum should also include the ratios for organic substances detected in the waste, between the measured concentration and the corresponding concentration limit; o Maximum for HP 5, HP 7, HP 10, HP 11 and HP 13.

If the sum / maximum of these ratios is lower than 1, the waste is not classified as hazardous for this property, and no other actions are necessary, especially speciation.

Conversely, if the sum / maximum of these ratios is greater than 1, the waste could be classified as hazardous by this element, and further speciation should be performed.

Note: Concentration of element or concentration of substance?

The important point in the calculation is to compare similar concentrations in the ratios: -either element concentration in the waste and a calculated element concentration limit, as previously described worst case approach, -or a (sometimes hypothetical) substance is attributed to the element, and this substance concentration is compared to the concentration limit provided by the regulation.

Generic entries

No speciation is necessary for the elements having a « generic entry » in the list of harmonized classification and labeling of hazardous substances (CLP Regulation 2008), subject to prove those elements are not under one of the other forms specified in the CLP Regulation annex.

The "generic" entries are presented in Table 2 (extract from CLP Regulation Table 3.1 of Annex VI). They have no CAS number. In practice, speciation is therefore important for copper, zinc and nickel, which have no generic entries:

Table 2: Generic entries of elements in the CLP

-Some copper substances have toxic and ecotoxic properties of level 1 and 2 due to the accompanying anions (CN, Se, SeO 3 , CrO 4 ). Copper sulphate has toxic properties of level 2 or 4 and acute and chronic ecotoxicity of level 1. Copper with oxidation level of one Cu(I) (i.e. Cu(I)Cl, Cu(I) 2 O) is considered as not present in oxidized waste; -Zinc sulphate and chloride have some toxic properties. Sulphate, chloride and oxide have acute and chronic exotoxicity code H400 and H410; -Nickel substances have ± 40 entries in the CLP. Some substances have hazard statement codes classifying for HP 4, 5, 6, 7, 10, 11 and 15. For HP 14, all M factors are set to 1 when the substances have a hazard statement code H400 or H410.

"Worst case with information" calculation

The method is identical to the previous one, but some substances are not taken into account on the basis of available information on waste: pH, redox potential, rare or highly reactive substances, anions, production process, knowledge of similar waste, etc... Expertise plays an important role. This method is called "worst case with information".

If the calculated mineralogical set does not trigger the classification as hazardous, the waste is considered to be non-hazardous for this classification rule. Otherwise, or if an element is not likely to be in the form of some hazardous substance, but data is lacking to be sure, the evaluation can be deepened by true speciation of only the element(s) identified as presenting issue of classification.

Speciation

In this case, there are several ways to determine the mineralogical set in the waste:

via the literature for waste from processes with composition known as constant, with statistical approach to mineral composition, or;

using different analytical methods (electron microscopy, XRD ... with LOQ of 5 -2 %w/w), or;

via a calculation from geochemical solubility measurements at different pH. This method is in practice the sole that can be used for trace elements. From solubility at 8 different pH from 2 to 12 (CEN/TS 14429, CEN 2005), mineralogy is derived by saturation index (matching between observed and calculated concentrations at different pH) taking into account all the the species in solution and particular reactive solid phases. A useful tool is the database and databrowser LeachXS and the associated (editable) geochemical code Orchestra (van der [START_REF] Van Der Sloot | A database, speciation modelling and decision support tool for soil, sludge, sediments, wastes and construction products[END_REF]. Un example can be foind in Turrel et al (2012). Unfortunately, hazard statement code will most of the time not be available for the minerals that have been found.

4. The specific case of HP 14

HP 14 is the most frequent hazardous properties (Hennebert et al, 2013). The proposition of DG ENV (2012a) is that a waste is hazardous if

If ∑(cc Aquatic Acute 1 H400 × M acute ) ≥ 25 %, or If (M chronic × 10 × ∑cc Aquatic Chronic 1 H410) + ∑(cc Aquatic Chronic 2 H411) ≥ 25%
M factor is a multiplicative substance factor used to adapt the concentration limits to information available on aquatic ecotoxicity of substances H400 and H410 (and to avoid multiple concentration limits). It is calculated from the lowest data available of EC 50 (concentration with 50% of biological effect) and NOEC (no observed effect concentration) of a substance among different organisms. If a substance has an EC 50 or a NOEC < 0.1 mg/l and 0.01 mg/l respectively, but has not a hazard statement code H400 or H410, M factors do not apply. M acute factors are available in the CLP annex (CLP 2008) for pesticides and nickel substances. A large panel of M acute and M chronic factors for mineral and organic substances, derived from the Portal of Chemical substances from INERIS (http://www.ineris.fr/substances/fr/) are reported in Hennebert and Rebischung, 2013.

3.4.1"Worst case" approach and generic entries when the mineral substances are not known

The Tables 5 and6 show the minimum EC 50 and NOEC values extracted from the Portal of chemical substances from INERIS (http://www.ineris.fr/substances/fr/) of March 2013 and other data source among the species of metallic elements and metalloids. The elements in bold have generic entries. No further speciation work is required, as far as you can prove or judge that the "compounds specified elsewhere in this Annex" are not present in the waste.

If the waste contains only one element that can form a substance with H400 or H410 hazard statement code (and no organic substances with those codes), in a worst case approach, compare the total content with the concentration limit (penultimate column). If it is lower, the waste will not be H400 or H410.

If the waste contains more than one element that can form a substance with H400 or H410 hazard statement code (and no organic substances with those codes), in a worst case approach, compute the sum of ratios (concentration/concentration limit). If it is < 1, the waste will not be H400 or H410.

Note: Concentration of element or concentration of substance ? In the worst case approach, normally the substance concentration is used for hazard calculation. But for HP 14, in the worst case approach, taking into account that EC 50 and NOEC of heavy metals and metalloids are frequently expressed in element concentrations (mg/l), the element concentration is used rather than the substance concentration. For the generic entries, the element concentration is used for hazard calculation. Table 6: Most hazardous substances by element (worst case approach) and corresponding concentration limit of element for HP 14 acute and chronic, for other elements than in Tables 14 and15 Element HP 14 Min.

3.4.2"Worst case" approach for acute ecotoxicity with the total concentrations and the minimal EC 50

The CLP regulation allows calculating the EC 50 of a part of a mixture like a waste by combining individual EC 50 of the substances and their total concentration. This should at best be done with EC 50 values of the same taxonomic group (CLP 2008 p.136). The result is a calculated EC 50m of the mixture. This is valid only for acute hazard (4.1.3.3.1 of CLP). The EC 50m of a mixture (the waste) is calculated from the concentration of substances and the EC of each substance:

where:

Ci = concentration of component i (weight percentage) L(E)C50 i = (mg/l) LC50 or EC50 for component i L(E)C50 m = L(E) C50 of the part of the mixture with test data

The mixture is classified according to Table 4.1.0 of CLP regulation: it is acute Category 1 if CE 50m ≤ 1 mg/l. This approach could be used in "worst case" calculation with the EC 50 values:

-If EC 50 m is lower than 1 mg/l, that part of the waste (sum of C i ) has a hazard statement code H400. If it is higher, it has no hazard statement code;

-If EC 50 m is lower than 0.1 mg/l, assign a M acute factor to that part of the waste with the Table 3;

-Calculate the acute ecotoxicity of the waste with that part of the waste (sum of C i ) and all the substances having H400 hazard statement code: the waste is Aquatic Acute if: ∑(c Aquatic Acute 1 × M) ≥ 25 %.

The total and leachate concentrations of elements are known

One could consider that the leachate concentration of elements could be used for classification for aquatic ecotoxicity.

In waste leachate with liquid/solid ratio of 10 l/kg, soluble substances are totally dissolved in the leachate and less soluble (partially dissolved) substances control the concentration of the element in the leachate (solid/liquid equilibrium). In both cases, the soluble concentration cannot be higher. The leachate concentration represents the maximum concentration of the element that will be in contact with organisms during aquatic ecotoxicity tests.

Proposition of Method

If the leachate concentration of an element is lower than the ecotoxic concentration (EC 50 and NOEC) of that element from a soluble form (Tables 5 and6), the substance(s) that contain(s) that element is/are not hazardous and receive no hazard statement code, whatever that substance is. The waste is then classified according to the total content. 5 and6; 3. If C L < EC 50 and NOEC, the substance containing that element is not soluble enough to be ecotoxic;

4. If C L ≥ EC 50 or NOEC, the substance containing that element is soluble enough to be ecotoxic: attribute the hazard statement code of the Tables (H400, H410, H411, or no code), the EC 50 and NOEC, and the M acute and Mc hronic factors to that substance.

Hazard assessment (in progress) for 41 waste for HP14 acute classifies 7 waste hazardous for with the worst case method (3.4.1), 3 waste for the mixture method (3.4.2) and 2 waste for the leachate method (3.4.3).

For HP 14 acute (the most frequent HP property), the scores are 25 times hazardous for with the worst case method (3.4.1) and 22 times for the leachate method (3.4.3).

PROPOSITION OF TESTS

4.1 Tests for HP 1 'Explosive', HP 2 'Oxidising' and HP 3 'Flammable'

According to the DG ENV proposal, a waste will be hazardous if it contains substances with given hazard statement codes Hxx, without concentration limits. The substances for HP 1 and 2 and some substances for HP 3 are not measured in routine by service laboratories. Most of the time the presence of those substances for HP 1 and HP 2 will be known by the origin of the waste rather than by analysis at laboratory. An easy alternative to that is laboratory tests.

In France the battery of test applicable to waste for (present) properties H1, H2 and H3 is defined by the Order of 08.07.03. The methods are listed in Table 7. These tests are conducted by laboratories specialised in product characterization.

Tests for ecotoxicity

A battery of test emerging from a ring test with 64 laboratories from European countries and the U.S. (Moser and Römbke, 2009) is proposed by Pandard and Römbke (2013). This step-wise approach begins with tests performed with waste eluates. The results of these tests can be expressed as EC x values (concentration of eluate or solid in the mixture with the control substrate producing an effect of x %) or as LID values (lowest ineffective dilution rate). Preparation of eluates (liquid/solid ratio = 10 l/kg dry matter, 24h) and mixtures of waste with control substrate are carried out according to EN 14735 (CEN 2006). If one of the EC values in the eluate tests is below a specific limit value (or one of the LID values is above a specific limit value), the waste is classified as hazardous. Otherwise, solid waste tests are carried out. The waste is considered as non-hazardous only if all the results are above the limit values.

Results of tests overwhelm results of calculations. If the results of calculations are dubious (by lack of information), the test battery (eventually step-wise) should be performed. The test is performed with various dilutions without pH adjustment, and the test is then repeated for dilution(s) with toxic pH adjustment between 6.5 and 8.5. (Pandard,2004). In practice, the test UN N1 (flammable solids) and EC method A9 (flash point of liquids) are the most frequent. An alternative is to use the analytical package results to detect substances with a flash point < 55 °C.

CONCLUSION

This paper proposes methods for some aspects that have not yet been fully defined for the assessment of the hazard waste. Within the European objectives of priority reuse, recycling and recovery, the hazard must be measurable.

A tiered approach and a unified analytical method for minimizing the effort of waste classification are proposed. The analytical results are useable for classification of product as well, in case of end-of-waste status.

Users are encouraged to share their experience to improve the methods or clarify the practical cases that are not covered here.

  -00-5 arsenic compounds, with the exception of those specified elsewhere in this Annex Acute Tox. 3 compounds, with the exception of cadmium sulphoselenide (xCdS.yCdSe), reaction mass of cadmium sulphide with zinc sulphide (xCdS.yZnS), reaction mass of cadmium sulphide with mercury sulphide (xCdS.yHgS)compounds, with the exception of the tetroxide (Sb 2 O 4 ), pentoxide (Sb 2 O 5 ), trisulphide (Sb 2 S 3 ), pentasulphide (Sb 2 S 5 -00-9 thallium compounds, with the exception of those specified elsewhere in this Annex Acute Tox. 2 * Acute Tox. 2

Figure 2 :

 2 Figure 2: Scheme of attribution of hazard statement to unknown substances with leachate concentration

Table 1 : Most hazardous substances by element (worst case approach) and corresponding concentration limit of element for HP 4 Element HP 4 Min. Concentration limit / substance Worst case substance Formula CAS# Worst case Concentration limit /element in this substance

 1

	Ag
	Al	1%	Aluminium lithium hydride	LiAlH 4	16853-85-3	0.71%
	As
	B	1%	Boron tribromide	BBr 3	10294-33-4	0.043%
	Ba	20%	BaS / Barium polysulphides	BaS	21109-95-5	16.21%
	Be	20%	BeSeO4:4H2O	BeSeO 4 :4H2O		0.80%
	Ca	10%	Calcium cyanamide	CCaN 2	156-62-7	5.00%
	Cd
	Co
	Cr III
	Cr VI	1%	Chromyl dichloride; chromic oxychloride	Cl 2 CrO 2	14977-61-8	0.34%

Element HP 4 Min. Concentration limit / substance Worst case substance Formula CAS# Worst case Concentration limit /element in this substance

	Cu	10%	Copper(II) methanesulfonate	C 2 H 6 CuO 6 S 2 54253-62-2	2.50%
	Fe	20%	Ferrous sulfate heptahydrate	FeSO 4 .7H2O	7782-63-0	4.02%
	Hg	20%	Mercury (I) chloride	Hg 2 Cl 2	10112-91-1	17.00%
	K	1%	Potassium hydroxide; caustic potash	KOH	1310-58-3	0.70%
	Li	1%	n-hexyllithium	C 6 H 13 Li	21369-64-2	0.075%
	Mg
	Mn
	Mo	20%	BeMoO4	BeMoO 4		11.36%
	Na	1%	Sodium hydroxide; caustic soda	NaOH	1310-73-2	0.57%
	Ni	1%	Nickel(II) octanoate	C 16 H 30 NiO 4	4995-91-9	0.17%
	P	1%	Phosphoryl trichloride	Cl 3 OP	10025-87-3	0.20%
	Pb	10%	Lead(II) methanesulphonate	C 2 H 6 O 6 PbS 2 17570-76-2	5.21%
	S	1%	Thionyl dichloride; thionyl chloride	Cl 2 OS	7719-09-7	0.27%
	Sb
	Se	20%	BeSeO4:4H2O	BeSeO 4 :4H2O		7.05%
	Si	1%	Trichlorosilane	HCl 3 Si	10025-78-2	0.21%
	Sn
	Sr
	Tl	20%	Dithallium sulphate; thallic sulphate	Tl 2 SO4	7446-18-6	16.19%
	U
	V	10%	Divanadyl pyrophosphate	H 5 O 30 P 5 V 6	65232-89-5	3.23%
	Zn	10%	ZnSO4:1H2O	ZnSO 4 :1H2O	7446-19-7	3.64%

Table 3 :

 3 Multiplying factors for highly toxic components or mixtures(CLP 2008)

	Acute toxicity	M acute factor		Chronic toxicity	M chronic factor
					Non-rapidly	Rapidly
					degradable	degradable
	L(E)C 50 value mg/l		NOEC value mg/l	components	components
	0.1 < L(E)C 50 ≤	1		. < NOEC ≤ .	1	-
	0.01 < L(E)C 50 ≤ .	10	0.	< NOEC ≤ .	10	1
	0.001 < L(E)C 50 ≤ .	100	.	< NOEC ≤ .	100	10
	0.0001 < L(E)C 50 ≤ .	1 000	.	< NOEC ≤ .	1 000	100
	0.00001 < L(E)C 50 ≤ .	10 000	.	< NOEC ≤ .	10 000	1 000
	(continue in factor 10 intervals)		(continue in factor 10 intervals)

Table 4 :

 4 Minimal EC 50 , maximal M acute factor, maximal concentration limit and cut-off value for "worst case" approach in HP 14 acute ecotoxicity

Element Acute ecotoxicity hazard statement code EC 50 min (mg element/l) Substance M acute Concentration limit acute (mg element/kg) Cut-off value acute (mg element/kg)

	Hg	H400	0.0007	n.s.	1 000	250	1
	Cd	H400	0.0034	CdCl 2	100	2 500	10
	Cu	H400	0.011*	n.s.	10	25 000	100
	As	H400	0.011	AsH 2 KO 4	10	25 000	100
	Pb	H400	0.026	Pb(NO 3 ) 2	10	25 000	100
	Cr(VI)	H400	0.030	K 2 Cr 2 O 7	10	25 000	100
	Zn	H400	0.032	ZnCl 2	10	25 000	100
	Ni	H400	0.060	NiCl 2	1	250 000	1 000
	Se	H400	not found		1	250 000	1 000
	Tl	-	0.01	n.s.	-	-	-
	U	-	0.04	n.s.	-	-	-
	Be	-	0.1	n.s.	-	-	-
	Sb	-	1.77	SbCl 3	-	-	-
	Ba	-	14.5	n.s.	-	-	-
	Mo	-	29	n.s.	-	-	-

n.s.: not specified / *: a lower value can be found in a European Commission -European Voluntary Risk Assessment Report (EU-VRAR) report but it is proposed to use this value instead

Table 5 :

 5 Minimal NOEC, maximal M chronic factor, maximal concentration limit and cut-off value for "worst case" approach in HP 14 chronic ecotoxicity

	Element	Chronic ecotoxicity hazard statement code	NOEC min (mg/l)	Substance	M chronic	Concentration limit chronic (mg element/kg)	Cut-off value chronic (mg element/kg)
	Hg	H410	0.0001	n.s.	100	250	10
	Cd	H410	0.00016	CdCl 2	100	250	10
	Se	H410	0.0018	Na 2 SeO 3	10	2 500	100
	Cu	H410	0.0022	CuCl 2	10	2 500	100
	Cr(VI)	H410	0.0047	K 2 Cr 2 O 7	10	2 500	100
	As	H410	0.0050	AsHNa 2 O 4	10	2 500	100
	Pb	H410	0.0063	n.s.	10	2 500	100
	Zn	H410	0.01	ZnSO 4	10	2 500	100
	Ni	H410	0.011*	NiCl 2	1	25 000	1 000
	Be	H411	0.0038	n.s.	-	250 000	10 000
	Sb	H411	1.13	SbCl 3	-	250 000	10 000
	Tl	H411	0.002	n.s.	-	250 000	10 000
	U	H411	0.0007	n.s.	-	250 000	10 000
	Ba	-	2.9	n.s.	-	-	-
	Mo	-	54	n.s.	-	-	-

n.s.: not specified / *: a lower value can be found in a European Commission -European Voluntary Risk Assessment Report (EU-VRAR) report but it is proposed to use this value instead

Concentration limit /substance Worst case substance Formula CAS# Worst case Concentration limit /element

		HP 14 Min.				Worst case
	Element	Concentration	Worst case substance	Formula	CAS#	Concentration
		limit /substance				limit /element
	Na	0.25%	Sodium arsenite	NaAsO 2	7784-46-5	0.044%
	P	0.025%	Trizinc diphosphide; zinc phosphide	P 2 Zn 3	1314-84-7	0.0060%
	S	0.25%	Propoxycarbazone-sodium	C 15 H 17 N 4 NaO 7 S	181274-15-7	0.019%
	Si	2.50%	Lead hexafluorosilicate	F 6 PbSi	25808-74-6	0.20%
	Sn	2.50%	SnSe 2	SnSe 2	20770-09-6	1.07%
	Sr	2.50%	SrSeO 4	SrSeO 4	7446-21-1	0.95%
	V	2.50%	Pb 3 (VO4) 2	Pb 3 (VO 4 ) 2		0.30%
	Ag	2.50%	Silver sodium zirconium hydrogenphosphate	AgNaZrHPO 4	155925-27-2	0.85%
	Al	0.25%	Aluminium phosphide	AlP	20859-73-8	0.12%
	B	2.50%	Trinickel boride	BNi 3	12007-02-2	0.14%
	Ca	0.25%	Calcium phosphide; tricalcium diphosphide	Ca 3 P 2	1305-99-3	0.055%
	Co	0.25%	Cobalt dinitrate	Co(NO 3 ) 2	10141-05-6	0.081%
	Cr III
	Fe	2.50%	Pb 2 Fe(Cyanide) 6	Pb 2 Fe(Cyanide) 6		0.22%
	K	0.25%	Potassium dichromate	K 2 Cr 2 O 7	7778-50-9	0.066%
	Li	2.50%	Cobalt lithium nickel oxide	CoLiNiO	131344-56-4	0.12%
	Mg	0.25%	Magnesium phosphide; trimagnesium diphosphide	Mg 3 P 2	12057-74-8	0.14%
	Mn	2.50%	MnSeO 4 :5H2O	MnSeO 4 :5H 2 O		0.48%

Table 7 :

 7 Tests for H 1, H 2 and H 3 applicable to waste in France, and proposed for HP 1, HP 2 and HP 3.

	H properties	Definition of "product"	Methods
		Substances and preparations which may
	H1 Explosive	explode under the effect of flame or which are more sensitive to shocks or friction	EC Method A14: thermal and mechanical sensitivities (impact and friction)
		than dinitrobenzene
	H2 Oxidizing	Substances and preparations which, in contact with other substances, particularly flammable substances, present a highly exothermic reaction	Gas: Method ISO 10156 (paragraph 5) Liquids: UN O2 test (liquid oxidizers) Solids: UN test O1 (oxidizing solids)
		Substances and preparations:
		in liquid form, with a flash point below 21	EC method A9
		°C, or
		which may become hot and finally catch fire in air at ambient temperature without any input of energy, or	Test UN N2 (pyrophoric solids) or UN N3 (pyrophoric liquids) and UN N4 (solid, self-heating)
		In the solid state, which may readily catch
	H3-A Highly flammable	fire after brief contact with a source of
		ignition and which continue to burn or to	Test UN N1 (flammable solids)
		be consumed after removal of the source
		of ignition, or
		in the gaseous state, which are flammable	A11 EC method or a method of ISO 10156 (paragraph
		in air at normal pressure, or	4) standard
		which, in contact with water or damp air, evolve highly flammable gases in hazardous quantities.	Test UN N5 (substances which, in contact with water, emit flammable gases)
		Liquid substances and preparations having
	H3-B Flammable	a flash point equal to or greater than 21 °C	EC method A9
		and less than or equal to 55 °C

Table 8 :

 8 Recommended test battery for assessing HP 14

				EC or LID limit
	Test		Endpoints	values: the waste	Duration	Standard
				is HP 14 if
	1.	Aquatic tests
	Inhibition of the light emission of Vibrio fischeri (Luminescent bacteria test)	Eluate concentration which results in 50% inhibition of light emission (EC 50 ), or Dilution step at which light emission is inhibited by more than 20% in comparison to the control	EC 50 ≤ % LID > 8	30 min	EN ISO 11348-3(2007)
	Freshwater algal growth	Eluate concentration which results in 50%	EC 50 ≤ %
	inhibition test with Desmodesmus subspicatus or Pseudokirchneriella	inhibition of population growth (EC 50 ), or Dilution step at which population growth is inhibited by more than 25% in comparison to the	LID > 8	72 h	EN ISO 8692 (2012)
	subcapitata		control
			Eluate concentration which results in 50%	EC 50 ≤ %
	Inhibition of the mobility	inhibition of mobility (EC 50 ), or		48 h	EN ISO 6341
	of Daphnia magna -	Dilution step at which mobility is inhibited by more	LID > 8		(2012)
			than 20% in comparison to the control
	2.	Terrestrial tests
	Soil contact test with Arthrobacter globiformis (bacteria contact test)	Waste concentration which results in 50% by more than 30% inhibition of enzyme activity (EC 50 ), or Dilution step at which enzyme activity is inhibited	EC 50 ≤ % LID > 8	6 h	ISO/DIS 10871 (2008)
	Effects of chemicals on the	Waste concentration which results in 50%	EC 50 ≤ %
	emergence and growth of higher plants (Avena	inhibition of growth (EC 50 ), or Dilution step at which growth is inhibited by more	LID > 8	14 d	ISO 11269-2 (2012)
	sativa, Brassica napus)	than 30%
	Avoidance test with earthworms (Eisenia andrei/fetida)	Waste concentration which affects behaviour by more than 40% 50% (EC 50 ), or Dilution step at which behaviour is impacted by	EC 50 ≤ % LID > 8	48 h	ISO 17512-1 (2007)


Recension De Muriel

Adrien Michael

W Cole

Rebecca Zorach

This dense work, which collects essays from scholars in widely ranging fields, oversteps conventional boundaries, extending past the 16th century and reaching out further than Europe-to which art history is sometimes confined-, opening onto issues of cross-cultural encounters and conflict.

In the wake of the path-breaking work of the Reformation historian Michael Camille, The Gothic Idol, the book deals with a broad spectrum of objects and texts that document attitudes toward the idol mainly in the early modern period, with a view to focusing on the positive contribution of iconoclasm to art, and how it resulted not only in the destruction of things, but also in the making of new objects, or new points of view on former objects.

Suzanne Preston Blier's chapter looks at the reinvention of the original intent of an object, which sometimes turned secular objects into instruments of worship. She takes examples from African art and examines how they were improperly recast in the European imaginary as threatening idols that had to be destroyed or secreted away, thereby providing a useful alibi to demonise the African population and justify slavery. A later chapter, by Claire Farago and Carol Komadina Parenteau, also shows how art objects, such as the Veytia Mexican manuscripts, were misrepresented and reframed within a Western system of beliefs.

In the context of the Netherlands' decades-long struggle for independence from Spanish rule and Protestant Reformation, Celeste Brusati examines the Perspectives of Pieter Saenredam (1627-1665), where church images were no longer treated as objects of religious veneration, but as artefacts commemorating history and testimonials of an artistic heritage contributing to the preservation and constitution of the identity of the nascent Dutch Republic. Saenredam drew from the historiographic protocol of descriptive geography to give his paintings documentary value (including observers, featuring eye-points…), and pays particular attention to the deformations of shifting vantage points-in line with Hans Vredeman de Vries's perspective treatise of 1604-, and thereby negotiating confessional and political divides. Saenredam's younger compatriot, Samuel van Hoogstraten, introduced his treatise on optical illusions by metaphorically linking perspective with the visibility of paintings coming into view or receding out of view according to periods of iconoclasm or iconophilia.

Although Pope Sixtus V (16 th century) modelled himself on Gregory the Great, the "Destroyer of Pagan idols", dismantling monuments of the pagan past, Michael Cole looks at how he sometimes used them as bases for Christian images, as in the case of obelisks or columns on top of which crosses or statues of saints were erected, for example. More than repairing them, he ambiguously restored them as salient urban features and cult objects, thereby preserving the force of images, be it in their power of exorcising that very same force. Therefore, the bronze or gold idols were used as models, and not just as counter-examples, for the Christian monuments that initially were to transform them, and had therefore functions ambivalently close to those they intended to eradicate.

Thomas Cummins pinpoints the ambivalence of the Spaniards who believed it was their mission to remove golden idols in South America (mirroring Continental iconoclasm) and yet refashioned Christian images with that gold or financed Christian Baroque wars with it. This dubious enterprise was in fact just another way of greedily and lustily worshipping gold; Cummins also draws a parallel with transubstantiation-another figuration of God deemed proper-which he contends is suggestive of the ritual cannibalism of the Indians.

Through the example of the Strozzi Chapel (S. Maria Novella, Florence), Philine Helas and Gerhard Wolf show how the god Mars is given lifelikeness and, in their own words, "vitalization"-particular animated appearance-, inspired by the living figures acting as statues in quattrocento festival cultures, thereby underlining Mars's central role in Florence's self-identification.

Megan Holmes explores the idolatrous dimension of votive offerings, focusing on wax and silver figurines and body parts, as well as life-sized multi-media effigies. Wax anatomical exvotos bore the very traces of physical imprint, and furthermore were displayed very close to body relics and cult images. Therefore, during the 15th century, the votive object was progressively invested with talismanic potency, and became a cult image itself and the locus of social competition, since its greater or lesser magnificence encoded markers of social identity. Donald McColl's essay deals with iconoclasm by water. "Provision of water has been associated with strong social discipline" (185), and therefore disposal and destruction by water drew on the "gestures and timing of carnival transgression" (186), although McColl argues that such a parallel has its limits. Iconoclasm by water had the further advantage of being strikingly visual-with the floating objects of corpses-, making the symbol more lasting. Such acts were reminiscent of Biblical punishment (the Flood, the Drowning of Pharaoh's men in the Red Sea), rites of purification, or the fact that some sacred images (especially the acheiropoeiton images) were borne out of water.

According to Walter Malion, Georg Mack the Elder's painted print of The Trinity resonates across confessional lines, in that Lutheran viewers are able to appropriate this initially Catholic print, where the Ancient of Days is inspired by Isaiah's portrait of God as divinely sovereign and humble, dramatizing the conjunction of exalted dignity and majesty and exemplary abasement.

Mia Mochizuki examines the three types of Japanese images that grew out of cross-cultural encounters with Europe:

• Western subject matter represented according to Japanese conventions.

• Experiences with Western pictorial techniques, such as aerial and linear perspective called "Western views" by Japanese, adapted to such themes as theatre or sumo fights. • Western-style depictions of Western matter-that is, copies or replicas adapted to a Japanese medium for a Japanese audience, and with a few Japanese stylistic characteristics, mainly Catholic devotional art created in mission workshop such as the Niccolo school. This third category was increasingly viewed as seditiousbecause it could harbour political loyalties of Japanese Catholic converts-, and it therefore came under attack. Mochizuchi then analyses the hybrid nature of map screens, which flourished because they did not emulate the mimetic representational paradigm of the devotional icon. In so doing, they detached likeness from value-since they integrated details that were unintelligible for a Japanese-but merely served as a signifier of Western knowledge and as a metaphor for a world view which depended on a specific geographic locale, hence neutralising any attempts at idolatry.

In the following essay, Dawn Odell traces shifting European conceptions as regards the mimetic abilities of written text and imagery. As an example, in Dutch merchant van Linschoten's Itinerario (1563-1611), the descriptive naturalism of the picture served as visual objective confirmation of the text, as if the verisimilitude of the image were necessary evidence the text could not provide. The non-mimetic non-transparent European language was suspected of misrepresenting the world, creating a parallel perceptual world, a potentially idolatrous human-created code. By contrast, Chinese was thought to be an offshoot of the Adamic language-the lost universal language after humanity's hubris in constructing the tower of Babel-, because of its close kinship to pictograms, containing the promise of transparency to the physical world.

As mariolatry became a widespread phenomenon, the most common cult image, Maria in Sole, deriving from the Apocalypse (12:1-6) and Genesis (3:14-15), appeared suddenly in great numbers just before the beginning of the 16th century, not only as three-dimensional, life-sized wooden sculptures but also in the form of prints, both engravings and woodcuts, by celebrated artists such as Albrecht Dürer as well as anonymous craftsmen. Larry Silver shows how her protective aid was invoked during Reformation wars, and how her triumphalist symbolism over the devil, over the moon (recalling the crescent of Islam, a visual potent counter-offensive to Islam's iconophobia) served as an emblem for the true Church. Its afterlife was particularly long as it resurfaced when it was necessary for the threatened Catholic faith to reaffirm itself: at Guadalupe in Mexico (1531), Lourdes in France (1858), Fatima in Portugal (1917), and also at Regensburg (early 16th century), or Mariazell (around 1520).

In the 15th century, widely circulating popular printed images did not lend themselves to destruction because they were considered innocuous as printed media, with merely a mnemonic function. Drawing on the wide circulation and standardization of mathematical printing, which expanded greatly in the years around 1500, Rebecca Zorach focuses on the didactic diagrammatical images of the French scholar Charles de Bovelles which he connects to mathematics in an effort to find a mystical language of the mind. These were doubly abstracted images, as printed matter and as mathematical reference, and thus avoided the deception of visual imagery suspected of producing idols.

The strengths of the book are also its weaknesses: its piecemeal nature as a series of case studies offers no synthetic all-embracing overview. But it does provide very stimulating insights on the ways in which idolatry was seized upon as a political or social alibi, and how those who combated idolatry ambivalently often reproduced the same sort of practice. It also highlights the link between idolatry and mimesis, and says how detachment from that mimesis pinpointed the geographic and contextual relativism of art, thereby opening new vistas for artistic creation. This richly documented edited collection is highly commendable to all those interested in the phenomenon of iconoclasm in the early modern era but also, more broadly, to all those interested in the ways images can be invested with power and reality, in that its many erudite historical examples can easily fuel more theoretical reflections.


Wuming Zhu

Julien Toulouse

Andreas Savin

János G Ángyán

Range-separated density-functional theory with random phase approximation applied to noncovalent intermolecular interactions

H2O)2 VQZ -3.81 -5.21 -4.63 -5.38 -4.71 -5.42 -4.71 -5.02 3 Formic acid dimer VTZ -14.94 -20.52 -17.50 -21.00 -16.89 -21.36 -16.90 -18.61 4 Formamide dimer VTZ -12.85 -16.42 -14.

Range-separated methods combining a short-range density functional with long-range random phase approximations (RPA) with or without exchange response kernel are tested on rare-gas dimers and the S22 benchmark set of weakly interacting complexes of Jurečka, Šponer, Černý, and Hobza (Phys. Chem. Chem. Phys. 8,1985,2006). The methods are also compared to full-range RPA approaches. Both range separation and inclusion of the Hartree-Fock exchange kernel largely improve the accuracy of intermolecular interaction energies. The best results are obtained with the method called RSH+RPAx which yields interaction energies for the S22 set with an estimated mean absolute error of about 0.5 -0.6 kcal/mol, corresponding to a mean absolute percentage error of about 7 -9%, depending on the reference interaction energies used. In particular, the RSH+RPAx method is found to be overall more accurate than the range-separated method based on long-range second-order Møller-Plesset (MP2) perturbation theory (RSH+MP2).

I. INTRODUCTION

Because the usual local or semi-local approximations of Kohn-Sham density-functional theory (DFT) [1,2] generally fail to describe non-covalent intermolecular interactions, many approaches have been proposed to remedy their deficiencies. The most widely applied scheme is perhaps the so-called DFT-D approach [3][4][5][6][7], in which an empirical dispersion term is added to usual densityfunctional approximations, using dispersion coefficients generally determined from atomic reference data. There are some efforts to make the DFT-D approach less empirical, for example by calculating dispersion coefficients through the properties of the exchange hole [8,9], or from the local response approximation [10]. Other more or less empirical approaches include using parameterized atom-centered nonlocal one-electron potentials [11] or highly-parameterized hybrid or double-hybrid density functionals (see, e.g., Ref. 12,13). Non-empirical approaches include nonlocal correlation functionals derived from response theory [14][15][16] (possibly combined with long-range corrected exchange functionals [17][18][19]), DFT-based symmetry-adapted intermolecular perturbation theory (see, e.g., Ref. 20) and range-separated density-functional theory (see, e.g., Ref. 21), in which a short-range density functional is combined with a longrange explicit many-body method such as second-order perturbation theory [22], coupled-cluster theory [23] or multi-reference second-order perturbation theory [24].

Recently, the random phase approximation (RPA) and other related approximations to the electron correlation energy have gained revived interest and, in particular, they appear to be viable approaches to the description of weak interactions in molecular and solid-state systems [25][26][27][28][29][30][31][32][33][34][35][36][37]. However, RPA overestimates short-range correlations between particles [38], giving a too negative correlation energy, which lead Perdew and coworkers [39][40][41] to propose the so-called RPA+ scheme in which the RPA correlation energy is corrected by a gen-eralized gradient approximation (GGA). Also, in a Gaussian localized basis, RPA correlation energies have a slow convergence with respect to the basis size [25]. These known flaws of RPA can be cured by the range-separated density-functional theory scheme. Toulouse et al. [42] developed a range-separated method combining a longrange RPA-type approximation including the long-range Hartree-Fock exchange kernel with a short-range density functional approximation. Janesko et al. [43][44][45] have also implemented a range-separated RPA scheme based on the ring-coupled-cluster formulation of RPA [33], with no exchange kernel. In their approach, the RPA correlation energy has been rescaled by an empirical coefficient and the range-separation parameter has been optimized in order to improve agreement with experiment.

While initial tests of the range-separated RPA methods for rare-gas dimers and some small molecular complexes show encouraging results [42][43][44], it is not clear how their performance is for weak interactions between larger, biologically important molecules, the main targets for which these hybrid methods were initially developed. In this work, we apply range-separated RPA methods to the S22 test set of Jurečka et al. [46]. The S22 set comprises 7 hydrogen-bonded systems, 8 dispersionbonded complexes, and 7 mixed complexes with electrostatic and dispersion interactions. For completeness and comparison, we also include data for homonuclear raregas dimers.

II. METHODS AND COMPUTATIONAL DETAILS

The theory of range-separated RPA was described in Ref. 42. We give here only a brief overview. In a first step, we perform a self-consistent range-separated hybrid (RSH) calculation [22]

E RSH = min Φ { Φ| T + Vne + Ŵ lr ee |Φ + E sr Hxc [n Φ ]}, ( 1
)
where T is the kinetic energy operator, Vne is the nucleielectron potential operator, Ŵ lr ee is a long-range electronelectron interaction operator, E sr Hxc [n] is the associated short-range Hartree-exchange-correlation density functional, and Φ is a single-determinant wave function. The long-range interaction is constructed with the error function, w lr ee (r ij ) = erf(µr ij )/r ij , where µ is the range separation parameter, whose inverse gives the range of the short-range part of the interaction. In this work, we take a fixed value µ = 0.5 bohr -1 , which seems to be a reasonable choice for a variety of systems [47]. Several approximations [21,23,[48][49][50][51][52]

E = E RSH + E lr c . (2)
The long-range correlation energy E lr c can be obtained perturbatively in different ways, for example by secondorder Møller-Plesset (MP2) perturbation theory [22,[53][54][55], coupled-cluster theory [23,56], RPA-type approximations [42,43], or multi-reference second-order perturbation theory [24]. In this work, we focus on RPA-type approximations in which E lr c can be expressed as an integral over an adiabatic connection [42]

E lr c = 1 0 dλ W lr c,λ = 1 2 1 0 dλ iajb ij| ŵlr ee |ab P lr c,λ iajb , (3)
where i, j and a, b refer to occupied and virtual RSH orbitals, respectively, ij| ŵlr ee |ab are long-range twoelectron integrals, and P lr c,λ is the correlation part of the spin-singlet-adapted two-particle density matrix calculated as [25]

P lr c,λ = 2 (A λ -B λ ) 1/2 M -1/2 λ (A λ -B λ ) 1/2 -1 , (4)
with

M λ = (A λ -B λ ) 1/2 (A λ + B λ )(A λ -B λ ) 1/2
, and the singlet orbital rotation Hessians A λ and B λ . When only the long-range Hartree kernel is included, A λ and B λ write

(A λ ) iajb = (ǫ a -ǫ i )δ ij δ ab + 2λ aj| ŵlr ee |ib , (5)
(B λ ) iajb = 2λ ab| ŵlr ee |ij , (6)
where ǫ i and ǫ a are the RSH orbital eigenvalues. We will refer to this method as RSH+RPA (which is equivalent to the method called "LC-ωLDA+dRPA" in Refs. [43][44][45] in the special case of the short-range LDA functional). When the long-range Hartree-Fock exchange kernel is also included, A λ and B λ write

(A λ ) iajb = (ǫ a -ǫ i )δ ij δ ab +2λ aj| ŵlr ee |ib -λ aj| ŵlr ee |bi , (7)
(B λ ) iajb = 2λ ab| ŵlr ee |ij -λ ab| ŵlr ee |ji , (8)
and we will refer to this method as RSH+RPAx, as in Ref. 42. At second order in the electron-electron interaction, the RSH+RPAx method reduces to the RSH+MP2 method of Ref. 22. The RSH+RPA and RSH+RPAx methods are expected to supersede RSH+MP2 in situations where second-order perturbation theory fails, i.e. when differences of the occupied and virtual orbital energies are small. The integration over the coupling constant λ in Eq. ( 3) can be performed accurately by a 7-point Gauss-Legendre quadrature [25], at least for systems not dominated by static correlation effects. In the case of RPA (without exchange-correlation kernel), this integration can also be performed analytically leading to the so-called plasmon formula, as recently emphasized by Furche [32]. The reformulation of RPA as a ring coupled-cluster-doubles theory by Scuseria et al. [33], which is equivalent to the plasmon formula, is another advantageous way of avoiding the numerical integration over λ. Although there is also a plasmon formula for RPA with the Hartree-Fock exchange kernel which appears in the literature [33,57,58], due to the breaking of antisymmetry of the two-particle density matrix P lr c,λ iajb under exchange of two indices, it does not provide the same correlation energy as Eq. ( 3) used here and in Ref. 42. Unfortunately, as far as we know, the RPAx correlation energy of Eq. ( 3) cannot be brought to a plasmon formula and the adiabatic connection integral cannot be avoided. However, we show now that it is possible to perform accurately the integration over λ by a single-point quadrature. By expanding the integrand in powers of λ

W lr c,λ = W lr,(1) c λ + W lr,(2) c λ 2 + W lr,(3) c λ 3 + • • • , (9)
we can express the long-range correlation energy as the following expansion

E lr c = 1 0 dλ W lr c,λ = W lr,(1) c 2 + W lr,(2) c 3 + W lr,(3) c 4 + • • • .
(10) Naively, one could think that a single-point quadrature formula could only be exact up to first order in λ. This is the case for example when choosing the quadrature point λ = 1 and weight 1/2

E lr c ≈ 1 2 W lr c,1 , (11)
or, slightly better, the point λ = 1/2 and weight 1

E lr c ≈ W lr c,1/2 . ( 12
)
In fact, because the expansion of the integrand starts at first order in λ (i.e., we already know the value of the integrand at the point λ = 0 which is zero), there is a singlepoint Radau-type [START_REF] Abramowitz | Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables[END_REF] quadrature formula that is exact up to second order in λ. Indeed, we find that the condition w W lr,( 1)

c λ + W lr,(2) c λ2 = W lr,(1) c /2 + W lr, (2) c
/3 is fulfilled for the point λ = 2/3 and weight w = 3/4

E lr c ≈ 3 4 W lr c,2/3 . (13)
Even better, in the case of the RSH+RPAx method, we can use the long-range MP2 correlation energy which corresponds to the first-order term in λ,

E lr c,MP2 = 1 0 dλ W lr,(1) c λ = W lr, (1) c
/2, in order to find a single-point quadrature formula that is exact up to third order in λ. Indeed, imposing the condition w W lr,( 2)

c λ2 + W lr,(3) c λ3 = W lr,(2) c /3 + W lr,(3) c
/4 leads to the point λ = 3/4 and weight w = 16/27, so we find

E lr c = E lr c,MP2 + 1 0 dλ W lr c,λ -2E lr c,MP2 λ ≈ E lr c,MP2 + 16 27 W lr c,3/4 -2E lr c,MP2 3 4 = 1 9 E lr c,MP2 + 16 27 W lr c,3/4 . (14)
Compared to the 7-point Gauss-Legendre quadrature, the single-point quadrature formulas of Eq. ( 13) or Eq. ( 14) significantly reduce the computational cost while introducing only a negligible extra error, as shown later. We will use the formula of Eq. ( 14) to check our RSH+RPAx results on the S22 set with larger basis sets. All calculations are done with a development version of the MOLPRO 2008 program [START_REF] Werner | Molpro, version 2008.2, a package of ab initio programs[END_REF]. The long-range RPA, RPAx and MP2 correlation energies are evaluated with RSH orbitals obtained with the short-range PBE functional of Ref. 23. The full-range RPA correlation energy is evaluated with Kohn-Sham orbitals obtained with the usual PBE functional [START_REF] Perdew | [END_REF]. The full-range RPAx, MP2 and CCSD(T) correlation energies are calculated with Hartree-Fock orbitals. We use the correlation-consistent basis sets of Dunning [62], or modifications of them. Core electrons are kept frozen in the RPA, RPAx, MP2 and CCSD(T) calculations (i.e. only excitations of valence electrons are considered). Basis set superposition error (BSSE) is removed by the counterpoise method.

For each rare-gas dimer interaction curve, we choose 16 to 19 intermolecular distances, with denser sampling around equilibrium distances. For the S22 set, geometries of the complexes are taken from Ref. 46 without reoptimization for the different computational methods. The geometries of the isolated monomers are fixed to those in the dimers, thus the so-called monomer deformation energy is not included in the interaction energy. Most of the calculations are done with the same basis sets as those used for the CCSD(T) calculations in Ref. 46. The dependence of the interaction energies on the size of basis set is checked by using larger basis sets. For each method, mean error (ME), mean absolute error (MAE) and mean absolute percentage error (MA%E) are given using as a reference the CCSD(T) values extrapolated to the complete basis set (CBS) limit [46].

III. RESULTS AND DISCUSSION

A. Rare-gas dimers

We start with rare-gas dimers, which are frequently used for initial tests of methods aiming at describing van der Waals bonded systems. Figure 1 shows the interaction energy curves of He 2 , Ne 2 , Ar 2 , and Kr 2 calculated with aug-cc-pV5Z basis sets. The accurate reference curves are from Ref. 63. Binding energies at the equilibrium distances obtained with different methods are listed in Table I. We can see that full-range RPA can hardly bind two He atoms, and also largely underestimates the binding energy of Ne 2 . Full-range RPAx and RSH+RPA recover more than half of binding energies for these two systems. RSH+RPAx significantly further improves the results. For larger dimers, Ar 2 and Kr 2 , full-range RPA, full-range RPAx and RSH+RPA all give similar underestimated interaction energies, whereas RSH+RPAx is clearly more accurate. This suggests that range separation and inclusion of the exchange kernel in Eqs. ( 7) and ( 8) are both important. For these systems, RSH+MP2 gives overall similarly accurate equilibrium binding energies than RSH+RPAx.

B. S22 test set

Although the rare-gas dimers usually constitute a good initial test for a method describing non-covalent bonding, they are still not sufficient to assess the reliability of a method for applications to biologically interesting systems [64]. It is necessary to include a few moderately large molecules in a reliable test set. We have then taken the S22 set of Jurečka et al. [46], which composes 22 weakly-bonded molecular complexes, including 7 hydrogen-bonded complexes (HB7 subset), 8 weaklyinteracting complexes with predominant dispersion contributions (WI8 subset) and 7 mixed complexes featuring multipole interactions (MI7 subset). We use the same names of the subsets introduced in Ref. 55. Recently, Marchetti and Werner did explicitly-correlated coupledcluster calculations for the S22 set and found close agreement with the original benchmark data [65]. When this paper is under review, Takatani et al. [66] published a new benchmark for the S22 test set, which is supposed to be more accurate. We still use the original benchmark data of Ref. 46 for detailed comparisons, but the overall effects of using other reference data are discussed at the end of this section. a VDZ, aVDZ, VTZ, and VQZ stand for cc-pVDZ, aug-cc-pVDZ, cc-pVTZ, and cc-pVQZ, respectively. In the modified VTZ-fd basis set, the set of f functions and the tight d functions are removed from cc-pVTZ basis (for hydrogen the set of d functions and the set of tight p functions are removed).

hydrogen the set of d functions and the set of tight p functions are removed). The rightmost column contains CCSD(T)/CBS estimates taken from Ref. 46 which serve as reference values. The mean absolute percentage error of each method for each subset and for the total S22 set are also shown in Fig. 2.

For the hydrogen-bonded systems (HB7 subset), fullrange RPA and RPAx underestimate the interaction energies on average by about 25% and 13%, respectively. Range separation greatly improves these two methods, the MA%E of RSH+RPA and RSH+RPAx on this subset being 4.0% and 5.1%, respectively. Note that all the range-separated methods overestimate the interac-tion energies, whereas all other methods underestimate them.

For the dispersion-bonded systems (WI8 subset), accurate treatment of correlation is crucial. While Hartree-Fock calculations account roughly for two thirds of the binding energy in the complexes of the HB7 subset, it does not predict any bonded complex in the WI8 subset. As expected, including short-range correlation does not help much. Except for stacked uracil dimer, RSH calculations (without long-range correlation) do not predict any bonded complex either. Standard DFT calculations with the PBE functional do give 5 bonded complexes out of 8, but the MA%E on the WI8 subset is still larger than II.

100%. It is clear that a good, physically well-founded description of long-range correlation is absolutely necessary. Full-range RPA recovers nearly half of the interaction energies for the complexes in the WI8 subset, except for the stacked indole-benzene complex for which it gives zero binding. Full-range RPAx is similar in performance but slightly worsens the results. Range separation improves RPA but the remaining mean absolute percentage error (about 46%) remains quite large. A much more significant improvement is obtained with RSH+RPAx which reduces the MA%E to about 28%. The two largest errors from the RSH+RPAx method are for stacked indolebenzene and stacked adenine-thymine, 3.5 kcal/mol and 4.4 kcal/mol, or 67% and 36%, respectively. They seem quite large but are still smaller than the basis set errors in CCSD(T), which are 89% and 56%, respectively. It turns out that at least half of the error is from using too small basis sets (see next subsection). With these small basis sets, MP2 and RSH+MP2 give more accurate interaction energies than RSH+RPAx with a MA%E on this subset of about 24% and 15%, respectively, but this apparently good performance can be mostly attributed to the basis set error which partially cancels the MP2 overestimation of the binding energies. The errors in MP2 and RSH+MP2 thus tend to increase as the basis set is enlarged. In fact, on the WI8 subset, the MA%E of MP2 extrapolated to CBS [46] is 33%, and the MA%E of range-separated MP2 (with local correlation and density fitting approximations) with aug-cc-pVTZ basis [55] is 24%. On the contrary, the errors in RSH+RPAx tend to decrease when we use larger basis sets, as it will be illustrated in the next section.

For the mixed complexes (MI7), the errors are somewhere in between those for the HB7 and the WI8 subsets. For RSH+RPAx, the largest error is for T-shaped indolebenzene, 1.3 kcal/mol or 23%. Again the larger part of the error is from incomplete basis set, as it will be shown in the next subsection.

Among the methods that we have investigated here, RSH+RPAx and RSH+MP2 appear to be the most accurate ones. We thus further investigate these two methods with larger basis sets.

RSH+RPAx and RSH+MP2 results with larger basis sets

For the largest systems in Table II, the stacked indolebenzene and stacked adenine-thymine complexes, only the cc-pVDZ basis set was used and this corresponds to the two largest errors in RSH+RPAx. Although rangeseparated methods converge much faster with respect to basis size than full-range methods [42], the cc-pVDZ basis set is so small that we may suspect that those errors are mainly a consequence of the incompleteness of the basis. We did RSH+RPAx and RSH+MP2 calculations with larger augmented basis sets, aug-cc-pVDZ and augcc-pVTZ, using the approximate single-point quadrature of Eq. ( 14) for RSH+RPAx to keep the computational cost acceptable, and the interaction energies are given in Table III. For the aug-cc-pVTZ basis set, as the calculations are expensive, we use for the largest systems the RSH+MP2 interaction energies with local correlation and density fitting approximations calculated by Goll et al. [55] and estimate the RSH+RPAx interaction energies from the aug-cc-pVDZ calculations by the simple correction formula: E int (RSH+RPAx/aVTZ) = E int (RSH+RPAx/aVDZ) + (E int (RSH+MP2/aVTZ) -E int (RSH+MP2/aVDZ)). This correction can be checked for the complexes for which we have the actual aug-cc-pVTZ calculations, and it appears to work well.

We have also checked that the single-point quadrature approximation does not introduce any significant error. By recalculating the RSH+RPAx interaction energies of the S22 set with the single-point quadrature of Eq. ( 14) with the same basis sets used in Table II and comparing to the interaction energies of Table II, which were obtained from a 7-point Gauss-Legendre quadrature, we find a mean error of -0.004 kcal/mol, or 0.11%. The largest difference is for stacked indole-benzene, which is -0.014 kcal/mol, or 0.81%, still significantly smaller than the error in the method itself. For comparison, the less accurate other single-point quadrature of Eq. ( 13) gives a mean error of +0.07 kcal/mol, or 0.5%, still a very good approximation.

Comparison of Tables II and III shows that the interaction energies of the complexes in the WI8 subset calculated with the cc-pVDZ or VTZ-fd basis are seriously underestimated. Note that the aug-cc-pVDZ basis is larger than the VTZ-fd basis and expectedly appears TABLE III: Interaction energies (in kcal/mol) for the complexes of the S22 set from the RSH+RPAx and RSH+MP2 methods with augmented basis sets. (aVDZ and aVTZ stand for aug-cc-pVDZ and aug-cc-pVTZ, respectively.) The adiabatic connection integration is done by the single-point quadrature of Eq. ( 14). The geometries of complexes and the reference CCSD(T)/CBS estimates in the rightmost column are taken from Ref. 46 The evolution from Table II to Table III is similar for the MI7 subset. For T-shaped indole-benzene, the error in RSH+RPAx is reduced from 1.3 kcal/mol to 0.3 kcal/mol, or from 23% to 5%. On this subset, the MA%E of RSH+RPAx decreases from 10% to 3.8% with aug-cc-pVTZ basis while the MA%E of RSH+MP2 increases from 9% to 17%.

The hydrogen-bonded systems are less sensitive to basis sets than the dispersion-bonded systems. The overestimation of the interaction energies by RSH+RPAx and RSH+MP2 for the HB7 subset is a bit reinforced with the augmented basis sets of Table III. The most serious overestimation is for the formic acid dimer, -2.6 kcal/mol and -3.0 kcal/mol with aug-cc-pVTZ for RSH+RPAx and RSH+MP2, respectively. The error is most likely due to a deficiency in the approximate short-range density functional, because the RSH calculation (without long-range correlation) predicts an interaction energy (-18.54 kcal/mol) already very close to the reference value (-18.61 kcal/mol). This conjecture is also supported by the comparison between the MP2 and RSH+MP2 columns in Table II. MP2 systematically underestimates whereas RSH+MP2 consistently overestimates interactions in the HB7 subset, reflecting an overbinding feature of the short-range functional that we used. This point has already been remarked by Goll et al. [55].

Overall, with aug-cc-pVTZ basis, RSH+RPAx yields interaction energies for the total S22 set with an estimated MAE of 0.61 kcal/mol or MA%E of 8.6%, while RSH+MP2 gives a MAE of 1.12 kcal/mol or MA%E of 16.9%. Using the reference data by Marchetti and Werner [65] would change these MAEs by less than 0.06 kcal/mol and corresponding MA%Es by less than 1%. If we use the latest benchmark from Takatani et al. [66], the MAE and MA%E for RSH+RPAx reduce to 0.46 kcal/mol and 6.7%, respectively, whereas the MAE and MA%E for RSH+MP2 increase to 1.17 kcal/mol and 18.9%, respectively.

IV. SUMMARY AND CONCLUSIONS

We have tested and compared four RPA-based methods, namely the full-range RPA and RPAx methods, and the range-separated RSH+RPA and RSH+RPAx methods, on homonuclear rare-gas dimers and the S22 set of weakly-interacting intermolecular complexes of Jurečka et al. [46]. Both range separation and inclusion of the Hartree-Fock exchange response kernel largely improve the accuracy of the predicted interaction energies. The best method, RSH+RPAx, gives satisfactory interaction energy curves of the rare-gas dimers and yields interaction energies of the S22 set with an estimated mean absolute error of about 0.5 -0.6 kcal/mol, corresponding to a mean absolute percentage error of about 7 -9% (depending on the reference interaction energies used), with adequate basis sets including diffuse functions. The RSH+RPAx method is found to be overall more accurate than the simpler RSH+MP2 method, although the latter remains a very reasonable approach for weak intermolecular interactions.

As RSH+RPAx still seems to underestimate systematically interaction energies for stacked complexes and to overestimate the strength of hydrogen bonds, further refinements to this approach are desired. One may improve the short-range density functional, for example by using a meta-GGA form [52]. One may improve the long-range correlation energy by using other variants or extensions of RPA-type approximations [67,68]. One may adjust the value of the separation parameter which was fixed to µ = 0.5 bohr -1 in this study. Finally, one may refine the form the decomposition of the electron-electron interaction [21,[69][70][71].

Although our current implementation remains expensive compared to standard DFT calculations, we have shown that the computational cost of the adiabatic connection integration can be reduced by using an approximate single-point quadrature [Eq. (13) or Eq. ( 14)], without any significant loss of precision. In view of the recent progress in the development of efficient RPA algorithms [32,33], further computational improvements of the RSH+RPAx method or other closely-related variants can be expected. Nevertheless, the tests performed with our current implementation have already demonstrated that RSH+RPAx is a feasible method and provides a reasonable description to non-covalent bonding in medium to large sized complexes, including biomolecules.

Note added in proof:

While proofreading the manuscript, a paper has been published online, Podeszwa et al., Phys.

Chem. Chem. Phys., DOI:10.1039/b926808a (2010), reporting an improved set of S22 reference interaction energies. Using these data the MAE and MA%E for RSH+RPAx become 0.49 kcal/mol and 7.0%, and for RSH+MP2, 1.19 kcal/mol and 19.1%, respectively. These deviations are very similar to those found with respect to the data of Ref. 66.

2 FIG. 1 :

 21 FIG. 1: Interaction energy curves of rare-gas dimers calculated by the RPA, RSH+RPA, RPAx and RSH+RPAx methods. Basis sets used are aug-cc-pV5Z. Accurate curves are from Ref. 63.

FIG. 2 :

 2 FIG.2: Mean absolute percentage errors for the S22 test set and for its three subsets from different methods with the relatively small basis sets used in Ref.46. The data are from TableII.

TABLE I :

 I Interaction energies (in mH) of rare-gas dimers at the equilibrium distance from different methods with aug-cc-pV5Z basis set. For RPA-type methods, the adiabatic connection integration is done by a 7-point Gauss-Legendre quadrature. Mean absolute percentage errors (MA%E) are given.

	Method	He2	Ne2	Ar2	Kr2 MA%E
	RPA	-0.0021 -0.0366 -0.269 -0.388	62
	RSH+RPA -0.0183 -0.0876 -0.308 -0.397	38
	RPAx	-0.0218 -0.0773 -0.289 -0.396	39
	RSH+RPAx -0.0255 -0.1111 -0.420 -0.542	17
	MP2	-0.0208 -0.0790 -0.483 -0.691	24
	RSH+MP2 -0.0202 -0.1024 -0.484 -0.671	19
	CCSD(T)	-0.0313 -0.1179 -0.414 -0.575	10
	Accurate a	-0.0349 -0.1342 -0.455 -0.639	0
	a Ref. 63
	1. Comparison of all the methods with small basis sets		as those used for the CCSD(T) calculations in Ref 46.
				The basis sets used for the 22 complexes are not uni-
	Interaction energies calculated with RPA, RSH+RPA, RPAx, RSH+RPAx, MP2, RSH+MP2 and CCSD(T) are given in Table II with the same relatively small basis sets		form because the size of complexes varies a lot. VTZ-fd basis sets are obtained by removing the set of f func-tions and the set of tight d functions from cc-pVTZ (for

TABLE II :

 II Interaction energies (in kcal/mol) for the complexes of the S22 set from different methods with the relatively small basis sets used in Ref.46. For the RPA-type methods, the adiabatic connection integration is done by a 7-point Gauss-Legendre quadrature. The geometries of complexes and the reference CCSD(T)/CBS estimates in the rightmost column are taken from Ref.46. Mean errors (ME), mean absolute errors (MAE) and mean absolute percentage errors (MA%E) are given.

	Complex	Basis set a	RPA RSH+RPA	RPAx RSH+RPAx	MP2 RSH+MP2 CCSD(T) CCSD(T)/CBS
	Hydrogen-bonded complexes (HB7)
	ME		3.33	-0.22	1.78	-0.69	1.72	-1.16	1.82	0.00
	MAE		3.33	0.52	1.78	0.77	1.72	1.16	1.82	0.00
	MA%E		24.6%	4.0%	12.7%	5.1%	11.0%	7.6%	11.8%	0.0%
	Complexes with predominant dispersion contribution (WI8)
	ME		2.89	2.14	3.10	1.49	0.74	-0.09	2.24	0.00
	MAE		2.89	2.14	3.10	1.49	1.25	0.64	2.24	0.00
	MA%E		57.9%	46.3%	62.4%	28.4%	24.2%	14.9%	39.2%	0.0%
	Mixed complexes (MI7)
	16 Ethene.ethine	VTZ	-0.93	-1.31	-1.24	-1.47	-1.43	-1.60	-1.24	-1.53
	17 Benzene.H2O	VTZ-fd	-1.97	-2.87	-2.35	-3.10	-2.81	-3.41	-2.48	-3.28
	18 Benzene.NH3	VTZ-fd	-1.24	-1.76	-1.39	-2.01	-1.99	-2.36	-1.63	-2.35
	19 Benzene.HCN	VTZ-fd	-2.99	-4.39	-3.78	-4.71	-4.41	-5.28	-3.71	-4.46
	20 Benzene dimer C2v	aVDZ	-1.71	-1.92	-1.65	-2.39	-3.10	-3.33	-2.21	-2.74
	21 Indole.benzene T-shape	VDZ	-2.57	-3.96	-2.90	-4.44	-4.51	-5.50	-3.21	-5.73
	22 Phenol dimer	VTZ-fd	-4.47	-6.28	-4.99	-6.81	-6.31	-7.72	-5.60	-7.05
	ME		1.61	0.66	1.27	0.32	0.37	-0.29	1.01	0.00
	MAE		1.61	0.66	1.27	0.39	0.47	0.36	1.01	0.00
	MA%E		41.2%	17.9%	31.8%	9.8%	11.8%	8.9%	24.9%	0.0%
	total ME		2.62	0.92	2.10	0.42	0.93	-0.49	1.71	0.00
	total MAE		2.62	1.15	2.10	0.91	1.15	0.72	1.71	0.00
	total MA%E		42.0%	23.8%	36.9%	15.1%	16.0%	10.7%	25.9%	0.0%

  . Italic numbers for RSH+MP2 with aVTZ basis were taken from Ref.55. Italic numbers for RSH+RPAx with aVTZ basis were estimated by Eint(RSH+RPAx/aVTZ) = Eint(RSH+RPAx/aVDZ) + (Eint(RSH+MP2/aVTZ) -Eint(RSH+MP2/aVDZ)). Mean errors (ME), mean absolute errors (MAE) and mean absolute percentage errors (MA%E) are given.

		RSH+RPAx	RSH+MP2	CCSD(T)/CBS
	Complex	aVDZ aVTZ	aVDZ aVTZ
	Hydrogen-bonded complexes (HB7)
	1 (NH3)2	-3.07 -3.19	-3.13	-3.25	-3.17
	2 (H2O)2	-5.33 -5.41	-5.37	-5.45	-5.02
	3 Formic acid dimer	-20.81 -21.18	-21.20 -21.57	-18.61
	4 Formamide dimer	-17.03 -17.22	-17.44 -17.64	-15.96
	5 Uracil dimer C 2h	-21.80 -22.00	-22.62 -22.82	-20.65
	6 2-pyridoxine.2-aminopyridine	-17.81 -17.55	-18.86 -18.60	-16.71
	7 Adenine.thymine WC	-17.29 -17.15	-18.26 -18.12	-16.37
	ME	-0.95 -1.03	-1.48	-1.57	0.00
	MAE	0.98	1.03	1.50	1.57	0.00
	MA%E	6.5%	6.6%	9.3% 10.0%	0.0%
	Complexes with predominant dispersion contribution (WI8)
	8 (CH4)2	-0.42 -0.45	-0.46	-0.48	-0.53
	9 (C2H4)2	-1.28 -1.38	-1.45	-1.55	-1.51
	10 Benzene.CH4	-1.23 -1.32	-1.62	-1.71	-1.50
	11 Benzene dimer C 2h	-2.05 -2.21	-4.08 -4.24	-2.73
	12 Pyrazine dimer	-3.78 -3.85	-5.97 -6.04	-4.42
	13 Uracil dimer C2	-9.38 -9.57	-11.76 -11.59	-10.12
	14 Indole.benzene	-3.70 -3.71	-6.95 -6.96	-5.22
	15 Adenine.thymine stack	-10.97 -10.57	-15.11 -14.71	-12.23
	ME	0.68	0.65	-1.14	-1.13	0.00
	MAE	0.68	0.65	1.18	1.14	0.00
	MA%E	17.4% 14.4%	22.8% 23.3%	0.0%
	Mixed complexes (MI7)
	16 Ethene.ethine	-1.48 -1.54	-1.62	-1.68	-1.53
	17 Benzene.H2O	-3.16 -3.33	-3.49	-3.68	-3.28
	18 Benzene.NH3	-2.11 -2.24	-2.49	-2.63	-2.35
	19 Benzene.HCN	-4.54 -4.77	-5.13	-5.38	-4.46
	20 Benzene dimer C2v	-2.39 -2.55	-3.33 -3.49	-2.74
	21 Indole.benzene T-shape	-5.17 -5.46	-6.55 -6.84	-5.73
	22 Phenol dimer	-7.07 -7.11	-8.05 -8.09	-7.05
	ME	0.17	0.02	-0.50	-0.66	0.00
	MAE	0.20	0.14	0.50	0.66	0.00
	MA%E	6.0%	3.8%	11.9% 16.6%	0.0%
	total ME	0.00 -0.08	-1.05	-1.12	0.00
	total MAE	0.62	0.61	1.06	1.12	0.00
	total MA%E	10.3%	8.6%	15.1% 16.9%	0.0%
	to be of a better quality. From Table II to Table III,
	the errors for the complexes number 12 to 15 are re-
	duced by about a factor of two or more. Correspondingly,
	the MA%E of RSH+RPAx on the WI8 subset decreases
	from about 28% to 14% with aug-cc-pVTZ basis. On
	the contrary, the MA%E of RSH+MP2 increases from
	15% to 23%, confirming that the good value in Table II
	was due to a fortuitous compensation of errors. Even for
	range-separated methods, including diffuse functions in
	the basis sets for dispersion-bonded systems is essential,
	in order to ensure a reasonable description of monomer
	polarizabilities.

ACKNOWLEDGMENTS

We thank Peter Reinhardt and Hermann Stoll for helpful discussion and technical assistance. This work is financed through ANR (French national research agency) via contract number ANR-07-BLAN-0272 (Wademecom).