Bonnet

Eve M Lepicard
email: evelepicard@ieepworld.fr.

Matthieu Maillot

Florent Vieux

Mélanie Viltard

Fabrice Bonnet

Quantitative and qualitative analysis of breakfast nutritional composition in French schoolchildren 9 to 11 years of age

Keywords: nutrition, breakfast, energy, schoolchildren, France

Quantitative and qualitative analysis of breakfast nutritional composition in French schoolchildren aged 9-11 years

Introduction

Eating breakfast is recommended and considered the most important meal of the day because it is associated with good health behaviours, reduced risk of chronic diseases, and improved cognitive and school performance [START_REF] Giovannini | Symposium overview: Do we all eat breakfast and is it important?[END_REF]. In addition, eating breakfast, especially a breakfast rich in proteins and low in glycaemic index carbohydrates, correlates with a normal body mass index (BMI), whereas skipping breakfast is frequently associated with overweight and obesity [START_REF] Szajewska | Systematic review demonstrating that breakfast consumption influences body weight outcomes in children and adolescents in Europe[END_REF]Ruszczynski, 2010, De La Hunty et al., 2013).

Breakfast composition varies across the world, but precisely defining how much energy it should provide is difficult, and national recommendations vary. The US Department of Agriculture established four definitions of breakfast [START_REF] Sackin | Breakfast for all and all for breakfast? School and Food Service Nutrition[END_REF]. The simplest definition is any food or beverage except water. The three other definitions constitute "substantial breakfasts" and include foods from at least two of the five major food groups (breads/grains, fruits, vegetables, meat/meat alternate, and milk). They provide, respectively, >10%, 15%, and 25% of the Recommended Dietary Allowances for energy (calories) and one-fourth of the Recommended Daily Allowance of nutrients based on the latest Dietary Guidelines for Americans (U.S. Department of Agriculture and U.S. Department of Health and Human Services, 2010).

France does not appear to have a specific recommendation on the percentage of energy provided by breakfast, although current recommendations are to eat at least one food containing cereals, one fruit or freshly squeezed juice or juice with no added sugar, and one dairy product (Agence Française De Sécurité Sanitaire Des Aliments, 2004). Quantities in grams or millilitres for each of these components are not provided in the recommendations but can be found in the revised version of the Recommandation Nutrition of the Groupe [START_REF] Hebel | Le petit-déjeuner en perte de vitesse[END_REF], but little detailed information is available about breakfast habits, and the most recent nutritional studies are more than a decade old [START_REF] Billon | Family resemblance in breakfast energy intake: the Stanislas Family Study[END_REF][START_REF] Preziosi | Breakfast type, daily nutrient intakes and vitamin and mineral status of French children, adolescents, and adults[END_REF].

In the current study, we analysed breakfast composition in France using data extracted from a recent survey examining breakfast water intake by schoolchildren 9-11 years of age [START_REF] Bonnet | French children start their school day with a hydration deficit[END_REF]. Our objectives were, first, to assess energy and nutritional quality of breakfast and, second, to identify the main breakfast patterns, that is, how foods and drinks were associated in the children's breakfasts. We also evaluated whether the children were meeting French national recommendations.

Methods

Study design and dietary record

The current analysis was based on data collected as part of a prospective, cross-sectional study carried out in Rennes, France between 2010 and 2011 [START_REF] Bonnet | French children start their school day with a hydration deficit[END_REF]. The protocol for the study was approved by AFSSAPS (French Health Products Safety Agency) and the Ethics Committee of Rennes Ouest V, France, and the study was conducted according to the guidelines laid down in the Declaration of Helsinki. Written informed consent was obtained from both parents and children.

Briefly, in the Rennes study, children 9 to 11 years of age were recruited on a voluntary basis through 14 primary schools from the city of Rennes and vicinity. This area includes urban as well as rural populations from various socioeconomic strata. All children were given a study pack to take home. The pack contained a study information document, a parent and child consent form, a questionnaire covering demographic information, height and weight, and breakfast composition. Breakfast was defined as the first meal of the day consumed in the morning. Breakfast intake data were reported for one day. To address potential difference between weekday and week-end breakfast composition, clinical investigators recommendation was to fill the questionnaire on a weekday only. Children were instructed to follow their usual morning routine and, if breakfast was eaten, to record consumption in a diary, including time of consumption, product brand name, cooking method, and portion size.

Children returned study materials, including the urine sample, to the teachers on designated days. Children were included if both parents had signed the informed consent and if they fulfilled the inclusion criteria, which included a usual intake of at least two main meals per day. Children were excluded if they currently or previously had a metabolic or digestive disease (with the exception of appendectomy) or renal disease (renal insufficiency etc.), if they had fever, or if they were prescribed a local or systemic treatment likely to interfere with evaluation of the study parameters, including hydration state in particular (diuretic treatment or treatment interfering with metabolism and eating behavior).

Overweight, obesity, and underweight were determined from the BMI and age according to the 2012 International Obesity Task Force cut-off values [START_REF] Cole | Extended international (IOTF) body mass index cut-offs for thinness, overweight and obesity[END_REF].

Energy and nutrient intakes

Dietary intake was determined using information recorded in diaries by children and/or parents. Breakfast skippers included children having no food and no fluid and children who took their first meal at lunch time. Having only a drink was considered as breakfast. All food and drink consumed at breakfast, or the last meal of the previous day in case of children not consuming breakfast, were recorded, including brand name and portion size (household measures or package weight) [START_REF] Bonnet | French children start their school day with a hydration deficit[END_REF]. Dietary data were entered in BILNUT 7.5 nutrition software (Nutrisoft, Mesa, AZ), which converts the amount of food eaten into individual energy, macronutrients, and micronutrients and assigns consumed foods to food groups and subgroups. For children consuming several foods, if the nutritional content of one or more foods was missing, no intake was assumed. If all foods were missing, the child's data were considered missing and therefore not included in the calculations. Foods were categorized as described previously [START_REF] Alexy | Breakfast trends in children and adolescents: frequency and quality[END_REF] and included the following food and drink categories: bread, ready-to-eat cereals (RTEC), sweets (biscuits, pastries, bakery goods, chocolate, jam, candy, honey, sugar, and syrup), fat/oil, fruits/vegetables, meat/fish/egg, dairy, water, milk, juices, flavoured milk, coffee, tea, soda/soft drink/sport drink, and miscellaneous.

The combination of milk and sweetened cocoa powder were considered as a single food (flavoured milk). For each individual, the total amount of food consumed, total energy intake, energy intake from liquids, and energy intake from solid foods were calculated.

Nutritional quality of breakfast

Energy intake from breakfast was compared to the daily recommended energy intake derived from the joint FAO/WHO/UNU Expert Consultation of 2001 (Joint Fao/Who/Unu Expert Consultation, 2001). Nutritional quality of breakfasts was estimated using the energy density (kcal/100 g) and the mean adequacy ratio (MAR). Energy density was the ratio between energy intake (kcal) and amount of foods (g) and was calculated first for total foods and then for solid foods only. The MAR was calculated as the mean percentage of daily recommended intakes for 23 key nutrients [START_REF] Maillot | Low energy density and high nutritional quality are each associated with higher diet costs in French adults[END_REF][START_REF] Vieux | High nutritional quality is not associated with low greenhouse gas emissions in self-selected diets of French adults[END_REF] in relation to the French recommendations [START_REF] Martin | Apports nutritionnels conseillés pour la population française[END_REF]. These 23 nutrients included protein, fibre, retinol, thiamine, riboflavin, niacin, vitamin B-6, folates, vitamin B-12, ascorbic acid, vitamin E, vitamin D, calcium, potassium, iron, magnesium, zinc, copper, iodine, docosahexaenoic acid (DHA), linoleic acid, linolenic acid, and selenium. The ratio for each nutrient was truncated at 100 so that a high intake of one nutrient could not compensate for the low intake of others.

Dietary patterns

Based on the amounts consumed of the 13 food categories, a principal component analysis including a Varimax rotation was used to extract latent variables explaining most variability in individual dietary habits. Only three subjects were considered as outliers and were removed from the PCA in order to to obtain homogeneous and robust dietary patterns. The first four latent variables were retained and used to run a hierarchical ascendant classification based on Ward criteria.

Statistical analysis

Averages of energy intake (total, solid, and liquid) and amount of foods (total, solid, and liquid), energy density (total and solid), MAR, and nutrients expressed in per cent of recommendations were calculated in the whole sample and by sex. Differences by sex were compared using a general linear model. Additional calculations included the percentage of breakfast skippers, the number of consumers, and the average amount consumed (g) by food category. The four most frequent breakfast patterns were determined by principal component analysis. P-values were calculated using a general linear model with food group as the dependant variable and the dietary pattern variable as the independent variable. A pair-wise statistical t-test was performed to compare the MAR between dietary patterns. Consumption of the different food categories was compared between breakfast patterns using a general linear model with food group as the dependant variable and the dietary pattern variable as the independent variable. Statistical analysis was performed using SAS for Windows, version 9.4 (SAS Institute, Cary, NC). Missing data were not replaced and no imputation was made. A p-value below 0.05 was considered to indicate statistical significance.

Results

Subjects

The analysis included 529 children from 9 to 11 years of age. Just over half (n=269; 50.8%) were boys. Using International Obesity Task Force cut-offs (Cole, 2012 A INTEGRER), according to BMI, 70.1% (n=371) had a normal weight, 5.9% (n=31) were overweight, 12.9% (n=68) were underweight, and none were considered obese. BMI could not be calculated for 59 subjects because of missing height and/or weight data. Mean BMI was 16.7 ± 1.9 in boys and 16.2 ± 2.0 kg/m 2 in girls. The mean body weight, 31.6 kg, was slightly higher than the values previously observed in a French population (Rolland-Cachera MF, Cole TJ, Sempe M, Tichet J, Rossignol C, Charraud A: Body mass Index variations: centiles from birth to 87 years. Eur J Clin Nutr 1991;45: 13-21 For breakfast consumers (n=477), the mean quantity of food consumed at breakfast was 442 ± 167 g (Table 1) and the mean energy intake was 445 ± 159 kcal (Table 1). Apart from the chocolate milk, other drinks consumed in big quantities by the children -mainly water and tea-provide no calorie at all. Thus the contribution of liquids to the total breakfast quantity is far greater than the contribution of liquids to the breakfast total energy: about three-quarters of the total quantity ingested was provided by drinks, whereas breakfast energy was mainly provided by food, reflecting the fact that children consumed drinks that had low calorie contents and that they consumed energy-rich foods. Total energy intake did not significantly differ between girls and boys (433 ± 151 vs. 457 ± 165 kcal; p=0.0995). Energy intake from foods and drinks also did not differ between girls and boys.

Sweets were the most frequently consumed food item, consumed by 67.7% of the subjects, and they accounted for 40.1 ± 25.3% of the total energy consumed for those who ate them (Table 2). Fat (mainly butter) (41.5%) and bread (46.8%) were also frequently consumed.

Flavoured milk accounted for the highest number of grams of food consumed and was consumed by nearly half (48.9%) of the children. RTECs, not a traditional breakfast food in France, were consumed by 28.1% of children.

Nutrient intake at breakfast

Nutritional quality as assessed by MAR was similar for boys (25.4 ± 8.9%) and girls (24.1 ± 9.9%), and overall, the MAR for breakfast was 24.7% (Table 3). Energy density from solid foods and total energy density were also similar between boys and girls. On average, breakfast provided 22.9% of the daily energy requirement according to international recommendations (Joint Fao/Who/Unu Expert Consultation, 2001) (Table 4). It also provided 49.2% of recommended protein (0.9g/kg, the main contributors to protein intake being flavored milk (33%), sweets (20%), and milk (15%) categories), 18.5% of fat, 28.3% of carbohydrates, and 15.9% of fibre. Breakfast contributed more than half the daily requirement of vitamin B2 (riboflavin; 51.2%) and more than 40% of the daily requirements for protein, phosphorus, pantothenic acid, and vitamin B12. However, breakfast provided less than 10% of linoleic acid, alpha-linolenic acid, DHA, selenium, and vitamin D.

The contribution of breakfast to the daily energy requirement was significantly different between boys and girls (21.74 ± 8.08% vs. 24.17 ± 9.49%; p= 0.0026) (Table 4). Breakfast contribution to daily requirements also differed between boys and girls for energy from solids (14.85 ± 6.97% vs. 16.28 ± 8.08%; p=0.0374), energy from liquids (6.89 ± 3.79% vs. 7.89 ± 4.93%; p=0.0134), fat (17.48 ± 9.91% vs. 19.51 ± 10.63%; p=0.0313), carbohydrates (26.89 ± 9.42% vs. 29.83 ± 12.24%; p=0.0033), saturated fatty acids (28.71 ± 17.45% vs. 34.47 ± 21.50% p=0.0014), and sodium (14.50 ± 8.12% vs. 16.27 ± 9.86%; p=0.0322).

The main contributor to total energy at breakfast was flavoured milk, followed by sweets and RTEC, milk, and dairy (Table 2). The highest MAR was provided by flavoured milk (15.5%), RTEC (11.3%), and milk (11.2%). Although sweets contributed substantially to energy intake, they contributed less to nutrient intake (MAR = 5.8%). Fruits and vegetables accounted for 8% of recommended values and 18% of total energy. After adjustment for energy, the food categories providing the most nutrients were, in decreasing order, RTEC, milk, flavoured milk, and fruits.

Dietary patterns

Four main dietary patterns were identified: "RTEC + milk breakfast" (18.1%), which included mainly RTEC, milk, and juice; "sweets breakfast" (40.0%), which included mainly flavoured (i.e. chocolate) milk and sweets, especially brioche and chocolate spread, plus water or juice; "traditional French breakfast" (27.2%), which included mainly flavoured milk, bread, fat (especially butter), and juice; and "dairy and juice breakfast" (9.5%), which included mainly dairy (especially whole milk yogurt or yogurt drink) , sweets, and tea or juice (Table 5).

On average, energy intake was slightly higher for the "traditional French breakfast" (496 kcal) and the "sweets breakfast" (440 kcal) than for the other two breakfast patterns (approximately 400 kcal each). When adjusted for total energy intake at breakfast, the mean MAR was higher for the "RTEC + milk breakfast" (30.2%), followed by the "sweets breakfast" (24.6%) and the "traditional French breakfast" (22.6%) and lower for the "dairy and juice breakfast" (18.0%).

Total energy density was lower for the "RTEC + milk breakfast" but not significantly different from the "dairy and juice breakfast".

Discussion

The study provided a snapshot of a single breakfast in over 500 schoolchildren 9-11 years old in France. Data were collected as part of a previous study examining fluid intake at breakfast [START_REF] Bonnet | French children start their school day with a hydration deficit[END_REF]. The sample included a similar number of girls and boys, and the majority of children were 9 to 10 years of age because they were recruited in primary schools.

Only 10% of the children skipped breakfast, which is less than in most developed countries [START_REF] Alexy | Breakfast trends in children and adolescents: frequency and quality[END_REF][START_REF] Vanelli | Breakfast habits of 1,202 northern Italian children admitted to a summer sport school. Breakfast skipping is associated with overweight and obesity[END_REF][START_REF] Deshmukh-Taskar | The relationship of breakfast skipping and type of breakfast consumption with nutrient intake and weight status in children and adolescents: the National Health and Nutrition Examination Survey 1999-2006[END_REF]. However, we observed a trend of declining breakfast with age. Skipping breakfast is more and more observed in many developed countries, with 10 to 30% children and adolescents having lunch More than half of breakfast consumers (58%) consumed fruit juice, and 11% consumed fruits.

Bread was consumed by 47% of breakfast consumers and RTEC by 28%. The amount of RTEC consumed (30.45 g) is very close to the portion recommended (30g). This rather high percentage is interesting, because RTEC are not traditionally consumed in France, and are not, as such, a recommendation of the PNNS.. The study showed that breakfast provided, on average, 22.9% of the recommended daily energy intake. This is slightly higher than in the Stanislas family study [START_REF] Billon | Family resemblance in breakfast energy intake: the Stanislas Family Study[END_REF] but similar to the 15-25% medium interval observed in France in 1999 [START_REF] Preziosi | Breakfast type, daily nutrient intakes and vitamin and mineral status of French children, adolescents, and adults[END_REF].

Flavoured milk was the main contributor to energy intake, followed by sweets, RTEC, milk, dairy, bread, fat/oil, fruits/vegetables, and juice, consistent with them being amongst the most consumed breakfast items in terms of grams and energy

The study also showed a MAR of breakfast of 24.7%, indicating that, on average, breakfast provided a substantial amount of the daily recommended intakes for 23 key nutrients. When adjusted for energy, the foods contributing most to total nutrient intake were, in decreasing order, RTEC, milk, flavoured milk, and fruits. Average intake of protein, carbohydrates, most minerals (e.g. calcium, magnesium, phosphorus, and potassium), and vitamins (e.g. vitamin B2, and pantothenic acid) appeared to be sufficient. Intake was below national recommendations for vitamin E, vitamin B12, vitamin D, eicosapentaenoic acid/DHA, essential fatty acids, copper, zinc, selenium, and fibre, whereas intake of saturated fatty acids was in excess of recommendations. Because other meals may not provide sufficient nutrients to reach adequate intake, substituting foods currently consumed at breakfast with others of nutritional content may be necessary. For instance, consuming bakery products or RTEC containing whole grains or whole wheat flour may help provide adequate fibre. By total grams consumed, the largest contributor to breakfast was flavoured milk, which was consumed by just over half (50.5%) of the children. For these children, milk provided 43% of their energy intake. In addition, the highest MAR was provided by flavoured milk (15.5%) and the third highest was from plain milk (11.2%). This agrees with the French Individual National Food Consumption Survey 2 in 2005-2007, which found that, in children, milk is a strong contributor of several nutrients, especially calcium, iodine, phosphorus, potassium, zinc, retinol, and vitamins B2, B12, B5, and D [START_REF] Coudray | The contribution of dairy products to micronutrient intakes in France[END_REF].

We identified two dominant breakfast patterns: "sweets breakfast", eaten by 45% of children and included mainly flavoured (i.e. chocolate) milk, fruit juice, and a Danish, biscuit, or pastry; and "traditional French breakfast", eaten by 27% of children and included bread, butter or margarine, and flavoured milk. The "RTEC + milk" breakfast pattern, which consisted of RTEC, milk, and fruit juice, was the most nutrient-dense but was eaten by only 18% of children. This suggests that although the traditional French breakfast (bread and butter) is still common, new patterns are emerging, including consumption of RTEC.

Nutritionally, the "RTEC + milk" pattern was the most advantageous pattern because it was low in total fat, saturated fatty acids, and cholesterol and was rich in fluids, vitamins B, vitamin C, calcium, and iron. The "dairy and juice breakfast" did not provide sufficient calcium, protein, or water. This may be due to the fact that, in France, by portion, dairy products have lower contents of these nutrients than milk.

This study has some limitations: fluid and food intake were estimated from a self-reported questionnaire, which could have led to inaccuracies in portion size as well as height and weight. Second, the classification we adopted was aimed essentially at defining the various breakfast patterns. To get even more information on the nutritional quality of foods eaten at breakfast, a classification with further groups would be useful. For instance, the sweets category could be subdivided into pastries (bringing complex and simple carbohydrates, as well as fats), sugar/jam (bringing simple carbohydrates) and chocolate spreads (bringing simple carbohydrates and fats).

This study is the first report on breakfast composition in French children. Based on a large sample size, it provides insights about the breakfast habits in school children and opens new perspectives in terms of nutritional education and public policies. Based on our results, some recommendations can be made to optimize the breakfast composition and the formula of breakfast food products and drinks. For instance, the breakfast composition of French children included all food and drink categories (one portion of cereal, one dairy product, and one drink) recommended in the PNNS except the fruit/100% fruit juice category. In all dietary patterns identified in our study, consumption of fresh fruit was low. Children preferred fruit juices as observed in the "RTEC + milk" and "Dairy & juice" patterns. However, this trend was not observed in all dietary patterns: fruit juice consumption was low in the "Sweets" and "traditional French" patterns. In addition, insufficient intake of some micronutrients including copper, zinc, selenium and vitamin B12 and vitamin D as well as EPA/DHA have been observed. Fortification of food and drink products may provide a solution to compensate these deficiencies. Fibers intake is also below recommendations. This could be improved by encouraging consumption of RTEC (with an adequate amount of salt and sugar) or breakfast bakery products containing cereals and/or whole flour. Finally, consumption of margarine with omega 6/omega 3/ vitamin E and partially skimmed milk could be encouraged to reduce intake of saturated fatty acids.

Conclusions

This study on breakfast consumption by French schoolchildren produced globally encouraging results: only 10% of children skipped breakfast, breakfast composition and energy intake were close to national recommendations, and breakfast provided a substantial amount of the daily recommended intake for 23 key nutrients. To optimize further the children breakfast composition, it is recommended to increase intake of some micronutrients (copper, zinc, selenium, vitamin B12, vitamin D, EPA/DHA) possibly via food and drink fortification as well as fiber intakes by encouraging the consumption of fruits and whole grain products. Meats, fish, eggs 0.0 ± 0.0 0.0 ± 0.0 0.0 ± 0.0 3.1 ± 12.6 NC

The four most frequent breakfast patterns were determined by principal component analysis. Three subjects considered as outliers were removed from the principal component analysis to obtain homogeneous and robust dietary patterns. P-values were calculated using a general linear model

  d'étude des Marchés de Restauration Collective et Nutrition GEM-RCN (Guide on Nutrition Recommendations for Mass Catering) (Groupe D'etude Des Marches De Restauration Collective Et Nutrition (Gem-Rcn), 2013) published by the French Ministry of Economic Affairs and Finance. Rates of breakfast consumption in French children 3 to 12 years of age were 91% in 2003 and 87% in 2010

  or even dinner as the first meal of the day (for review, seeRampersaud, G. C., Pereira, M. A., Girard, B. L., Adams, J., & Metzl, J. D. (2005). Breakfast habits, nutritional status, body weight, and academic performance in children and adolescents. Journal of the American Dietetic Association, 105, 743-760; quiz 761-762. doi:10.1016/j.jada.2005.02.007)."Almost half of the children (48.6%) consumed a breakfast that included cereals, dairy, fruit/fruit juice in accordance with the recommendations of France's Programme National Nutrition Santé (National Health Nutrition Programme). All children consumed at least one beverage. Most breakfast consumers (83%) consumed milk, flavoured milk, a dairy product, or a combination of them. As a beverage, flavoured milk has a lower energy density than solid foods. It contributes to several nutrient recommendations without providing many calories.

  . REF A INTEGRER) but prevalence of both obesity and excessive weight observed in our study was lower than that reported in Europe for children of the same age (De Henauw et al, Obes Rev. 2015 Dec;16 Suppl 2:16-29; Pigeot et al, International Journal of Obesity (2009) 33, 1103-1110 REF A INTEGRER).

	Breakfast intake
	Overall, 9.8% of the children (n=52) skipped breakfast. The frequency of breakfast skipping
	increased with age (8.2% at 9 years of age, 11.4% at 10 years of age, and 16.7% at 11 years of
	age).

Table 1 . Total amounts and energy consumed at breakfast Category Mean amount ± SD P-value (girls vs. boys)

 1

	Overall	Girls	Boys
	N=477	N=230	N=247

Table 2 . Consumption by food category for breakfast consumers (N=477)

 2

							Mean
			Grams			MAR	Nutrient
			consumed, mean	% of total grams	% of total energy,	provided	density,
	Food category	Frequency, n (%)	± SD	consumed, mean ± SD	mean ± SD	(%)	%/100kcal
	Bread	223 (46.8)	41.75 ± 21.36	10.14 ± 7.24	25.54 ± 11.15	2.49	2.28
	Fat/oil	198 (41.5)	12.20 ± 4.82	3.17 ± 2.84	19.41 ± 8.30	1.28	1.39
	Fruits/vegetables	52 (10.9)	123.94 ± 47.27	26.49 ± 14.02	17.96 ± 15.40	8.52	6.84
	Juice	249 (52.2)	150.24 ± 32.24	37.98 ± 18.96	17.32 ± 8.39	5.47	7.81
	Milk	126 (26.4)	280.79 ± 124.54	59.14 ± 20.85	31.22 ± 14.88	11.15	8.66
	Dairy	55 (11.5)	110.81 ± 36.50	33.87 ± 17.67	27.03 ± 15.97	4.81	5.34
	Flavoured milk	233 (48.9)	324.99 ± 119.19	65.28 ± 18.19	42.87 ± 15.53	15.51	7.82
	Sweets	323 (67.7)	49.18 ± 41.23	13.67 ± 14.21	40.10 ± 25.31	5.83	2.12
	RTEC	134 (28.1)	30.45 ± 16.09	8.06 ± 5.35	32.14 ± 16.38	11.27	10.13
	Soda, soft drinks	7 (1.5)	172.86 ± 61.84	37.50 ± 18.06	18.09 ± 4.81	0.45	0.64

Table 3 . Main breakfast patterns and compositions in breakfast consumers (n=474) RTEC + milk breakfast Sweets breakfast Traditional French breakfast Dairy and juice breakfast

 3

	Composition/category	N=86	N=214	N=129	N=45	P-value
	Nutritional quality, mean ± SD
	MAR (%)	30.2 ± 8.0	24.6 ± 9.1	22.6 ± 8.7	18.0 ± 8.3	0.001
	Solid energy density (kcal/100 g)	359 ± 89	380 ± 81	344 ± 97	207 ± 94	0.001
	Total energy density (kcal/100 g)	92 ± 28	116 ± 58	114 ± 47	112 ± 51	0.001
	Total quantity (g)	456 ± 163	426 ± 171	471 ± 163	391 ± 149	0.013
	Quantity from foods (g)	73 ± 51	84 ± 55	117 ± 69	174 ± 61	0.001
	Quantity from drinks (g)	382 ± 150	342 ± 169	354 ± 160	217 ± 175	0.001
	Energy (kcal)	395 ± 125	440 ± 165	496 ± 151	399 ± 152	0.001
	Energy from foods (kcal)	227 ± 99	294 ± 151	351 ± 120	332 ± 134	0.001
	Energy from drinks (kcal)	168 ± 65	146 ± 81	145 ± 79	68 ± 55	0.001
	Grams consumed by food group, mean ± SD

p values referred to a parametric test (i.e. GLM) adjusted for total energy intake. SD, standard deviation

Acknowledgments

The authors thank Dr Yves M. Darmon for his critical reading of the manuscript. Medical writing was provided by Dr. Phillip S. Leventhal (4Clinics, Paris, France). This study was funded by the Institute for European Expertise in Physiology (Paris, France) and Nestlé Dairy (Vevey, Switzerland).

Declaration of interest


Yuly Vesga

Carlos Diaz

Jeanne Crassous

Florencio E Hernandez
email: florencio.hernandez@ucf.edu

Two-Photon Absorption and Two-Photon Circular Dichroism of a Hexahelicene Derivative with a Terminal Donor-Phenyl-Acceptor Motif

Herein, we report on the theoretical-experimental analysis of the two photon absorption and circular dichroism spectra of 1-(2-pyridyl)-4-methoxy-carbo[6]helicene derivative (P6). The primary outcomes of our investigation on this particular helicene derivative with a donor-acceptor motif on one end led to two important conclusions: 1) The lengthening of the π-electron delocalization within the helical core of P6 predominantly increases the contribution of the magnetic dipole transition moment to the TPCD signal; 2) The electric quadrupole transition moment contribution to the TPCD signal is enhanced by the intramolecular charge transfer (ICT) produced by the donor-acceptor combination on one end of the molecule. In order to corroborate our results, we performed a comparative theoretical analysis of the effect of the energy gap and ICT on TPCD on a series of P6-like helicenes with different donor-acceptor combinations. Twophoton absorption (TPA) and two-photon circular dichroism (TPCD) spectra were obtained using the double L-scan technique over a broad spectral range (400-900 nm) using 90 fs pulses at a low repetition rate (2-50 Hz) produced by an amplified femtosecond system. The theoretical simulations were calculated using Time-Dependent Density Functional Theory (TD-DFT) at the CAM-B3LYP/6-311++G(d,p) level of theory.

INTRODUCTION

The interpretation of the high optical activity in helicenic systems and its combination with other properties like strong absorption and emission in the visible spectral range and redox activity [START_REF] Shen | Helicenes: Synthesis and Applications[END_REF][START_REF] Gingras | One Hundred Years of Helicene Chemistry. Part 3: Applications and Properties of Carbohelicenes[END_REF][START_REF] Chen | Helicene Chemistry: From Synthesis to Applications[END_REF] has been the focus of investigation during the last twenty years. Chiral molecules such as helicenes are becoming more and more popular because of their direct application in asymmetric catalysis, 4- 5 chiroptical switches, [START_REF] Isla | Helicene-based chiroptical switches[END_REF] enantioselective fluorescence detectors, [START_REF] Reetz | 2,15-Dihydroxy-hexahelicene (HELIXOL): Synthesis and Use as an Enantioselective Fluorescent Sensor[END_REF] circularly polarized emitters for chiral OLEDs, [START_REF] Field | Circularly Polarized Luminescence from Bridged Triarylamine Helicenes[END_REF][START_REF] Hassey | Probing the Chiroptical Response of a Single Molecule[END_REF] and nonlinear optical (NLO) devices. [START_REF] Verbiest | Strong Enhancement of Nonlinear Optical Properties Through Supramolecular Chirality[END_REF][START_REF] Verbiest | Electric-Field-Modulated Circular-Difference Effects in Second-Harmonic Generation from a Chiral Liquid Crystal[END_REF] Great efforts have been made in the development and application of two techniques, circular dichroism (CD) and optical rotatory dispersion (ORD). [START_REF] Nakanishi | Circular Dichroism: Principles and Applications[END_REF] CD is known as electronic circular dichroism (ECD) when linked to transitions between electronic states and it is expressed as the difference between left (LCPL) and right (RCPL) circularly polarized light of one-photon absorption. [START_REF] Condon | Theories of Optical Rotatory Power[END_REF][START_REF] Caldwell | The Theory of Optical Activity[END_REF] Although, ECD has been the most common technique for the analysis of conformational and physical-chemistry properties of optically active molecular systems, [START_REF] Nakanishi | Circular Dichroism: Principles and Applications[END_REF] it presents significant challenges for their study in the UV region. [START_REF] Tinoco | Absorption, Scattering, and Imaging of Biomolecular Structures with Polarized Light[END_REF] Among the most predominant are: absorption from buffers and solvents in the same spectral region, as well as scattering enhancement from heterogeneous samples. These could result in the hindrance of the ECD signal at shorter wavelengths.

In order to circumvent aforementioned shortcomings of ECD, scientist in the field have proposed multiple linear [START_REF] Nafie | Vibrational Optical Activity: Principles and Applications[END_REF][START_REF] Barron | Molecular Light Scattering and Optical Activity[END_REF][START_REF] Mason | Practical Guide to Magnetic Circular Dichroism Spectroscopy[END_REF][START_REF] Miles | Synchrotron Radiation Circular Dichroism Spectroscopy of Proteins and Applications in Structural and Functional Genomics[END_REF] and non linear [START_REF] Cameron | Observation of Two-Photon Optical Rotation by Molecules[END_REF][START_REF] Ji | Toward Chiral Sum-Frequency Spectroscopy[END_REF][START_REF] Fischer | Nonlinear Optical Spectroscopy of Chiral Molecules[END_REF][START_REF] Rizzo | Ab Initio Study of the Circular Intensity Difference in Electric-Field-Induced Second Harmonic Generation of Chiral Natural Amino Acids[END_REF] polarization dependent methods. The latter includes two-photon circular dichroism (TPCD), [START_REF] Toro | Two-Photon Absorption Circular Dichroism: A New Twist in Nonlinear Spectroscopy[END_REF] which is the nonlinear counterpart of ECD, i.e. the difference in two-photon absorption cross-sections obtained with LCPL and RCPL at a specific wavelength (∆𝛿𝛿 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 (𝜆𝜆) = 𝛿𝛿 𝐿𝐿 𝑇𝑇𝑇𝑇𝑇𝑇 (𝜆𝜆) -𝛿𝛿 𝑅𝑅 𝑇𝑇𝑇𝑇𝑇𝑇 (𝜆𝜆)). [START_REF] Tinoco | Two-Photon Circular Dichroism[END_REF][START_REF] Power | Two-Photon Circular Dichroism[END_REF][START_REF] Hernández | Two-Photon Polarization Dependent Spectroscopy in Chirality: a Novel Experimental-Theoretical Approach to Study Optically Active Systems[END_REF] . Since typical excitation wavelengths in TPA are approximately two folds longer (degenerate case) than in OPA, negligible absorption at the excitation wavelength and minimization of scattering are observed. [START_REF] Denk | Two-Photon Laser Scanning Fluorescence Microscopy[END_REF][START_REF] Cumpston | Two-Photon Circular Dichroism of Molecular Structures Simulating L-tryptophan Residues in Proteins with Secondary Structures[END_REF] TPA is known for its intrinsic spatial resolution and penetration, [START_REF] Cumpston | Two-Photon Circular Dichroism of Molecular Structures Simulating L-tryptophan Residues in Proteins with Secondary Structures[END_REF] as well as better background discrimination and reduced photodamage to living specimens. [START_REF] Denk | Two-Photon Laser Scanning Fluorescence Microscopy[END_REF] All these advantages combined with the characteristic sensitivity of TPCD to structural changes and accessibility to the far ultra violet (far-UV) 30 make of this technique an excellent candidate for studying conformational and structural distortions of optically active chiral molecules in the far-UV.

The first experimental attempt to measure TPCD was made in 1995 by Richardson and coworkers, who used the fluorescence-detected two-photon circular dichroism (FD-TPCD) method. [START_REF] Gunde | Fluorescence-Detected Two-Photon Circular Dichroism of Gd 3+ in Trigonal Na3[Gd(C4H4O5)3] • 2NaClO4 • 6H2O[END_REF] However, it was not until the advent of the double L-scan technique that full experimental TPCD spectra in optically active molecules were measured. [START_REF] De Boni | Synchronized Double L-Scan Technique for the Simultaneous Measurement of Polarization-Dependent Two-Photon Absorption in Chiral Molecules[END_REF] Since then, TPCD became one of the best option for the structural study and conformational understanding of chiral molecules.

In the quest to increase the current understanding of the structure-property relationship of TPCD, we have been working on the theoretical-experimental analysis of the TPCD response in various molecular systems. [START_REF] Toro | Two-Photon Absorption Circular Dichroism: A New Twist in Nonlinear Spectroscopy[END_REF]30,[START_REF] Díaz | Two-Photon Circular Dichroism of an Axially Dissymmetric Diphosphine Ligand with Strong Intramolecular Charge Transfer[END_REF][START_REF] Díaz | Conformational Study of an Axially Chiral Salen Ligand in Solution using Two-Photon Circular Dichroism and the Fragment-Recombination Approach[END_REF][START_REF] Diaz | Overcoming the Existent Computational Challenges in the Ab Initio Calculations of the Two-Photon Circular Dichroism Spectra of Large Molecules using a Fragment-Recombination Approach[END_REF][START_REF] Diaz | The Effect of the π-Electron Delocalization Curvature on the Two-Photon Circular Dichroism of Molecules with Axial Chirality[END_REF][START_REF] Lin | Computational Challenges in Simulating and Analyzing Experimental Linear and Nonlinear Circular Dichroism Spectra. R-(+)-1,1'-bis(2-naphthol) as a Prototype Case[END_REF] With these investigations, we have nurtured our knowledge of TPCD in organic molecules. However, more systems need to be examined in order to fully explore this nonlinear optical property and its capability. In order to achieve this goal, herein, we present the theoretical-experimental analysis of the effect of pseudo-localized intramolecular charge transfer on the TPA and TPCD signal of a specific organic molecule with extended πelectron delocalization, helical chirality, and different donor-acceptor group combinations on one end. We first demonstrate that the lengthening of the π-electron delocalization within the helical core of P6 due to the presence of the pyridine moiety, predominantly increases the contribution of the magnetic dipole transition moment to the TPCD signal. This is explained by the observed Page 3 of 30

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The Journal of Physical Chemistry decrease in the corresponding HOMO-LUMO energy gap and its direct correlation with the molecular angular momentum. Next, we show that the replacement of the pyridine moiety present in P6 by stronger electron withdrawing substituents (eWS) enhances the electron transfer towards eWS. This effect results in a higher electric quadrupole transition moment contribution to the TPCD signal.

EXPERIMENTAL SECTION

P-(+) and M-(-) enantiomers of 1-(2-pyridyl)-4-methoxy [6]helicene (P6) were synthesized according to a published procedure. [START_REF] Shen | Straightforward Access to Mono-and Bis-cycloplatinated Helicenes Displaying Circularly Polarized Phosphorescence by Using Crystallization Resolution Methods[END_REF] Circular dichroism spectra (in M -1 cm -1 ) were measured on a Jasco J-815 Circular Dichroism Spectrometer (IFR140 facility -Université de Rennes 1) in dichloromethane and at concentrations around 5x10 -5 M.

OPA measurements were carried out in a single-beam spectrophotometer (Agilent 8453 Diode Array UV-Vis) from 190 to 600 nm in a 0.1 cm quartz cuvette in solutions with a concentration range from 2.0x10 -5 to 2.0x10 -4 M in THF. ECD spectra were performed in a J-815 CD spectropolarimeter (Jasco Corp., Tokyo, Japan). Solutions were prepared at a concentration of 1.0x10 -5 M in THF, at 25 o C, and in a 4 mm quartz cuvette. The ECD spectral region scanned ranged from 190 nm to 600 nm with a 1 nm step and a scan speed of 50 nm/min.

TPA and TPCD experiments were completed by using the Double L-scan technique in solutions with concentration of 8.7x10 -2 M in THF. Two-photon excitation was generated with a computer-controlled femtosecond optical parametric amplifier (OPerA Solo) pumped by an amplified laser system from COHERENT, Inc. The entire system is capable of generating 90 fs (FWHM) pulses over a wavelength range from 240 nm to 2.6 µm, and pulse energies of up to 350 µJ. Measurements were done at a repetition rate ranging from 2 to 50 Hz to avoid any contribution from cumulative effects. The pulse width was measured by a single-shot autocorrelator from COHERENT, Inc. and a frequency-resolved optical gaiting (FROG) from Swamp Optics, LLC.

COMPUTATIONAL METHODS

The molecular structure of M-(-) and P-(+)-P6 and the other donor-acceptor helicenes (Figure 1) were optimized using Density Functional Theory (DFT), [START_REF] Runge | Density-Functional Theory for Time-Dependent Systems[END_REF] with the Coulomb attenuating method-Becke's three-parameter exchange, Lee, Yang and Parr correlation (CAM-B3LYP) [START_REF] Yanai | A new Hybrid Exchange-Correlation Functional using the Coulomb-Attenuating Method (CAM-B3LYP)[END_REF] hybrid functional in combination with the 6-311++G(d,p) [START_REF] Krishnan | Self-Consistent M olecular Orbital Methods. XX. A Basis Set for Correlated Wave Functions[END_REF][START_REF] Clark | Efficient Diffuse Function-Augmented Basis Sets for Anion Calculations. III. The 3-21+G Basis Set for First-Row Elements, Li-F[END_REF] basis set, employing Gaussian 09 [START_REF] Frisch | Gaussian 09, Revision A.1[END_REF] .

Solvent effects were taken into consideration through the polarizable continuum model (PCM) 44 Then, we calculated the oscillator strengths (𝑓𝑓 0𝑓𝑓 ) and velocity rotatory strengths (𝑅𝑅 0𝑓𝑓 𝐸𝐸𝑇𝑇𝑇𝑇 ) for the first 100 electronic excited states for P6 and all the donor-acceptor helicene derivatives employing Time-Dependent DFT (TD-DFT) [START_REF] Runge | Density-Functional Theory for Time-Dependent Systems[END_REF] at the CAM-B3LYP 40 /6-311++G(d,p) 41-42 level of theory. CAM-B3LYP was selected as XCF because it has been proven to be more reliable than B3LYP in the prediction of excited states of molecules with ICT. Solvent effects were included in the calculations by using PCM [START_REF] Tomasi | Quantum Mechanical Continuum Solvation Models[END_REF] in Gaussian 09 [START_REF] Frisch | Gaussian 09, Revision A.1[END_REF] . The convoluted theoretical OPA and ECD spectra were obtained using Equations ( 1) and ( 2) with a Lorentzian shape and linewidth (Γ) of 0.28 eV (FWHM). OPA spectra are reported in molar absorptivity (ε),

𝜀𝜀 𝑂𝑂𝑇𝑇𝑇𝑇 (𝜔𝜔) ≈ 1.05495 × 10 3 × 𝜔𝜔 � 𝑔𝑔�𝜔𝜔, 𝜔𝜔 0𝑓𝑓 , Γ� 𝑓𝑓 0𝑓𝑓 𝜔𝜔 0𝑓𝑓 , 𝑓𝑓 (1)
where ω is the circular frequency of the incident light and 𝑔𝑔�𝜔𝜔, 𝜔𝜔 0𝑓𝑓 , Γ� is the line broadening function centered at 𝜔𝜔 = 𝜔𝜔 0𝑓𝑓 .

ECD spectra were calculated from 𝑅𝑅 0𝑓𝑓 𝐸𝐸𝑇𝑇𝑇𝑇 , and they are reported in molar absorptivity difference (Δε),

Δ𝜀𝜀 𝐸𝐸𝑇𝑇𝑇𝑇 (𝜔𝜔) ≈ 2.73719 × 10 1 × 𝜔𝜔 ∑ 𝑔𝑔�𝜔𝜔, 𝜔𝜔 0𝑓𝑓 , Γ�𝑅𝑅 0𝑓𝑓 𝐸𝐸𝑇𝑇𝑇𝑇 , 𝑓𝑓 (2)
The units of OPA and ECD are mol -1 cm -1 l, if the elements in equation ( 1) and ( 2) are in atomic units.

Finally, TPA probabilities (𝛿𝛿 ̅ 0𝑓𝑓 𝑇𝑇𝑇𝑇𝑇𝑇 (𝜔𝜔 0𝑓𝑓 )) and TPCD rotatory strength (𝑅𝑅 0𝑓𝑓 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 (𝜔𝜔 0𝑓𝑓 )) for P6 and all the eight theoretical donor-acceptor P6 derivatives were computed using TD-DFT 39 in DALTON 2013. [START_REF] Aidas | The Dalton Quantum Chemistry Program System[END_REF] CAM-B3LYP [START_REF] Yanai | A new Hybrid Exchange-Correlation Functional using the Coulomb-Attenuating Method (CAM-B3LYP)[END_REF] hybrid functional was employed in combination with 6-311++G(d,p) basis set [START_REF] Krishnan | Self-Consistent M olecular Orbital Methods. XX. A Basis Set for Correlated Wave Functions[END_REF][START_REF] Clark | Efficient Diffuse Function-Augmented Basis Sets for Anion Calculations. III. The 3-21+G Basis Set for First-Row Elements, Li-F[END_REF] for the calculation of the first 60 electronic excited states for all the molecules. The number of excited states was selected based on the experimental spectral range (200 to 450 nm) covered by the measurements. No solvent effects were taken into account in the nonlinear calculations due to the high computational cost. The convoluted theoretical TPA and TPCD spectra were obtained by a normalized Lorentzian shape with a linewidth (Γ) of 0.2 eV (FWHM).The 𝑅𝑅 0𝑓𝑓 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 (𝜔𝜔 0𝑓𝑓 ) were calculated from the electronic transitions employed in equations ( 3) and ( 4), where TPA spectra were simulated with,

𝛿𝛿 𝑇𝑇𝑇𝑇𝑇𝑇 (𝜔𝜔) ≈ 8.35150 × 10 -4 × 𝜔𝜔 2 � 𝑔𝑔�2𝜔𝜔, 𝜔𝜔 0𝑓𝑓 , Γ�𝛿𝛿 ̅ 0𝑓𝑓 𝑇𝑇𝑇𝑇𝑇𝑇 �𝜔𝜔 0𝑓𝑓 �, (3)
𝑓𝑓 here 𝑔𝑔�2𝜔𝜔, 𝜔𝜔 0𝑓𝑓 , Γ� is the line broadening function and 𝛿𝛿 ̅ 0𝑓𝑓 𝑇𝑇𝑇𝑇𝑇𝑇 is the orientationally averaged twophoton probability for the degenerate case.

TPCD spectra were computed from,

Δ𝛿𝛿 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 (𝜔𝜔) ≈ 4.87555 × 10 -5 × 𝜔𝜔 2 � 𝑔𝑔�2𝜔𝜔, 𝜔𝜔 0𝑓𝑓 , Γ�𝑅𝑅 0𝑓𝑓 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 �𝜔𝜔 0𝑓𝑓 �, (4)
𝑓𝑓 TPA and TPCD spectra computed from ( 3) and ( 4) are reported in G𝑜𝑜ppert-Mayer (GM), which is equivalent to 10 -50 cm 4 s mol -1 photon -1 when the elements of the equations are in atomic units.

In order to justify the use of the CAM-B3LYP hybrid functional for P6 we calculated the molecular orbitals involved in the most important electronic excitation on the red side of the theoretical ECD (#3) spectrum. The obvious ICT observed in Figure 2, makes the selection of CAM-B3LYP reliable for our analysis. Similar evidences have already been reported by Rizzo and co-workers in various molecular systems. [START_REF] Díaz | Two-Photon Circular Dichroism of an Axially Dissymmetric Diphosphine Ligand with Strong Intramolecular Charge Transfer[END_REF][START_REF] Lin | Computational Challenges in Simulating and Analyzing Experimental Linear and Nonlinear Circular Dichroism Spectra. R-(+)-1,1'-bis(2-naphthol) as a Prototype Case[END_REF][START_REF] Diaz | Two-photon Absorption and Twophoton Circular Dichroism of Hexahelicene Derivatives: A Study of the Effect of the Nature of Intramolecular Charge Transfer[END_REF][START_REF] Lin | Theory for Vibrationally Resolved Two-Photon Circular Dichroism Spectra. Application to (R)-(+)-3-Methylcyclopentanone[END_REF][START_REF] Guillaume | Computational Study of the One-and Two-Photon Absorption and Circular Dichroism of (L)-Tryptophan[END_REF] Page 7 of 30

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RESULTS AND DISCUSSION

In Figure 3 (TPA and TPCD) spectra -linear and nonlinear excited states were computed using TD-DFT. For the linear calculations (100 electronic excited states), solvent effects were considered using PCM.

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The Journal of Physical Chemistry 10

For the nonlinear theoretical spectra, the lowest 60 excited states were obtained without taking solvents effects into account due to high computational cost. In order to obtain a better overlapping between theoretical and experimental bands, the theoretical linear and nonlinear spectra were spectrally shifted by the amount reported in the caption of Figure 4. This is a common practice for theoretical-experimental works. 24, 33-34, 36-37, 46, 49 The first interesting observation to highlight from Figure 4 is the remarkable theoreticalexperimental overlapping in all four spectra. The theoretical spectra extraordinarily reproduced the shape, position of the bands, and the fano-type shape profile of the experimental spectra. As mentioned before, the great performance of the chosen XCF is attributed to the presence of ICT in

P6.

The second important observation is the differences in TPA cross-sections between theoretical and experimental spectra, where the former is larger than the latter. This differences have been previously observed in other molecules [START_REF] Diaz | Two-photon Absorption and Twophoton Circular Dichroism of Hexahelicene Derivatives: A Study of the Effect of the Nature of Intramolecular Charge Transfer[END_REF][START_REF] Vesga | Study of the Effect of the Pulse-Width of the Excitation Source on the Two-Photon Absorption and Two-Photon Circular Dichroism Spectra of Biaryl Derivatives[END_REF] and are very hard to explain considering the fact that the measurements were performed in the femtosecond regime where excited state absorption is almost negligible. [START_REF] Wu | Two-Photon Absorption and Two-Thoton Assisted Excited-State Absorption in CdSe0.3S0.7 quantum dots[END_REF][START_REF] Hernandez | Three-and Four-Photon Absorption of a Multiphoton Absorbing Fluorescent Probe[END_REF] Next, it is worth noting that the sign and relative intensities of the two main bands (290 and 260 nm) in TPCD were notably reproduced.

In order to gain more insight about the effects of a structural motif on the linear and nonlinear chiroptical properties of conjugated organic molecules with helical chirality, we embarked on a theoretical investigation of several molecular systems with different terminal donor-acceptor motifs on the helicene core of P6-like structures (see Figure 1). We performed calculations of OPA, ECD, TPA, and TPCD on four different moieties on position 1 and four different substituents in position 4 (see Figure 1). The substituents were selected based on their ability to affect the electron density of the helicene core. In order to perform a systematic selection of the corresponding substituents, we used the Hammet parameter (σ), which provides a qualitative (negative σ for electron releasing and positive for electron withdrawing substituents) and quantifiable scale for the electron withdrawing and releasing strength of the groups (see Tables 1 and2). [52][START_REF] Pandith | Electron Transport and Nonlinear Optical Properties of Substituted Aryldimesityl Boranes: a DFT Study[END_REF] Page 11 of 30

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The Journal of Physical Chemistry In Figure 5, we present the comparative plot of the OPA, ECD, TPA and TPCD theoretical spectra for all four different substituents for position 4, as well as the theoretical spectra for P6. In TPA, two main bands are identified, the first at approximately 260 nm and the second at 200 nm. The intensity of the first band is similar in all five derivatives. However, the second band changes its intensity from 20 GM in H to 34 GM in NHCOCH3. In the TPCD spectra, one can also notice that the first band is unaffected by the substitution in position 4. However, the apparent change in intensity observed in the second band of the -NHCOCH3 derivative is attributed to the fusion of the double-peak band present in the other four molecules to produce an intense single-peak band.

Next, we varied the substituent in position 1, keeping the moiety in position 4 as in P6 (see the combinations in Figure 1). In Figure 6, we present the OPA spectra of the four derivatives of the second series. Interesting to highlight is the small red shift (30 nm) experienced by the band centered at approximately 320 nm in -CN, -SO3H, and P6. Likewise in ECD, we see a similar shift in the same three derivatives. This interesting result reveals the extension of the conjugation length introduced by the pyridine moiety on the outside of the helicene core in P6, an effect not present in the other four derivatives.

Moving on to the TPA spectra, another interesting point to highlight, which is only observed in the two strongest electron withdrawing groups, is the presence of a strong band at approximately 180 nm, which TPA cross section varies from 28 GM for P6 to 48 GM for the -SO3H substituted.

This result is supported by previous theoretical results published by Yan and co-workers (2012) ,

where they demonstrated that conjugated molecules with a push-pull motif present an enhanced TPA cross section as a result of the intramolecular charge transfer, which increases the electric dipole transition moments between the ground and excited states. [START_REF] Hu | Theoretical Study of Twophoton Absorption Properties and Up-conversion Efficiency of New Symmetric Organic πconjugated Molecules for Photovoltaic Devices[END_REF] To corroborate this finding, we calculated the resultant electric dipole transition moment for the 3 rd electronic excited state (see Table 3) -same electronic excited state selected previously for corroborating the charge transfer character of P6. As expected, one can clearly see that, at least for this electronic excited state, the resultant electric dipole transition moment is larger for CN and SO3H than for P6.

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The Journal of Physical Chemistry The molecular orbitals for the most important single excitations contributing to the 3 rd excited state of SO3H presented in Figure 7, evidently expose the greater ICT character of -SO3H when compared to P6 (see Figure 3). On the one hand, in the HOMO and HOMO-1 energy levels, one can see that the electrons are mainly delocalized in the aromatic ring of the molecular system. In the LUMO and LUMO+1 energy levels, the electron density goes more towards the -SO3H group due to its higher electron withdrawing character. Consequently, the ICT effect is more evident in the helicene with the -SO3H substituent than in P6. Finally, we analyzed the TPCD spectra of all five substituents in position 1 (Figure 6). Once again, the positive band that appears towards the red side of the spectra seems to be unaffected by the donor-acceptor combination of the substituents. However, the band located at approximately 200 nm changed in shape and sign. In the case of P6 and -Cl, one can notice a negative doublepeak band in this region. For -CN and -SO3H, this band emerges as a negative single-peak band at 210 nm that turns into a positive band at 180 nm. Knowing that TPCD signal directly depends on the different contributions from the electric quadrupole transition moment (accounted for on the molecular parameter B2) and the magnetic dipole transition moment (accounted for on the molecular parameters B1 and B3), a comparison of the sum of the absolute values of molecular parameters B1+B3 and B2 for all five substituents in position 1 and 4 is presented in Figure 8. to their donor-acceptor character. It can be observed that Σ|B1+B3| is always greater for P6 than the P6-like molecules with different substituents. However, the contribution of the electric quadrupole transition moment (Σ|B2|) to the TPCD spectra is larger for P6 on the electron releasing moieties and larger for -CN on the electron withdrawing series. In order to explain these trends, we calculated the HOMO and LUMO energies for each P6-like derivative, P6 included, employing DFT. The calculated energies, as well as the energy gaps of these molecules are presented in Figure 9.

From Figure 9.a, which compares the effect of the strength of donor groups in position 4, one can deduce that as the electron releasing character increases, so does the LUMO energy of the helicene derivatives. This is corroborated by the change in tendency observed in a weak electron withdrawing substituent such as -CH3) (the LUMO energy increases again, Figure 9.a). Now, in The Journal of Physical Chemistry between the two. Through this analysis, an inverse dependency between the magnetic dipole transition moment contribution to the TPCD and the energy gap was noticed, i.e. the lower the energy gap the higher ∑|B1+B3 |. This can be explained based on previous works reporting that a decrease in energy gap causes and increase in the angular momentum . [START_REF] Dalafi | Theoretical Investigation of Anomalies in 162 Er[END_REF] Therefore, because the angular momentum is directly correlated with the magnetic moment, an increase in the angular momentum results in a higher magnetic dipole transition moment. 56 In order to corroborate the established correlation between ∑|B1+B3 | and ∑|B2 | and the donoracceptor combination in P6 derivatives, we calculated the frontier molecular orbitals (FMOs) of all nine molecules (see Figure 10). The FMOs were obtained using DFT. In Figure 10.a, one can observe, in most of the derivatives, that the electron density over the substituents on one end of the molecule is higher in the HOMO than in the LUMO. This reveals the strong electron withdrawing character of the helical core in P6-like derivatives with different electron donating moieties. On the contrary, the FMOs presented in Figure 10.b show a strong ICT between the two moieties with push-pull arrangement on one end on the derivatives rather than through the helicene

Figure 1 .

 1 Figure 1. Chemical structures of P-(+)-1-(2-pyridyl)-4-methoxy[6]helicene (P6) and eight donor-acceptor P6 derivatives.

Figure 2 .

 2 Figure 2. Molecular orbitals (MOs) involved in the 3rd electronic excited state of P6. The MOs were obtained from CAM-B3LYP/6-311++G(d,p) TD-DFT calculations in THF using PCM in Gaussian 09. The percent contribution of each single excitation ([HOMO-x] → [LUMO + y] to the excited state is indicated next to each arrow.

Figure 3 .

 3 Figure 3. Experimental a) TPCD and b) ECD spectra for P-(+)-P6 and M-(-)-P6 in THF and dichloromethane, respectively.

Figure 4 .

 4 Figure 4. Experimental (black solid and scattered line) and theoretical (green dotted line) of: a) UV-Vis, b) ECD, c) TPA, and d) TPCD spectra of P-(+)-P6. Colored symbols display the oscillator strength in the case of UV-Vis and ECD and TPA probabilities and rotatory strength in the case of TPA and TPCD, respectively. The OPA and ECD were calculated for the 100 lowest electronic excited states at the CAM-B3LYP/6-311++G(d,p) level of theory using Gaussian 09 in THF employing PCM. The theoretical linear spectra are only shown within the measurable spectral range (200-450 nm) with +10 nm spectral shift. 𝛤𝛤 = 0.28 eV (FWHM) was used for OPA and ECD. The TPA and TPCD spectra were computed for the first 60 excited states at the CAM-B3LYP/6-311++G(d,p) level of theory in vacuo using Dalton 2013. The theoretical shift for the

First, we decidedFigure 5 .

 5 Figure 5. OPA, ECD, TPA, and TPCD theoretical spectra of all different substituents of position 4 including P6. OPA and ECD were obtained from the Lorentzian convolution (Γ = 0.2 eV FWHM) of the first 60 excited states of their optimized structures calculated at the CAM-B3LYP/6-311++G(d,p) level of theory in THF using PCM employing Gaussian 09. TPA and TPCD spectra of all optimized structures were obtained from the Lorentzian convolution (𝛤𝛤 =0.2 eV (FWHM)) of the first 60 excited states. The nonlinear calculations were performed at CAM-B3LYP/6-311++G(d,p) level of theory in vacuo using Dalton 2013.

Figure 6 .

 6 Figure 6. OPA, ECD, TPA and TPCD theoretical spectra of all five different substituents. OPA and ECD spectra were obtained from the Lorentzian convolution (Γ = 0.2 eV FWHM) of the first 100 electronic excited states of the optimized structures of all different five substituents at the CAM-B3LYP/6-311++G(d,p) level of theory in THF using PCM and employing Gaussian 09.TPA and TPCD spectra of the optimized structures were calculated from the Lorentzian convolution (Γ = 0.2 eV FWHM) for the first 60 electronic excited states. TPA and TPCD

Figure 7 .

 7 Figure 7. Molecular orbitals (MOs) involved in the 3rd electronic excited state of SO3H. The MOs were obtained from CAM-B3LYP/6-311++G(d,p) TD-DFT calculations in THF using PCM in Gaussian 09. The percent contribution of each single excitation ([HOMO-x] → [LUMO + y]) to the excited state is indicated next to each arrow.

Figure 8 .

 8 Figure 8. Comparative bar graph of a) ∑|B1+B3| and b) ∑|B2| for all substituents of a) position 4 and b) position 1.

Figure 9 .

 9 Figure 9.b, which assesses the effect of the strength of attractor groups in position 1, one can

Figure 9 .

 9 Figure 9. Calculated HOMO energies, LUMO energies, and energy gaps of all the donoracceptor combinations substituents for a) position 4 and b) position 1.

  summary, the presence of strong withdrawing substituents such as -CN and -SO3H in position 1 tend to originate a larger contribution to TPCD through the electric quadrupole transition moment, while the pure existence of an aromatic ring like pyridine in P6 that can extend the length of the π-electron delocalization beyond the helical core creates a stronger contribution to TPCD through the magnetic dipole transition moment.

Figure 10 .

 10 Figure 10. The Frontier Molecular Orbitals (FMOs) of all substituents of a) position 4 and b) position 1. The molecular orbitals were obtained using DFT at the CAM-B3LYP/6-311++G(d,p) level of theory in THF using PCM and employing Gaussian 09.

Table 1 .

 1 Hammet σ-constant for substituents of position 4.

	Substituent Position 4	Hammet σ-constant
	H	0
	OH	-0.37
	P6	-0.27
	NHCOCH3	-0.15
	CH3	0.23

Table 2 .

 2 Hammet σ-constant for substituents of position 1.

	Substituent Position 1	Hammet σ-constant
	CN	0.66
	SO3H	0.30
	Cl	0.23
	P6	-0.05
	OH	-0.37

Table 3 .

 3 Comparison of the resultant of the electric dipole transition moment of the two groups with the highest electron withdrawing character (CN and SO3H) and P6.

	State 3	Resultant of the Electric
		dipole transition moment
		(AU)
	CN	2.14327
	SO3H	2.00440
	P6	1.57353

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ACKNOWLEDGEMENTS

Jeanne Crassous thanks the Ministère de l'Education Nationale, de la Recherche et de la Technologie and the Centre National de la Recherche Scientifique (CNRS). This work has been partially supported by the National Science Foundation through Grant Number NSF/ARRA-0840431 and NSF/DBI-1422826. The extended computing time provided by STOKES ARCC/UCF is gratefully acknowledged.

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The Journal of Physical Chemistry

ACS Paragon Plus Environment The Journal of Physical Chemistry ACS Paragon Plus Environment The Journal of Physical Chemistry ACS Paragon Plus Environment The Journal of Physical Chemistry The Journal of Physical Chemistry Effects of terminal push pull groups on the TPCD signal of Hexahelicene Derivatives. 64x50mm (300 x 300 DPI)