The oral administration of vitamin B12 offers a potentially simpler and cheaper alternative to parenteral administration, but its effectiveness has not been definitively demonstrated. The following protocol was designed to compare the effectiveness of orally and intramuscularly administered vitamin B12 in the treatment of patients â‰¥65â€‰years of age with vitamin B12 deficiency.The proposed study involves a controlled, randomised, multicentre, parallel, non-inferiority clinical trial lasting one year, involving 23 primary healthcare centres in the Madrid region (Spain), and patients â‰¥65â€‰years of age. The minimum number of patients required for the study was calculated as 320 (160 in each arm). Bearing in mind an estimated 8-10% prevalence of vitamin B12 deficiency among the population of this age group, an initial sample of 3556 patients will need to be recruited.Eligible patients will be randomly assigned to one of the two treatment arms. In the intramuscular treatment arm, vitamin B12 will be administered as follows: 1â€‰mg on alternate days in weeks 1 and 2, 1â€‰mg/week in weeks 3â€“8,and 1â€‰mg/month in weeks 9â€“52. In the oral arm, the vitamin will be administered as: 1â€‰mg/day in weeks 1â€“8 and 1â€‰mg/week in weeks 9â€“52. The main outcome variable to be monitored in both treatment arms is the normalisation of the serum vitamin B12 concentration at weeks 8, 26 and 52; the secondary outcome variables include the serum concentration of vitamin B12 (in pg/ml), adherence to treatment, quality of life (EuroQoL-5D questionnaire), patient 3satisfaction and patient preferences. All statistical tests will be performed with intention to treat and per protocol. Logistic regression with random effects will be used to adjust for prognostic factors. Confounding factors or factors that might alter the effect recorded will be taken into account in analyses.The results of this study should help establish, taking quality of life into account, whether the oral administration of vitamin B12 is an effective alternative to its intramuscular administration. If this administration route is effective, it should provide a cheaper means of treating vitamin B12 deficiency while inducing fewer adverse effects. Having such an alternative would also allow patient preferences to be taken into consideration at the time of prescribing treatment.This trial has been registered with ClinicalTrials.gov, number NCT 01476007, and under EUDRACT number 2010-024129-20. Vitamin B12 , along with other derivatives of folic acid, is a nutrient essential for the synthesis of DNA. Its deficiency is manifested through changes in the number and morphology of erythrocytes, leucocytes and platelets, and by neurological alterations owed to the progressive demineralisation of the nervous system (a consequence of defective myelin synthesis). Vitamin B12 is found mostly in food of animal origin. It is separated from ingested food through the action of the gastric acid, and in the duodenum the vast majority binds to intrinsic factor (IF). The vitamin B12/IF complex formed, which is very resistant to digestion, is then absorbed by endocytosis in the terminal ileum. Only 1-2% of vitamin B12 absorption occurs independent of IF .In the primary healthcare setting, the most commonly seen causes of vitamin B12 deficiency are related to abnormalities of digestion  or absorption , and, to a lesser extent, a lack of exogenous supply. The exact prevalence of vitamin B12 deficiency in industrialised countries is unknown; indeed, different studies using different definitions have reported it as between 5% and 60% . ResultsIn the elderly, the symptoms of vitamin B12 deficiency caused by deficient diets and/or digestive and/or absorption problems can be nonspecific, making a diagnosis of deficiency more difficult. For example, up to 40% of elderly people show no haematological alterations. Further, neurological symptoms may appear before those of anaemia; indeed, only about 60% of elderly people with vitamin B12 deficiency are anaemic .The trial protocol was approved by the Madrid Region Clinical Research Ethics Committee  in the last five years for vitamin B12 deficiencyÂ· serious neurological or psychiatric symptoms, including psychotic problemsÂ· dementia preventing the giving of informed consent to take partÂ· atrophy of the optic nerveÂ· serum folic acid concentration of <2.3â€‰ng/mlÂ· stage 4 kidney disease 4 (estimated glomerular filtration rate [GFR] 15â€“29â€‰ml/min)Â· having received/suffering malabsorption-related:â—‹ surgery or diseases affecting the jejunum-ileumâ—‹ inflammatory-intestinal disease, e.g., Crohnâ€™s disease, ulcerative colitisâ—‹ celiac diseaseÂ· chronic pancreatitisÂ· myelodisplasia or malignant blood diseaseÂ· haemophilia or other coagulation problems contraindicating parenteral administrationÂ· severe systemic diseaseÂ· having been involved in any other trial involving the administration of any experimental treatment in the 28â€‰days prior to the start of the present studyÂ· being treated for HIV, HVB or HVC infectionÂ· hypersensitivity to vitamin B12, or any of the vitamin preparationâ€™s excipientsÂ· receiving anticoagulation treatmentÂ· being away from home and with no intention of residing for the following year in the health district where consultation was madeÂ· failing to meet any inclusion criterionÂ· limitations regarding oral treatmentParticipants will be enrolled consecutively by their general practitioners when attending a primary healthcare centre in the study area Figure . All patThe sample size required was determined bearing in mind the results of Kuzminski et al. . In the Assuming that the percentage of patients showing an increase in serum vitamin B12 concentration to above 179â€‰pg/ml in both groups is 70%, means the study requires at least 304 patients (152 in each arm) for a threshold of non-inferiority of 10% and a statistical power of 60% with significance set at pâ€‰<â€‰0.05. Given the type of patients to be studied, i.e., patients who have come to the health centres for consultation, plus the fact that their own family doctors are members of the research team, a loss to follow-up of under 5% is expected. The minimum starting sample size for each arm was therefore deemed to be nâ€‰=â€‰160. With an expected prevalence of vitamin B12 deficiency of 8-10% , the original number of patients to be enrolled so that 320 with a vitamin B12 deficiency can be guaranteed is 3556.In studies with the present design it is impossible to blind the patient to the treatment received. However, this limitation is compensated for by the objective measurement of the main outcome variable (the serum vitamin B12 concentration) and the randomisation of the patients to the treatment groups. Further, the persons charged with the statistical analysis of the data will be blind to the identity of the patients in each treatment arm.The pharmaceutical formulations to be used in the study are commercially available in Spain. The treatments will involve:Â· Intramuscular route: 1â€‰mg of vitamin B12 on alternate days during weeks 1 and 2; 1â€‰mg/week over weeks 3â€“8 ; and 1â€‰mg/month from weeks 9â€“52Â· Oral route: 1â€‰mg/day of vitamin B12 for 8â€‰weeks; 1â€‰mg/week from weeks 9â€“52Patients in both arms will undergo analytical monitoring in weeks 8, 26 and 52. They will receive appointments for the appropriate dates. The response to treatment will be recorded alongside adherence to treatment and the appearance of any adverse effects.Before work begins, the project will be presented to all the research team members in a special meeting. Training sessions lasting 2â€“3â€‰h will also be held at each participating health centre. These will involve a review of the inclusion and exclusion criteria, provide instructions regarding the intervention, and examine the ethical requirements to be met for the trial to be held.The procedures to be followed and information to be recorded at each of a patientâ€™s visits to a participating health centre is as follows:Selection VisitÂ· Signing of informed consentAssessment of inclusion/exclusion criteriaRecording of demographic data (age and sex)Analysis: serum vitamin B12. If concentration is <179 pg/ml the following analyses are to be requested: haemogram, biochemical analysis , ferritin, folic acid, anti-IF antibody level. If serum vitamin B12 concentration is >179 pg/ml: patient preference questionnaireRandomisation of patients to treatment groupVisit 1 (start of treatment)Â· Anamnesis: record whether the patient lives alone or with others, lifestyle habits, use of alcohol, whether a vegan diet is followed, whether the patient has undergone gastrectomySymptoms: record paresthesia, asthenia, loss or reduction of appetite, sadness or change in state of mind, concomitant pharmacological treatmentPhysical examination: for Hunterâ€™s glositis, positional and vibrational sensitivityQuestionnaires: Lobo cognitive mini-exam, EuroQoL-5DRecord concomitant treatmentRequest analyses to be performed one week before next visit: haemogram and serum vitamin B12Therapeutic plan: patient in oral arm â€“ provision of medication; patient in intramuscular arm â€“ provide appointments for injectionsVisit 2 (week 8)Â· Anamnesis: record lifestyle habits and use of alcoholSymptoms: if pathological at the first visit, record paresthesia, asthenia, loss or reduction of appetite, sadness or change in level of happiness, and concomitant pharmacological treatmentPhysical examination: if pathological at the first visit examine for Hunterâ€™s glositis, positional and vibrational sensitivityRecord concomitant treatmentRequest analyses to be performed one week before next visit: haemogram and serum vitamin B12Questionnaires: EuroQoL-5DAssessment of adverse effectsTherapeutic plan: patient in oral arm â€“ provision of medication; patient in intramuscular arm â€“ provide appointments for injectionsAssess adherence to treatment: oral route â€“ count number of vials used; intramuscular route: count injections givenVisit 3 (week 26)Â· Anamnesis: record lifestyle habits and use of alcoholSymptoms: if pathological at the first visit, record paresthesia, asthenia, loss or reduction of appetite, sadness or change in level of happiness, and concomitant pharmacological treatmentPhysical examination: if pathological at the first visit examine for Hunterâ€™s glositis, positional and vibrational sensitivityRecord concomitant treatmentRequest analyses to be performed one week before next visit: haemogram and serum vitamin B12Questionnaire: EuroQoL-5DAssessment of adverse effectsTherapeutic plan: patient in oral arm â€“ provision of medication; patient in intramuscular arm â€“ provide appointments for injectionsAssess adherence to treatment: oral route â€“ count number of vials used; intramuscular route: count injections givenVisit 4 (week 52)Â· Anamnesis: record lifestyle habits and use of alcoholSymptoms: record paresthesia, asthenia, loss or reduction of appetite, sadness or change in level of happiness, and concomitant pharmacological treatmentPhysical examination: for Hunterâ€™s glositis, positional and vibrational sensitivityRecord concomitant treatmentQuestionnaires: EuroQoL-5D, satisfaction and preferencesAssessment of haemogram and serum vitamin B12 concentrationAssessment of adverse effectsAssess adherence to treatment: oral route â€“ count number of vials used; intramuscular route: count injections givenThe main outcome to be measured is the normalisation of the serum vitamin B12 concentration (>179â€‰pg/ml) at 8, 26 and 52â€‰weeks. The secondary outcomes will be the serum vitamin B12 concentration (pg/ml), adverse events , adherence to treatment , quality of life (measured using the EuroQoL-5D questionnaire), and patient satisfaction and preferences.Including age, sex, whether the patient lives alone or with others, whether a vegan diet is followed, and the use of alcohol (g/week).Symptoms such as paresthesia, asthenia, loss or reduction of appetite, sadness or change in state of mind (anamnesis), Hunterâ€™s glositis, positional and vibrational sensitivity , and cognitive decline (Lobo test).Haemogram (complete blood cell and platelet count) and biochemical analysis . Blood analyses will be performed in plasma or serum as required and under standard conditions.Recording of the taking of protein pump inhibitors, H2 receptor antagonists, antacids, potassium, metformin, colchicine, neomycin, p-aminosalicylic acid, parenteral chloramphenicol, Fe, vitamin C and other vitamin supplements.Patients will be removed from the trial if any of the following conditions are met:Â· Serum vitamin B12 concentration still <179â€‰pg/ml after 8â€‰weeks of treatment. Treatment will be deemed to have failed in these patients, and they will be further studied and treated outside the trial according to normal clinical practice.Â· Serious adverse events.Â· Voluntary withdrawal or violation of the protocol.At least two attempts will be made to contact by telephone those patients who do not come for their scheduled visits. All patients will be informed that they can abandon the study at any time without this affecting their future medical treatment in any way.The trial will involve a descriptive statistical analysis of the baseline characteristics of patients in both treatment arms. Quantitative variables will be described in terms of their measure of central tendency, mean or median (for those showing asymmetric distributions), and the corresponding dispersion, standard deviation or interquartile range. Qualitative variables will be described in terms of proportions and their corresponding confidence intervals.The Student t test or Mannâ€“Whitney U test  will be used to determine whether the two treatment arms are comparable based on their quantitative baseline characteristics and known prognostic factors. Comparisons on qualitative variables will be undertaken using the Pearson Chi-squared test or Fisherâ€™s Exact test as required. If cases of inequality are detected, the confounding factors will be defined and appropriate adjustments made.Intention-to-treat and per-protocol analyses will both be performed, as is recommended for non-inferiority studies .The effectiveness of treatment will be analysed by examining the therapeutic success achieved in each arm at 8, 26 and 52â€‰weeks, determining the 95% confidence interval for the percentage of patients in each treatment arm whose serum vitamin B12 concentrations become normalised. If the confidence intervals do not fall outside the non-inferiority limit (10%), it can be concluded that the oral treatment is not inferior to the intramuscular treatment. The within-patient percentage change in serum vitamin B12 concentration at each monitoring point will be determined, and the confidence intervals for the difference in the mean values for each arm calculated.If the distribution of confounding factors differs in the two arms, explicative regression analysis will be performed in which the dependent variable will be the normalisation of the serum vitamin B12 concentration, and the independent variable will be the treatment group.Repeated measures ANOVA will be used to examine the change in serum vitamin B12 concentration in each group at each monitoring point.The incidence of adverse events in the two arms will be compared using the Pearson Chi-squared test or Fisherâ€™s Exact test as required.-based quality of life values.The perception of quality of life by the patients of each arm will be assessed by comparing the EuroQol 5D scores  and the transformation of these scores into utilityAdherence to treatment will be examined via the counting of oral doses taken in the oral arm, and the number of injections given in the intramuscular arm. An operative indicator variable will then be defined to describe the degree of adherence.th 2011). It will be performed by qualified medical and scientific staff. The rights and welfare of the patients will be respected at all times. All patients will be adequately informed, both verbally and in writing, of the nature of the trial, its aim, and its risks and possible benefits. Given that the study is a non-inferiority trial, all patients will be informed that the oral treatment is expected to be as effective as the standard intramuscular treatment. Signed, dated consent to be included will be required from each patient.The trial has been approved by the Madrid Region Clinical Research Ethics Committee (February 8Convenio de Oviedo) (1997).Spanish law regarding the use of human subjects in clinical trials will be adhered to. The trial will respect all basic ethical principles of autonomy, justice, goodness of intent and absence of malintent according to the standards of good clinical practice enshrined in the Declaration of Helsinki  and the Oviedo Agreement  that quality scientific information supports the effectiveness of the therapeutic options on offer, and 2) that heterogeneous groups of patients have recorded their satisfaction with these options. The present trial provides for information in this respect to be gathered  and therThe trial is also designed to provide information on the effect of the normalisation of serum vitamin B12 concentrations by both treatments on patient-perceived quality of life. Physicians commonly assume that taking oral supplements will be associated with a feeling of greater well-being, although this has never been proven . The preThe trial suffers from the practical limitation of having to enrol a large number of patients to meet its sample size requirements. However, a high degree of motivation is expected of the research team since its clinical assistance members are those involved in the enrolment process. Further, the fact that the patients to be enrolled will be seeking medical help  suggests few will be lost to follow-up. A further possible limitation is the low statistical power used in the calculation of the sample size. The 60% power contemplated requires a sample size of 304 patients (152 in each arm) â€“ higher powers would increase the sample size required and the enrolment of such numbers cannot be guaranteed. However, given the results reported in previous studies  that used moderate/high doses of vitamin B12, it should be possible to demonstrate the non-inferiority of the oral treatment with this power level. If the 95% confidence interval were to cross the non-inferiority threshold, i.e., showing the results to be inconclusive, the intramuscular treatment would remain the treatment of choice. To determine the degree of adherence to treatment (and thus avoid outcome dilution effects) , the numThe decision not to take serum methylnalonic acid and homocysteine concentrations into account as diagnostic markers and outcome variables was made bearing in mind that these are not normally determined, either at diagnosis or during follow-up, in patients with a vitamin B12 deficiency.Finally, given the pragmatic nature of the proposed trial, the decision was taken to include consecutive patients seeking medical help at the participating centres, thus ensuring the enrolment of subjects similar to those that would be seen in normal clinical practice.Fe: Ferrum; g: Gram; GFR: Glomerular filtration rate; GGT: Gamma-glutamyl transpeptidase; GOT: Glutamic oxaloacetic transaminase; GP: General practitioner; GPT: Glutamic-pyruvic transaminase; HIV: Human immunodeficiency virus; HVB: Hepatitis B virus; HVC: Hepatitis C virus; IF: Intrinsic factor; Î¼g: Microgram; MMA: Methylmalonic acid; mg: Milligrams; ng: Nanograms; pg: Picograms.The authors declare that they have no competing interests.PGE y RRF conceived of the study and participated in its design. TSC; RRF; SGE; IdCG; JMF; EEM; participated in the design and coordination of the study. FRS; MGS; RGG; MAMS; COL; MLSP; CMR; BMB; AVP; FGBG; JEMS; RRB; GAC; LMCB; EPC; MRB; MTRM; SSD; SMI; RRG; IBL; MVN; JSD; TGG; MDC; AAB participated in different phases of the design. TSC; RRF; SGE; IdCG; JMF; EEM directed the writing of the manuscript. All authors OB12 Group read and approved the final manuscript.Healthcare Centre (HC) Barajasx: GermÃ¡n Reviriego JaÃ©n, Cristina Montero GarcÃa, Ana Isabel Sanz Lorente, Ma del Pilar Serrano Simarro, JuliÃ¡n DÃaz SÃ¡nchez, Irma Ma Ramos GutiÃ©rrez, Josefa Ma San Vicente RodrÃguez, Pilar Huelin MartÃn, Ma Inmaculada GonzÃ¡lez GarcÃa, Margarita Camarero Shelly, Clarisa Reinares MartÃnez, Laura Villanova Cuadra, Rosa Maâ€‰GÃ³mez del Forcallo. HC Doctor Cirajas: Francisco Endrino GÃ³mez, Ma Rosario Ferreras Eleta, Luis De Vicente Aymat, MarÃa Santos Santander GutiÃ©rrez, Alicia Mateo Madurga. HC Juncal: Nuria Caballero RamÃrez, Ana MorÃ¡n Escudero, Mercedes RodrÃguez Franco, MÂª Luz MeiriÃ±o PÃ©rez, MÂª Mar Zamora GÃ³mez, Francisco Vivas Rubio, MarÃa MartÃn MartÃn. HC Miguel de Cervantes: Rafael PÃ©rez Quero, MÂª Isabel Manzano MartÃn, Raimundo Pastor SÃ¡nchez, Alicia Herrero de Dios, Cesar Redondo LuciÃ¡Ã±ez. HC Reyes Magos: Cristina Casado RodrÃguez, Luisa MarÃa AndrÃ©s Arreaza, Pilar Hombrados Gonzalo, Soledad Escolar Llamazares, Francisco LÃ³pez Ortiz, Luz MÂª del Rey Moya, Isabel RodrÃguez LÃ³pez. HC Calesas: Diego MartÃn Acicoya, Pilar Kloppe Villegas, Isabel GarcÃa Amor, Magdalena Canals Aracil, JosÃ© Javier GÃ³mez Marco, Alberto GonzÃ¡lez Ã�lvaro, Fco Javier San AndrÃ©s Rebollo, InÃ©s GonzÃ¡lez LÃ³pez, Isabel Herreros Hernanz, Antonio Revuelta Alonso, Nieves Calvo Arrabal, MÂª Milagros Jimeno GalÃ¡n, Rosa GarcÃa HernÃ¡ndez. HC Guayaba: TomÃ¡s GÃ³mez GascÃ³n, ConcepciÃ³n Vargas-Machuca CabaÃ±ero, MÂª Isabel GutiÃ©rrez SÃ¡nchez, MÂª Angeles FernÃ¡ndez Abad, Margarita Beltejar RodrÃguez, Javier MartÃnez Suberviola, Miguel Angel Real PÃ©rez, Carmen Coello AlarcÃ³n, Carlos San AndrÃ©s Pascua, JosÃ© Antonio Granados Garrido. HC General Ricardos: Santiago MachÃn Hamalainen, Raquel Mateo FernÃ¡ndez, Cristina de la CÃ¡mara Gonzalez, JosÃ© D.GarcÃ©s Ranz, AsunciÃ³n Prieto Orzanco, MÂª Teresa MarÃn Becerra, Paulino Cubero GonzÃ¡lez, Francisco R. AbellÃ¡n LÃ³pez, Olga Ã�lvarez Montes, Mercedes Canellas Manrique, MÂª JosÃ© San Telesforo Navarro, MÂª Mercedes Parrilla Laso, MÂª Ã�ngeles Aragoneses CaÃ±as, Angela AuÃ±Ã³n Muelas HC Los YÃ©benes, Esther ValdÃ©s Cruz, Consuelo Mayoral Lopez, Teresa Gijon Seco, Francisca Martinez Vallejo. HC Valle InclÃ¡n: Ana Isabel MenÃ©ndez FernÃ¡ndez, MÂª del Mar De la PeÃ±a GonzÃ¡lez, MÂª Ã�ngeles Maroto GarcÃa, MarÃa SÃ¡nchez CristÃ³bal. HC LavapiÃ©s: MÂª Carmen Ã�lvarez Orviz, JesÃºs Herrero HernÃ¡ndez, MÂª Veredas GonzÃ¡lez MÃ¡rquez, MÂª JesÃºs LÃ³pez RodrÃguez, MÂª de las Maravillas Almarza GarcÃa, MÂª Teresa San Clemente Pastor, MÂª Ã�mparo Corral Rubio. HC Colmenar Viejo Norte: Gonzalo Ruiz Zurita, Ã�ngela Allue Bergua, Marta Cabrera Orozco, MÂª del Puerto De Antonio GarcÃa, Ana Isabel Cerezo Diviu, Inmaculada Solsons Roig, Pilar GÃ³mez de Abia. HC Fuentelarreina: MarÃa ConcepciÃ³n DÃaz Laso, MÂª Luisa Asensio Ruiz, Carmen Siguero PÃ©rez. HC PresentaciÃ³n Sabio: Antonio Molina Siguero, Inmaculada Cerrada Puri, Paloma RodrÃguez Almagro, Rosa Rosanes GonzÃ¡lez, MÂª Carmen PÃ©rez GarcÃa. HC Cuzco: Mar Noguerol Ã�lvarez, MÂª Ã�ngeles de Miguel Abanto, MÂª Lourdes Reyes MartÃnez, Pilar GutiÃ©rrez ValentÃn, Jorge GÃ³mez Ciriano, Raquel Calzada Benito, Carolina Torrijos Bravo, David Ferreiro GonzÃ¡lez, Judit LeÃ³n GonzÃ¡lez. HC San MartÃn de Valdeiglesias: Nuria TomÃ¡s GarcÃa, Alberto AlcalÃ¡ FaÃºndez, Eva FernÃ¡ndez LÃ³pez, InÃ©s Melero Redondo, Ricardo GonzÃ¡lez GascÃ³n. HC Pedroches: Jeannet SÃ¡nchez YÃ©pez, Mercedes del Pilar FernÃ¡ndez GirÃ³n, Beatriz LÃ³pez Serrano, MÂª Teresa RodrÃguez Monje, Paloma Morso Pelaez, MarÃa Cortes Duran, Carolina LÃ³pez Olmeda, Almudena GarcÃa- Uceda Sevilla, Dolores Serrano GonzÃ¡lez, Inmaculada SantamarÃa LÃ³pez. HC MendiguchÃa Carriche: Francisca GarcÃa De Blas GonzÃ¡lez, Alberto LÃ³pez GarcÃa-Franco, Amaya Azcoaga Lorenzo, Mar Ã�lvarez Villalba, BelÃ©n Pose GarcÃa. HC Santa Isabel: Rosa FernÃ¡ndez GarcÃa, Francisco de Alba GÃ³mez, Antonio Redondo Horcajo, Beatriz Pajuelo MÃ¡rquez, JosÃ© Luis Gala Paniagua, EncarnaciÃ³n Cidoncha CalderÃ³n, Ã�ngel Delgado Delgado, MÂª JesÃºs GÃ³mez MartÃn, JosÃ© Francisco Ã�vila Tomas. HC El Greco: JosÃ© Enrique MariÃ±o SuÃ¡rez, JosÃ© Luis Quintana GÃ³mez, JosÃ© Antonio GonzÃ¡lez-Posada Delgado, Enrique Revilla Pascual, Esperanza Duralde RodrÃguez, Milagros Beamud Lagos. HC Arroyo de la Media Legua: Leonor GonzÃ¡lez GalÃ¡n, MarÃa Verdugo Rosado, Luis Nistal MartÃn de Serranos, MÂª JesÃºs LÃ³pez Barroso, Mariano Rivera Moreno, Margarita Torres Parras, MÂª Reyes Delgado Pulpon, Elena AlcalÃ¡ Llorente. HC Federica Montseny: Sonsoles MuÃ±oz Moreno, Ana MarÃa Ribao Verdugo, MarÃa JesÃºs Fidalgo Baz, Isabel Vaquero TuriÃ±o, Ana MarÃa JeÃº Fidalgo Baz, Clementa Sanz Sanchez, Ana MarÃa SÃ¡nchez Sempere, Javier MartÃnez Sanz, MarÃa Isabel Arratibel Elizondo. HC Buenos Aires: Paloma GonzÃ¡lez Escobar, Javier MuÃ±oz GutiÃ©rrez, Raquel BaÃ±os Morras, Carmen Molins Santos, Ana MarÃa Ibarra SÃ¡nchez, Cecilio GÃ³mez AlmodÃ³var, Cristina Cassinello Espinosa.Ministerio de Sanidad, PolÃtica Social e Igualdad, Spain  and by CAIBER - Spanish Clinical Research Network. The authors thank the following persons for their contributions to this work: Dolores Otero-Criado, Carlos Carvajales FernÃ¡ndez, Rosa Zurdo-Baz and Raisa GonzÃ¡lez-PÃ©rez.This study was funded by the The pre-publication history for this paper can be accessed here:http://www.biomedcentral.com/1471-2458/12/394/prepub


The asymmetric unit further contains one 4-methoxybenzoate anion, one nicotinamide (NA) ligand and one coordinated and one uncoordinated water molecule; all ligands are monodentate. The four O atoms in the equatorial plane around the NiII ion form a slightly distorted square-planar arrangement, while the slightly distorted octahedral coordination is completed by the two pyridine N atoms of the NA ligands in the axial positions. The dihedral angle between the carboxylate group and the attached benzene ring is 7.2 (1)°, while the pyridine and benzene rings are oriented at a dihedral angle of 72.80 (4)°. An intramolecular O—H⋯O hydrogen bond links the uncoordinated water molecule to one of the carboxylate groups. In the crystal structure, intermolecular O—H⋯O, N—H⋯O and C—H⋯O hydrogen bonds link the molecules into a three-dimensional network.In the mononuclear title compound, [Ni(C N,N-diethylnicotinamide, see: Bigoli et al. 2(C6H6N2O)2(H2O)2]·2H2O = 0.026                           wR(F                           2) = 0.067                           S = 1.04                           3740 reflections228 parametersH atoms treated by a mixture of independent and constrained refinementmax = 0.41 e Å−3                        Δρmin = −0.32 e Å−3                        Δρ                                 APEX2  used to solve structure: SHELXS97 (Sheldrick, 2008SHELXL97 (Sheldrick, 2008ORTEP-3 for Windows (Farrugia, 1997WinGX (Farrugia, 1999PLATON (Spek, 2009Data collection: 10.1107/S1600536810025985/ci5126sup1.cif            Crystal structure: contains datablocks I, global. DOI: 10.1107/S1600536810025985/ci5126Isup2.hkl            Structure factors: contains datablocks I. DOI:  crystallographic information; 3D view; checkCIF report            Additional supplementary materials:


The two pyridine rings in L form a dihedral angle of 50.0 (2)°. L ligands bridge adjacent HgCl2 units into polymeric chains propagating in [010]. The crystal packing is further stabilized by weak intermolecular C—H⋯Cl hydrogen bonds and π–π interactions between the pyridine rings, with a centroid–centroid separation of 3.529 (9) Å.In the title coordination polymer, [HgCl DOI: 10.1107/S1600536812035775/cv5327Isup2.hklStructure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF reportAdditional supplementary materials:


The small deviations from the ideal tetrahedral geometry around the P atoms are illustrated by C—P—C angles ranging from 104.08 (9) to 106.46 (9)°. In the crystal, the molecules are linked by weak C—H⋯F, C—H⋯O and C—H⋯π interactions.In the title compound, [Ir(C DOI: 10.1107/S1600536812035593/hb6932Isup2.hklStructure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF reportAdditional supplementary materials:


IV atom in the centrosymmetric title complex, [Sn2(CH3)4(NCS)2(OH)2], adopts a distorted trigonal–bipyramidal coordination environment defined by two methyl C atoms and one bridging hydroxide group in the equatorial plane while the other bridging hydroxide group and the N atom of the thiocyanate anion are in the apical >positions. The dinuclear species are linked through O—H⋯S and C—H⋯ S hydrogen-bonding interactions into a three-dimensional network.The Sn For str al. 2007; Ng 4(NCS)2(OH)2] = 0.026wR(F2) = 0.056S = 1.111603 reflections71 parameters1 restraintH atoms treated by a mixture of independent and constrained refinementmax = 1.06 e Å−3Δρmin = −0.64 e Å−3ΔρCOLLECT  used to solve structure: SIR97  I, global. DOI: Click here for additional data file.10.1107/S1600536812043462/wm2689Isup2.hklStructure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF reportAdditional supplementary materials:


II ion in the title complex, [Pd(NCS)2(C14H10N4)], is four-coordinated in a distorted square-planar environment by the two pyridine N atoms of the chelating 2,3-di-2-pyridylpyrazine (dpp) ligand and two S atoms from two thiocyanate anions. The pyridine rings are considerably inclined to the least-squares plane of the PdS2N2 unit [maximum deviation = 0.027 (1) Å], making dihedral angles of 70.3 (2) and 69.2 (1)°. The pyrazine ring is almost perpendicular to the PdS2N2 plane, with a dihedral angle of 86.3 (1)°. The thiocyanate ligands are located on opposite sides of the PdS2N2 unit plane and are almost linear [N—C—S angles = 177.8 (6) and 178.9 (6)°]. The complex molecules are stacked in columns along the b axis and are connected by intermolecular C—H⋯N hydrogen bonds, forming chains along the a axis.The Pd X2(dpp)] , see: Ha ] = 0.046wR(F2) = 0.100S = 1.003247 reflections226 parametersH-atom parameters constrainedmax = 0.89 e Å−3Δρmin = −0.66 e Å−3ΔρSMART  used to solve structure: SHELXS97  global. DOI:  crystallographic information; 3D view; checkCIF reportAdditional supplementary materials:


II complex, [Cd2(C7H5O4)4(C12H8N2)2(H2O)2], the CdII cation is coordinated by a bidentate phenanthroline (phen) ligand, three dihydroxybenzoate (dhba) anions and one water molecule in a distorted CdN2O4 octahedral geometry. Among the dhba anions, two anions bridge two CdII cations to form the dimeric complex with significant different Cd—O bond distances of 2.2215 (19) and 2.406 (2) Å. The centroid–centroid distance of 3.4615 (19) Å between two nearly parallel benzene rings of the dhba and phen ligands coordinating to the same CdII cation indicates the existence of intramolecular π–π stacking in the complex. Extensive O—H⋯O hydrogen bonding and intermolecular weak C—H⋯O hydrogen bonding help to stabilize the crystal structure. One hydroxy group of the monodentate dhba ligand is disordered over two sites with a site-occupancy ratio of 0.9:0.1.In the title centrosymmetric dimeric Cd DOI: 10.1107/S1600536810021252/ng2775Isup2.hkl            Structure factors: contains datablocks I. DOI:  crystallographic information; 3D view; checkCIF report            Additional supplementary materials:


The –C CH and the chlorine ligands are disordered over two equivalent positions (0.5 occupancy each). The coordination geometry is distorted octahedral, with the –C CH fragment and the Cl ligand in trans positions. The four P atoms occupy the equatorial plane of the octahedron and the chloride and acetylide ligands the axial positions.The molecular structure of the title compound,  Cl(C26H24P2)2] = 0.030wR(F2) = 0.072S = 1.096470 reflections293 parametersH-atom parameters constrainedmax = 0.49 e Å−3Δρmin = −0.48 e Å−3ΔρCrysAlis PRO  used to solve structure: SHELXS97  global, I. DOI: Click here for additional data file.10.1107/S1600536812044558/bg2483Isup2.hklStructure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF reportAdditional supplementary materials:


The asymmetric unit contains two complex cations, two hexafluoridophosphate anions and one uncoordinated water molecule. In one of the hexafluoridophosphate anions, four of the F aroms are disordered over two sets of sites in a 0.632 (11):0.368 (11) ratio. In the crystal, the cations, anions and water molecules are connected by O—H⋯O and O—H⋯F hydrogen bonds. π–π interactions are present between the pyridine rings [centroid–centroid distance = 3.814 (1) Å].In the title complex, [Co(C DOI: 10.1107/S1600536811023270/hy2438Isup2.hkl            Structure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF report            Additional supplementary materials:


The crystal packing exhibits weak intermolecular Cl⋯Cl contacts of 3.279 (4) Å, π–π interactions between the substituted Cp rings of two neighbouring 2-chloro-1-ferrocenylethanone molecules [centroid–centroid distance = 3.534 (3) Å], and weak intermolecular C—H⋯O and C—H⋯Cl hydrogen bonds. In the title co-crystal, [Fe(C DOI: 10.1107/S1600536811038244/cv5144Isup2.hkl            Structure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF report            Additional supplementary materials:


Each paddle-wheel unit is joined to four such neighbours through bridging dicarboxylate ligands, producing a two-dimensional undulating layer parallel to (-101). Adjacent sheets are stacked in a parallel fashion to form a three-dimensional supramolecular structure which is stabilized by interlayer π–π interactions between benzene rings, with a centroid–centroid distance of 3.722 Å. The range of Zn—O bond lengths is 2.0440 (17)–2.1256 (15) Å and the Zn—Cl bond length is 2.2622 (6) Å.The title compound, [Zn(C Cl] = 0.027wR(F2) = 0.078S = 1.072640 reflections181 parametersH-atom parameters constrainedmax = 0.45 e Å−3Δρmin = −0.45 e Å−3ΔρSMART  used to solve structure: SHELXS97  I, global. DOI: 10.1107/S1600536812020077/bg2452Isup2.hklStructure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF reportAdditional supplementary materials:


The thiophene rings form different dihedral angles [40.15 (9) and 15.43 (10)°] with the pyrazine ring. A strong π–π stacking interaction occurs between adjacent pyrazinephenanthroline units with an interplanar distance of 3.4352 (16) Å.The molecule of the title compound, C DOI: 10.1107/S160053681201522X/aa2049Isup2.hklStructure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF reportAdditional supplementary materials:


The MnII atom is coordinated by four N atoms [Mn—N = 2.2168 (14) and 2.2407 (14) Å] from two 2,2′-biimidazole ligands and two water molecules [Mn—O = 2.2521 (14) Å] in a distorted octahedral geometry. Intermolecular N—H⋯O and O—H⋯O hydrogen bonds consolidate the crystal packing, which also exhibits π–π interactions between five-membered rings, with a centroid–centroid distance of 3.409 (2) Å.The asymmetric unit of the title compound, [Mn(C DOI: 10.1107/S160053681202199X/cv5293Isup2.hklStructure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF reportAdditional supplementary materials:


The 2,2′-bipyridine molecule is slightly twisted with a dihedral angle between the pyridine rings of 7.35 (12)°. Intramolecular C—H⋯S hydrogen bonds are present. In the crystal, molecules are stacked along the c axis by π–π interactions, with centroid–centroid distances of 3.6021 (15) and 3.6401 (16) Å. The crystal structure also features weak C—H⋯π interactions.In the title benzene-solvated heteroleptic lithium complex, [Li(C DOI: Click here for additional data file.10.1107/S160053681300456X/rz5044Isup2.hklStructure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF reportAdditional supplementary materials:


The CuII atoms are linked by the bridging ligands into a layer parallel to (101). The presence of intralayer O—H⋯O hydrogen bonds and π–π interactions between the pyridine and benzene rings [centroid–centroid distances = 3.808 (2) and 3.927 (2) Å] stabilizes the layer. Further O—H⋯O hydrogen bonds link the layers and the dimethylformamide solvent molecules.In the title compound, {[Cu(C DOI: Click here for additional data file.10.1107/S1600536813006430/hy2619Isup2.hklStructure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF reportAdditional supplementary materials:


The product contains an unusual six-membered thiolate–carboxylate chelate ring. This slightly distorted octahedral complex exhibits cis angles ranging from 77.55 (11) to 97.30 (8)° due to the presence of the thiolate–carboxylate chelate ring and the constrained bipyridine group. The crystal packing appears to be controlled by a combination of π-stacking [centroid–centroid distance = 3.611 (2) Å] and C—H⋯O interactions.The title complex, [Pt(CH DOI: 10.1107/S1600536811013626/tk2735Isup2.hkl            Structure factors: contains datablocks I. DOI:  crystallographic information; 3D view; checkCIF report            Additional supplementary materials:


In the crystal, molecules are linked by intermolecular O—H⋯O hydrogen bonds into chains along [100]. These chains are further linked by weak π–π interactions with centroid–centroid distances in the range of 3.609 (2)–3.758 (1) Å, forming a three-dimensional supramolecular network.In the title centrosymmetric tetranuclear complex, [Mn DOI: 10.1107/S1600536810049433/lh5168Isup2.hkl            Structure factors: contains datablocks I. DOI:  crystallographic information; 3D view; checkCIF report            Additional supplementary materials:


The AgI ion exhibits a slightly distorted tetrahedral coordination geometry formed by a P atom from a triphenylphosphane ligand, two metal-bridging S atoms from thiosemicabazide ligands and one chloride ion. The S atoms bridge two symmetry-related AgI ions, forming a strictly planar Ag2S2 core with an Ag⋯Ag separation of 2.7802 (7) Å. There is an intramolecular N—H⋯Cl hydrogen bond. In the crystal, N—H⋯Cl and N—H⋯S hydrogen bonds link complex molecules, forming layers parallel to (001). These layers are connected through π–π stacking interactions [centroid–centroid distance = 3.665 (2) Å], leading to the formation of a three-dimensional network.The dinuclear title complex, [Ag For pot al. 1999; Wujec e al. 2009; Mohareb al. 2009; He et a al. 2012. For exa al. 2012; Lobana  al. 2008.2Cl2(CH5N3S)2(C18H15P)2] = 0.026wR(F2) = 0.069S = 1.065026 reflections251 parameters5 restraintsH atoms treated by a mixture of independent and constrained refinementmax = 0.38 e Å−3Δρmin = −0.55 e Å−3ΔρSMART  used to solve structure: SHELXS97  I, global. DOI: Click here for additional data file.10.1107/S1600536812051562/lh5573Isup2.hklStructure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF reportAdditional supplementary materials:


The dihedral angle between the central benzene ring and each of the two symmetry-related outer benzene rings is 5.1 (2)°. The crystal structure is stabilized by intermolecular π–π interactions with centroid–centroid distances in the range 3.466 (2)–3.6431 (16) Å.In the title complex, [Cu(C DOI: 10.1107/S1600536810042789/lh5150Isup2.hkl            Structure factors: contains datablocks I. DOI:  crystallographic information; 3D view; checkCIF report            Additional supplementary materials:


Within the mononuclear complex molecule, intramolecular π–π stacking interactions are observed, the first between a coordinated phen molecule and a DHB ligand [centroid–centroid distance = 3.7291 (16) Å], and the second between a coordinated phen molecule and an uncoordinated phen ligand [centroid–centroid distance = 3.933 (2) Å]. Intermolecular π–π stacking is observed between adjacent complexes [interplanar distance = 3.461 (3) Å]. Intra- and intermolecular O—H⋯O hydrogen bonds are observed in the DHB ligands and between a water molecule and DHB ligands, respectively. O—H⋯N hydrogen bonds are also observed in the DHB ligands and between uncoordinated phen molecules and aqua ligands.In the title compound, [La(C DOI: 10.1107/S1600536810047318/vm2058Isup2.hkl            Structure factors: contains datablocks I. DOI:  crystallographic information; 3D view; checkCIF report            Additional supplementary materials:


The Bi—O bond lengths are 2.283 (3) and 2.309 (2) Å, but as a result of additional long Bi⋯O interactions [2.787 (3) and 2.734 (3) Å], one of the C—Bi—C angles is 148.62 (13)°. In the crystal, weak C—H⋯O hydrogen bonds connect pairs of molecules into inversion dimers. These dimers are further connected by weak C—H⋯π interactions into chains along [100] .In the title molecule, [Bi(C DOI: Click here for additional data file.10.1107/S1600536813013317/lh5612Isup2.hklStructure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF reportAdditional supplementary materials:


The independent Fe2S2 fragment [Fe—Fe = 2.527 (1) Å] is in a butterfly conformation, and each Fe atom displays a pseudo-square-pyramidal coordination geometry. The phosphane group occupies an apical position [Fe—P = 2.2670 (14) Å]. In the crystal, weak intermolecular C—H⋯O hydrogen bonds link the molecules into chains along [110]. In the title compound, [Fe DOI: 10.1107/S160053681105584X/cv5221Isup2.hklStructure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF reportAdditional supplementary materials:


The CuII ion and the water O atom lie on a twofold axis. The CuII ion exhibits a six-coordinate distorted octahedral geometry, with two N atoms from the bipy ligand [Cu—N = 1.9996 (16) Å] and four O atoms from two 3-methoxybenzoate ligands [Cu—O = 1.9551 (15) and 2.6016 (16) Å]. The molecules are linked by O—H⋯O and C—H⋯O hydrogen bonds, forming a three-dimensional network.The title compound, [Cu(C DOI: 10.1107/S1600536811005563/rn2078Isup2.hkl            Structure factors: contains datablocks I. DOI:  crystallographic information; 3D view; checkCIF report            Additional supplementary materials:


It has an E conformation with respect to the azomethine double bond and a Z conformation about the amide C=N bond. The CuII atom has a slightly distorted square-pyramidal coordination geometry. The crystal packing involves intermolecular C—H⋯O, C—H⋯N and C—H⋯π and two types of π–π interactions, with centroid–centroid distances of 3.9958 (10) and 3.7016 (13) Å.The binuclear molecule of the title compound, [Cu DOI: 10.1107/S1600536812031467/fj2577Isup2.hklStructure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF reportAdditional supplementary materials:


The [Co(CN)6]3− anion exhibits an octahedral geometry. In the structure, cations and anions are linked alternatively through O—H⋯O, O—H⋯N, N—H⋯O and N—H⋯N hydrogen bonds, π–π interactions [centroid–centroid distances = 3.523 (2)–4.099 (2) Å] and van der Waals forces, forming a three-dimensional supramolecular network.The structure of the title compound, (C DOI: Click here for additional data file.10.1107/S1600536813003632/rz5042Isup2.hklStructure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF reportAdditional supplementary materials:


III compound, {[Sm(C9H7O3)3(H2O)]·H2O}n, was obtained under hydrothermal conditions. Its structure is isotypic with the analogous Eu complex. The latter was reported incorrectly in space group P1 by Yan et al. . This was corrected by Marsh  to P-1. The SmIII ion is nine-coordinated by O atoms from one coordinating water molecule and the remaining ones from the 3-(3-hydroxyphenyl)prop-2-enoatate anions , leading to a distorted tricapped trigonal–prismatic coordination polyhedron surrounded by solvent water molecules. In the crystal, extensive intermolecular O—H⋯O hydrogen-bonding interactions and π–π interactions [centroid–centroid separation = 3.9393 (1) Å] lead to the formation of a three-dimensional supramolecular network.The title Sm DOI: 10.1107/S1600536812013724/zj2052Isup2.hklStructure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF reportAdditional supplementary materials:


N. The proposed method has an O(N3 · Multiplication(N) + N4) preprocessing time, after which a binomial coefficient C with 0 ≤ Q ≤ P ≤ 2N − 1 can be computed modulo 2N in O(N2 · log(N) · Multiplication(N)) time. Multiplication(N) denotes the time complexity of multiplying two N-bit numbers, which can range from O(N2) to O(N · log(N) · log(log(N))) or better. Thus, theoverall time complexity for evaluating M binomial coefficients C modulo 2N with 0 ≤ Q ≤ P ≤ 2N − 1 is O((N3 + M · N2 · log(N)) · Multiplication(N) + N4). After preprocessing, we can actually compute binomial coefficients modulo any 2R with R ≤ N. For larger values of P and Q, variationsof Lucas' theorem must be used first in order to reduce the computation tothe evaluation of multiple (O(log(P))) binomial coefficients C  modulo 2N with 0 ≤ Q′ ≤ P′ ≤ 2N − 1.I present a new algorithm for computing binomial coefficients modulo 2 N  (N ≥ 1). The definition of the binomial coefficient C is the usual one:In this paper I present a novel efficient algorithm for computing binomial coefficients modulo 2P ≤ 2N − 1, and after fully handling this case, we will discuss how to compute C modulo 2N for P ≥ 2N.We will mainly consider the case where O(N3 · Multiplication(N) + N4) time, where Multiplication(N) is the time complexity for multiplying two N-bit numbers. Multiplication(N) can range from O(N2)  to O(N · log(N) · log(log(N))) or slightly better . FFODD will be equal to the product (modulo  2N) of all the odd numbers from the interval . Thus, we will haveWe will first evaluate FODD is easy to compute. If Q(1) = 0, then FFODD = 1; otherwise it is equal to SOSP(Q(1), 0).FFODD(i > 1. Let X(i) be equal to 2Q(1) + ⋯+2Q(i−1). If Q(i) = 0, then FFODD = (X(i) + 1) mod 2N. Otherwise we can write FFODD asLet us consider now the case By using Newton's binomial theorem, we can rewrite  as(27)∑j up to min{2Q(i)−1, N − 1}, because for j ≥ N, the corresponding term of the sum is zero modulo 2N. We should also notice that SSP(Q(i) − 1, j) is multiplied by 2j. Since its precision is larger than N − j, the multiplication of SSP(Q(i) − 1, j) and 2j is exact modulo 2N. Then we iterate with j in descending order. For the initial value of j, we compute XP(i) = (X(i)−1)j; for the other values, we only multiply XP(i) by (X(i)−1)−1 in order to obtain XP(i) as (X(i)−1)j. We now have an algorithm performing O(N) multiplications of N-bit numbers for computing FFODD. Overall, we have an algorithm performing O(N2) multiplications of N-bit numbers for computing FODD(P) (O(N) multiplications for each of the O(N) bits of P). However, we can do better by rewriting  is even. In fact, it is a multiple of 2Q(i−1), meaning that it is at least a multiple of 2Q(i)+1. For j > (N/(Q(i) + 1)), each term of the sum will be zero modulo 2N. Thus, we only need to consider at most N/(Q(i) + 1) + 1 terms (from j = 0 to j = N/(Q(i) + 1)). We will start with XP(i) = 1 when j = 0, and then for each subsequent value of j, we will multiply XP(i) by X(i) in order to have XP(i) = X(i)j at each iteration.Note that O(N · log(N)) terms for computing FODD(P)(O(N + N/(Q(2) + 1) + N/(Q(3) + 1)+⋯+N/(Q(K) + 1))); for each such term, an N-bit multiplication needs to be performed.Overall we only need to consider P), we can use it in order to write F2(P > 1) asNow that we have a method of efficiently computing FODD(F2(0 ≤ P ≤ 1) is equal to 1. Since P is of the order of magnitude of 2N and FODD(P) can be evaluated with O(N · log(N))  N-bit multiplications, computing F2(P) will require O(N2 · log(N))  N-bit multiplications, obtaining an O(N2 · log(N) · Multiplication (N)) time complexity.C with 0 ≤ Q ≤ P ≤ 2N − 1. In order to evaluate it modulo 2N we will first need to compute F2(P), F2(Q), and F2(P − Q). Then, we will need to find the largest exponent exp(X) such that 2X)exp  N-bit multiplications. Computing exp(X) where X ≤ 2N − 1 can be performed in O(N2) time (O(N) bit shifts to the right and O(N)  N-bit number additions). Thus, the time complexity for computing the binomial coefficient modulo 2N is dominated by the computation of F2(P), F2(Q), and F2(P − Q).As discussed earlier, the multiplicative inverse of an odd number by using , using OC modulo 2N for P ≥ 2N (and 0 ≤ Q ≤ P), we need to make use of some variations of Lucas' theorem [P = P1 · 2N + P0 and Q = Q1 · 2N + Q0, then, according to [In order to compute a binomial coefficient  theorem . If P = rding to , we haveC modulo 2N, we will need to evaluate O(log(P)) binomial coefficients C, where 0 ≤ Q′, P′ ≤ 2N − 1. After the O(N3 · Multiplication(N)) preprocessing stage, evaluating C modulo 2N will take only O(N2 · log(N) · log(P) · Multiplication(N) + log2(P)) time (the log2(P) factor appears when P ≥ 2N because we need to perform O(log(P)) divisions, each of which takes O(log(P)) time because they can be implemented by shifting bits to the right, in order to obtain the O(log(P)) binomial coefficients or factorials which are needed in order to compute C modulo 2N).Thus, in order to compute C modulo 2N (for P ≥ 2N) to the computation of multiple (O(log(P))) factorials P′! (of a restricted type) with P′ ≤ 2N − 1 were presented in [Other methods for reducing the computation of ented in .C modulo R, where R is a prime number. The computation of C is reduced to the computation of multiple (O(log(P))) binomial coefficients C modulo R, with 0 ≤ Q′ ≤ P′ ≤ R − 1. In [M is to evaluate them modulo the  prime powers which are divisors of M and then use the Chinese Remained Theorem [M , but inerved in  a more derved in .O(log2(P) + v4 · log(P) · log(u) + v4 · u · log3(u)) time for computing C modulo uv, where u is a prime number  + N4 · log(P) + N4). If we consider Multiplication(N) = O(N2), our algorithm takes O(N5) time for preprocessing and O(N4 · log(N) · log(P) + log2(P)) in order to compute C in the general case. These time complexities are slightly worse than the ones obtained in [N) = O(N · log(N) · log(log(N))) [O(N4 · log(N) · log(log(N))) time complexity for the preprocessing stage and an O(N3 · log2(N) · log(log(N)) · log(P) + log2(P)) time complexity for actually computing the binomial coefficient modulo 2N. In this case our time complexities are slightly better than the ones presented in [P) > log(N) · log(log(N))). However, it is not clear which time complexity for the multiplication of two N-bit numbers was considered in [An algorithm for computing binomial coefficients modulo prime powers (for any prime) was presented in . The algtated in , but a sained in . Howeverog(N))) , 2, we oented in  .In this paper I presented a novel efficient algorithm for computing binomial coefficients modulo 2The time complexity of the presented algorithm is comparable with that of state-of-the-art algorithms for computing binomial coefficients modulo prime powers . In factN . If the values SSP defined in P, Q) values in a more efficient manner.When computing a small number of binomial coefficients , the bottleneck of the algorithm (in the preprocessing stage) consists of the computation of sums of products of elements of subsets having sizes 0 to


The dimethylamino groups are orientated at 41.80 (7) and 36.43 (7)° with respect to the borazine ring. The nitrooxy group is almost normal to the borazine ring [dihedral angle = 85.33 (14)°]. The methyl C atom trans to the NO3 group is displaced by −0.512 (3) Å from the ring plane, whereas the two ortho-methyl C atoms are displaced by 0.239 (3) and 0.178 (3) Å.In the title compound, C DOI: Click here for additional data file.10.1107/S1600536813007484/hb7055Isup2.hklStructure factors: contains datablock(s) I. DOI: Click here for additional data file.10.1107/S1600536813007484/hb7055Isup3.cmlSupplementary material file. DOI:  crystallographic information; 3D view; checkCIF reportAdditional supplementary materials:


The mean bond lengths in the biferrocene unit are Fe—C = 2.048 (10) Å and C—C = 1.427 (8) Å within the cyclopentadienyl rings. The B—N bond lengths of the BH3 protected amine is 1.631 (3) Å. The interplanar angle between the two connected cyclopentadienyl rings is 54.29 (8)° and the corresponding Fe—Cg—Cg—Fe torsion angle is −52.5°. The conformation of the molecule is stabilized by an intramolecular C—H⋯Br interaction.The title structure, [Fe DOI: 10.1107/S1600536811049270/bq2322Isup2.hkl            Structure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF report            Additional supplementary materials:


The crystal packing is controlled by C—H⋯O hydrogen bonding and π–π stacking interactions involving the benzene rings, with a centroid–centroid distance of 3.4220 (1) Å.In the title compound, (C DOI: 10.1107/S160053681002893X/pv2307Isup2.hkl            Structure factors: contains datablocks I. DOI:  crystallographic information; 3D view; checkCIF report            Additional supplementary materials:


The amide group is almost perpendicular to the plane of the substituted Cp ring, with a C—N—C—C torsion angle of 101.3 (2)°, and the N and O atoms in the ethanoyl group are coplanar, with a C—N—C—O torsion angle of −0.7 (3)°. Weak C—H⋯O hydrogen bonds link adjacent molecules.In the title compound, [Fe(C DOI: 10.1107/S1600536812016303/hy2528Isup2.hklStructure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF reportAdditional supplementary materials:


The four O atoms in the equatorial plane around the NiII cation form a slightly distorted square-planar arrangement, while the slightly distorted octahedral coordination is completed by the two N atoms of the NA ligands in the axial positions. The dihedral angle between the carboxylate group and the adjacent benzene ring is 23.67 (8)°, while the pyridine and benzene rings are oriented at an angle of 89.04 (4)°. The coordinating water molecule links with the carboxylate group via an O—H⋯O hydrogen bond. In the crystal, N—H⋯O, O—H⋯O and weak C—H⋯O hydrogen bonds link the molecules into a three-dimensional supramolecular network. π–π contacts between benzene rings [centroid–centroid distance = 3.8414 (7) Å] may further stabilize the structure. A weak C—H⋯π interaction also occurs.In the title complex, [Ni(C N,N-diethylnicotinamide, see: Bigoli et al. 2(C6H6N2O)2(H2O)2] = 0.023wR(F2) = 0.063S = 1.073492 reflections216 parametersH atoms treated by a mixture of independent and constrained refinementmax = 0.40 e Å−3Δρmin = −0.42 e Å−3ΔρAPEX2  used to solve structure: SHELXS97  I, global. DOI: 10.1107/S1600536812026943/xu5564Isup2.hklStructure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF reportAdditional supplementary materials:


In the crystal, there are no hydrogen bonds  present, and only very weak π–π interactions  are observed [centroid–centroid distance = 3.985 (4) Å], which connect neighbouring tetranuclear units into a chain motif along the b axis.In the title centrosymmetric tetranuclear complex, [Cu DOI: 10.1107/S1600536811026468/su2284Isup2.hkl            Structure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF report            Additional supplementary materials:


II atom in the title salt, [Cu(C10H24N4)(H2O)2][CH3(CH2)5CO2]2·2H2O, is chelated by the four N atoms of the 1,4,8,11-tetraazacyclotetradecane (cyclam) ligand and is coordinated by two water molecules in a tetragonally Jahn–Teller-distorted octahedral geometry. The CuII atom lies on a center of inversion. The cations, anions and uncoordinated water molecules are linked by N—H⋯O and O—H⋯O hydrogen bonds, forming a layer structure parallel to (100). The alkyl chain of the anion is disordered over two positions in a 0.82 (1):0.18 (1) ratio.The Cu DOI: 10.1107/S1600536810025687/bt5285Isup2.hkl            Structure factors: contains datablocks I. DOI:  crystallographic information; 3D view; checkCIF report            Additional supplementary materials:


In each complex molecule, the Cu atom is O,N,O′-chelated by the tridentate Schiff base ligand and N,N′-chelated by the 1,10-phenanthroline ligand in a distorted square-pyramidal geometry. The Cu—N bond distances in the apical directions are 2.298 (4) and 2.268 (4) Å. In the crystal, intermolecular O—H⋯O and C—H⋯O hydrogen bonds together with C—H⋯π interactions result in a three-dimensional supramolecular structure.The asymmetric unit of the title complex, [Cu(C DOI: 10.1107/S160053681004554X/xu5077Isup2.hkl            Structure factors: contains datablocks I. DOI:  crystallographic information; 3D view; checkCIF report            Additional supplementary materials:


The CuII atom is located about an inversion centre. The molecule consists of three planar units , adopting a staircase-like structure. The six-membered metallocycles have a sofa conformation with the Cu atom out of the plane of the 1,3,5-triazapentadienyl ligands by 0.246 (5) Å. The ipso-C atoms of the CCl3 substituents are slightly out of the 1,3,5-triazapentadienyl planes by 0.149 (6) and −0.106 (6) Å. The CCl3 groups of each 1,3,5-triazapentadienyl ligand are practically in the energetically favourable mutually eclipsed conformation. In the crystal, the molecules are packed in stacks along the a axis. The molecules in the stacks are held together by two additional axial Cu⋯Cl interactions of 3.354 (2) Å. Taking the axial Cu⋯Cl interactions into account, the CuII atom exhibits a distorted [4 + 2]-octahedral coordination environment. The stacks are bound to each other by weak intermolecular attractive Cl⋯Cl [3.505 (2)–3.592 (3) Å] interactions.The title compound, [Cu(C DOI: 10.1107/S1600536812036124/aa2069Isup2.hklStructure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF reportAdditional supplementary materials:


The molecule is located about a twofold rotation axis. The coordination environment of the SnIV atom is a distorted octahedron, with two bidentate 2-pyridineselenolate ligands inclined to each other at an angle of 83.96 (7)°. The two Sn—Cl and two Sn—N bonds are in cis configurations, while the two Sn—Se bonds of 2.5917 (3) Å are in a trans configuration, with an Se—Sn—Se angle of 157.988 (15)°. In the crystal, π–π interactions between the pyridine rings [centroid-to-centroid distance of 3.758 (3) Å] and weak intermolecular C—H⋯Cl hydrogen bonds link the molecules into chains along the c axis.The title compound, [SnCl DOI: 10.1107/S1600536813014657/cv5413Isup2.hklStructure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF reportAdditional supplementary materials:


Each AgI ion is coordinated by two N atoms from two bridging bipy ligands, forming chains along [101]. π–π interactions between the pyridine rings [centroid–centroid distances = 3.638 (8) and 3.688 (8) Å] connect the chains. Intermolecular O—H⋯O hydrogen bonds link the uncoordinated water molecules and the perchlorate anions.In the title compound, {[Ag DOI: 10.1107/S1600536811040153/hy2472Isup2.hkl            Structure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF report            Additional supplementary materials:


One of the two I− anions is disordered over two sets of sites, with refined occupancies of 0.66 (5) and 0.34 (5). The CdII ions are bridged by bmi ligands, leading to the formation of a chain along [001]. Dimethylformamide solvent molecules are located between these chains. Classical N—H⋯O hydrogen bonding between the bmi ligands and the solvent molecules leads to a consolidation of the structure.In the title complex, {[CdI N-heterocyclic ligands, see: Meng et al. ]·C3H7NO = 0.035                           wR(F                           2) = 0.071                           S = 1.15                           3950 reflections218 parametersH-atom parameters constrainedmax = 0.42 e Å−3                        Δρmin = −0.77 e Å−3                        Δρ                                 CrystalClear  used to solve structure: SHELXS97  global, I. DOI: 10.1107/S1600536811050823/wm2569Isup2.hkl            Structure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF report            Additional supplementary materials:


The bond lengths  and angles (C—Fe—Fe and Fe—S—Fe) are within expected ranges. The S⋯S distance [2.9069 (12) Å] and the dihedral angle between two Fe—S—Fe planes [78.5 (3)°] of the butterfly-shaped Fe2S2 core are enlarged compared with related bridged dithiolate diiron analogues. The calculated 4-benzothiazolebenzyl best planes are almost parallel [dihedral angle = 3.7 (7)°].The title compound, [Fe DOI: 10.1107/S1600536812007581/vm2158Isup2.hklStructure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF reportAdditional supplementary materials:


A short Cd⋯N contact [2.890 (3) Å] to the monodentate sulfadiazinate ion also occurs. The dihedral angles between the planes of the aromatic rings of the anions are 86.81 (14) and 68.65 (14)°. The crystal structure features intermolecular N—H⋯O, O—H⋯O and O—H⋯N hydrogen bonds.In the title compound, [Cd(C DOI: 10.1107/S1600536811019635/hb5888Isup2.hkl            Structure factors: contains datablocks I. DOI:  crystallographic information; 3D view; checkCIF report            Additional supplementary materials:


The employed α-diimine opens up, forming a highly asymmetric ammonium that has its protons at one of the N atoms [N—C= 1.264 (4) and 1.516 (4) Å]. One of the C=N double bonds was oxidized to C—N, which is consistent with the bond length of 1.516 (4) Å. Meanwhile SnIV was reduced to SnII. The (SnCl)3− anion is trigonal–pyramidal. In the crystal, molecules are linked by C—H⋯Cl, N—H⋯Cl, N—H⋯N and C—H⋯N bonds. The crystal studied was twinned by pseudo-merohedry.In the title compound, (C DOI: 10.1107/S1600536812014729/hp2032Isup2.hklStructure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF reportAdditional supplementary materials:


The NiII ion is six-coordinated in a distorted octahedral geometry by two N, two O and two S atoms. An intramolecular C—H⋯S hydrogen bond generates an S(6) ring motif. In the crystal, molecules are linked through intermolecular N—H⋯S, N—H⋯O, C—H⋯N, C—H⋯O and C—H⋯S hydrogen bonds into infinite two-dimensional network parallel to the ab plane. The structure is further stablized by weak C—H⋯π interactions. The dimethylformamide solvent molecule is disordered over two sets of sites in a 0.514 (15):0.486 (15) ratio.The asymmetric unit of the title compound, [Ni(C DOI: 10.1107/S1600536812012834/zj2062Isup2.hklStructure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF reportAdditional supplementary materials:


Two O atoms of one bidentate 2-methoxybenzoate ligand are each disordered over two positions, with site-occupancy factors of 0.579 (4) and 0.421 (4). In the crystal, molecules are linked by C—H⋯O hydrogen bonds, forming a two-dimensional network lieing parallel to the bc plane. The crystal packing is further stablized by π–π stacking interactions between the dmphen rings of neighboring molecules, with distances between their parallel dmphen ring planes of 3.517 (3) and 3.610 (3) Å.In the title compound, [Cd(C DOI: 10.1107/S1600536812010835/bg2438Isup2.hklStructure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF reportAdditional supplementary materials:


The asymmetric unit consists of half a Lindquist anion and one [Cu(phen)(PPh3)2]+ cationic complex. In the cation, there are intramolecular π–π interactions [centroid–centroid distances = 3.617 (2) and 3.7272 (18) Å]. This inorganic–organic adduct is connected by C—H⋯O hydrogen bonds, forming a two dimensional network lying in the ab plane. These networks are connected by C—H⋯π interactions into a three-dimensional structure.The title compound, [Cu(C DOI: 10.1107/S1600536812036367/hg5234Isup2.hklStructure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF reportAdditional supplementary materials:


Extensive intermolecular N—H⋯O, N—H⋯N, O—H⋯O and O—H⋯N hydrogen bonds, as well as weak intermolecular C—H⋯N and C—H⋯O interactions occur in the crystal. π–π stacking between between pyrazine rings of coordinating ligands and lattice molecules [centroid–centroid distance = 3.5669 (14) Å] may further stabilize the structure.In the title compound, [Cd(NO DOI: 10.1107/S1600536812028577/xu5577Isup2.hklStructure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF reportAdditional supplementary materials:


Fe—O bond lengths are in the range 1.9818 (18)–1.9957 (18) Å. The trans O—Fe—O angles are 169.06 (13) and 171.54 (8)°, whereas the corresponding cis angles are in the range 84.81 (10)–100.68 (12)°. In the crystal, molecules are linked via C—H⋯Cl interactions.In the title compound, [Fe(C DOI: 10.1107/S1600536812023215/im2375Isup2.hklStructure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF reportAdditional supplementary materials:


The Cu—N bond lengths in the base of the resulting CuN5 pyramid are in the range 2.016 (3)–2.024 (3) Å and the apical Cu—N( C) distance is 2.385 (4) Å. Based on the τ parameter, the shape of the coordination polyhedron is tetragonal–pyramidal (τ = 0). All atoms of the square-planar tetracyanidopalladate(II) moiety and the CuII ion are located on a mirror plane. The electroneutral molecules interact by N—H⋯N hydrogen bonds, resulting in the formation of a three-dimensional network.The title compound, [Cu(NH II complexes see: Escorihuela et al. 4] = 0.025wR(F2) = 0.061S = 1.001051 reflections81 parametersH-atom parameters constrainedmax = 0.54 e Å−3Δρmin = −1.26 e Å−3ΔρX-AREA  used to solve structure: SHELXS97  I, global. DOI: Click here for additional data file.10.1107/S1600536813011033/ff2104Isup2.hklStructure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF reportAdditional supplementary materials:


The anions are disordered each over two sets of sites, with an occupancy ratio of 0.617 (6):0.383 (6). The distances from the Fe atoms to the centroids of the unsubstituted and substituted cyclopentadienyl (Cp) rings are 1.645 (1)/1.657 (1) and 1.644 (1)/1.647 (1) Å. The dihedral angles between the two Cp rings are 2.49 (3) and 1.45 (4)° in the two ferrocenyl groups of the cations.The asymmetric unit of the title complex, [Fe(C DOI: 10.1107/S1600536812001766/hy2506Isup2.hklStructure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF reportAdditional supplementary materials:


In each molecule, four pentafluorobenzoate anions bridge the quadruply bonded Mo2               4+ unit that is, in addition, axially coordinated by two O atoms of tetrahydrofuran (THF) molecules. In the two independent molecules, the mean Mo—Mo bond length is 2.110 Å. Since the THF molecules are equally disordered over two sets of sites, there are four different Mo—O distances in both half-molecules with an overall mean of 2.542 Å. A zigzag chain is formed by π–π stacking interactions between pentafluorophenyl rings, indicated by a centroid–centroid distance of 3.7054 (11) Å and a centroid-to-plane distance of 3.4169 (3) Å. The extension of the unit gives a three-dimensional network structure with the THF molecules located in the voids.In the asymmetric unit of the title compound, [Mo DOI: 10.1107/S1600536811033411/wm2516Isup2.hkl            Structure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF report            Additional supplementary materials:


The four O atoms in the equatorial plane around the CoII cation form a slightly distorted square-planar arrangement, while the slightly distorted octahedral coordination is completed by the two N atoms of the NA ligands in the axial positions. The dihedral angle between the carboxylate group and the adjacent benzene ring is 22.3 (3)°, while the pyridine ring and the benzene ring are oriented at a dihedral angle of 84.59 (13)°. Intramolecular O—H⋯O hydrogen bonding occurs between the carboxylate group and coordinated water molecule. In the crystal, N—H⋯O, O—H⋯O and weak C—H⋯O hydrogen bonds link the molecules into a three-dimensional supramolecular network.In the title complex, [Co(C N,N-diethylnicotinamide, see: Bigoli et al. 2(C6H6N2O)2(H2O)2] = 0.046wR(F2) = 0.110S = 1.163618 reflections203 parameters6 restraintsH atoms treated by a mixture of independent and constrained refinementmax = 2.60 e Å−3Δρmin = −2.03 e Å−3ΔρAPEX2  used to solve structure: SHELXS97  I, global. DOI: 10.1107/S160053681201330X/xu5493Isup2.hklStructure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF reportAdditional supplementary materials:


The FeIII cation has an approximate octahedral geometry, defined by six N atoms from two bpca− anions. The nearly parallel [dihedral angle = 1.50 (1)°] bpca− anions form two-dimensional supermolecules along the a axis by the way of weak π–π stacking inteactirons . Intra- and intermolecular C—H⋯O hydrogen bonding occurs. The water molecule [occupancies 0.520 (5) and 0.480 (5)], two carbonyl O atoms [occupancies 0.622 (7) and 0.378 (7)] and the four perchlorate O atoms [occupancies 0.887 (4) and 0.113 (4)] are each disordered over two positions.The structure of the title salt complex, [Fe(C DOI: 10.1107/S1600536811047684/jj2105Isup2.hkl            Structure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF report            Additional supplementary materials:


In the crystal, intermolecular O—H⋯O hydrogen bonds lead to a three-dimensional supramolecular network. Intramolecular O—H⋯N hydrogen bonds and π–π interactions between the benzene rings and between the benzene and triazole rings [centroid–centroid distances = 3.657 (1) and 3.752 (1) Å] are observed.In the title compound, [Cu(C DOI: 10.1107/S1600536811018356/hy2429Isup2.hkl            Structure factors: contains datablocks I. DOI:  crystallographic information; 3D view; checkCIF report            Additional supplementary materials:


The average Ru—S bond length is 2.41 (1) Å and the average S—Ru—S bite angle is 81.13 (19)°.In the title complex, [Ru(C DOI: Click here for additional data file.10.1107/S1600536813014141/hy2626Isup2.hklStructure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF reportAdditional supplementary materials:


The packing of the structure involves weak π–π interactions between the pyridyl and benzene rings of neighbouring ppaBr ligands [centroid–centroid distance = 3.928 (2) Å] and interactions between the Br atom on the ppaBr ligand and the hfac ligand [Br⋯C = 3.531 (2) Å].In the title complex, [Co(C DOI: 10.1107/S1600536810032757/zs2056Isup2.hkl            Structure factors: contains datablocks I. DOI:  crystallographic information; 3D view; checkCIF report            Additional supplementary materials:


The Co2+ ion, coordinated by three O atoms from two different carboxylate groups and three water molecules, displays a distorted octahedral environment. In the crystal, π–π interchain interactions, with centroid–centroid distances of 3.656 (2) and 3.669 (2) Å between the benzene rings of the ligands, assemble the chains into sheets parallel to (100). O—H⋯O hydrogen-bonding interactions between the coordinating water molecules and carboxylate O atoms link the sheets into a three-dimensional network.The polymeric title compound, {[Co(C DOI: 10.1107/S1600536812009580/wm2597Isup2.hklStructure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF reportAdditional supplementary materials:


The crystal structure is made up of ∞               1[Nb2PS10] chains expanding along [010]. These chains are built up from bicapped trigonal-prismatic [Nb2S12] units and tetrahedral [PS4] groups and are linked through a linear S—Ag—S bridge, forming a two-dimensional layer. These layers then stack on top of each other, completing the three-dimensional structure with an undulating van der Waals gap. The disordered Cs+ ions reside on sites with half-occupation in the voids of this arrangement. Short [2.8843 (5) Å] and long [3.7316 (4) Å] Nb—Nb distances alternate along the chains, and anionic S2               2− and S2− species are observed. The charge balance of the compound can be represented by the formula [Cs+]0.5[Ag+]0.5[Nb4+]2[PS4               3−][S2               2−]3.The quinternary thiophosphate Cs DOI: 10.1107/S1600536810021768/wm2357Isup2.hkl            Structure factors: contains datablocks I. DOI:  crystallographic information; 3D view; checkCIF report            Additional supplementary materials:


In the coordination cation, the CuII atom is coordinated by four N atoms from two 1,10-phenanthroline ligands and two O atoms from a bridging–chelating carboxylate group of the pyridine-2,6-dicarboxylate anion, completing a distorted N4O2 octahedral coordination environment. The TbIII atom, located on a twofold rotation axis, is nine-coordinated by three tridentate pyridine-2,6-dicarboxylate anions forming an N3O6 donor set. The intramolecular Cu⋯Tb distance of 5.0592 (11) Å indicates weak interactions between the CuII and TbIII atoms. The coordination cations, nitrate anions and water molecules are connected via O—H⋯O hydrogen bonds into layers parallel to the (001) plane. Moreover, there are extensive π–π stacking interactions [centroid–centroid distances = 4.332 (7) and 3.878 (5) Å] between the phenanthroline ligands and between phenanthroline and pyridine-2,6-dicarboxylate ligands.The asymmetric unit of the title compound, [Cu For the al. 2010; Yang et al. 2006.2Tb(C7H3NO4)3(C12H8N2)4]NO3·4H2O = 0.041wR(F2) = 0.134S = 1.046454 reflections479 parameters27 restraintsH atoms treated by a mixture of independent and constrained refinementmax = 0.88 e Å−3Δρmin = −1.09 e Å−3ΔρAPEX2  used to solve structure: SHELXS97  I, global. DOI: 10.1107/S1600536812031686/gk2483Isup2.hklStructure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF reportAdditional supplementary materials:


The central ion is coordinated by the thiazole N atom, the thioureido N and the S atom of the deprotonated thiosemicarbazone ligand. The other ligand is linked with the central ion through the C=S group. The deprotonated ligand intramolecularly hydrogen bonds to the thiazole ring N atom, while the ligand forms an intermolecular hydrogen bond to the thiolate S atom of the second ligand. The deprotonation of the tridentate ligand and its coordination to the CdII ion via the S atom strikingly affects the C—S bond lengths. The C—S bond lengths in the neutral and deprotonated ligands in the metal complex are 1.709 (3) and 1.748 (2) Å, respectively, whereas it is 1.671 (3) Å in the free ligand. In the metal complex, the Cd—S distances are 2.6449 (6) and 2.5510 (6) Å. The Cd—I bond length is 2.7860 (2) Å.In the title complex, [Cd(C I(C12H12N4S2)] = 0.027wR(F2) = 0.060S = 1.028142 reflections354 parameters3 restraintsH atoms treated by a mixture of independent and constrained refinementmax = 0.92 e Å−3Δρmin = −0.60 e Å−3ΔρAPEX2  used to solve structure: SHELXS97  global, I. DOI: Click here for additional data file.10.1107/S160053681300915X/bv2219Isup2.hklStructure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF reportAdditional supplementary materials:


The distorted trans square-planar environment is completed by two P atoms [Rh—P = 2.3251 (4) Å] from two diphenyl(4-vinylphenyl)phosphane ligands. The vinyl group is disordered over two sets of sites in a 0.668 (10):0.332 (10) ratio. The crystal packing exhibits weak C—H⋯Cl and C—H⋯O hydrogen bonds and π–π interactions between the phenyl rings of neighbouring molecules, with a centroid–centroid distance of 3.682 (2) Å.In the title compound,  DOI: 10.1107/S1600536812013669/cv5270Isup2.hklStructure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF reportAdditional supplementary materials:


The CdII ion is in a strongly distorted CdN2O5 pentagonal-bipyramidal geometry, defined by two N atoms from one 2,2′-bipyridine ligand and five O atoms from three 2-phenylquinoline-4-carboxylate ligands, one monodentate, two bidentate. Weak intermolecular π–π interactions [centroid–centroid distance = 3.712 (3) Å] help to establish the packing of the structure.The neutral binuclear title complex, [Cd DOI: 10.1107/S1600536810049640/bh2323Isup2.hkl            Structure factors: contains datablocks I. DOI:  crystallographic information; 3D view; checkCIF report            Additional supplementary materials:


In the crystal, the components are linked into a three dimensional network by O—H⋯O, N—H⋯O, N—H⋯N and C—H⋯O hydrogen bonds and a π–π interaction with a centroid–centroid distance of 3.6080 (8) Å.In the complex anion of the title compound, (C DOI: 10.1107/S1600536811011147/is2693Isup2.hkl            Structure factors: contains datablocks I. DOI:  crystallographic information; 3D view; checkCIF report            Additional supplementary materials:


In the crystal, noncovalent interactions play an important role in the stabilization of the structure, involving O—H⋯O, N—H⋯O and weak C—H⋯O hydrogen bonds and π–π stacking interactions between the pyridine rings of the pyridine-2,6-dicarboxylate ligands [centroid–centroid distance = 3.7138 (15) Å] and between the 8-hydroxy-2-methylquinolinium cations .In the title compound, (C DOI: 10.1107/S1600536811021015/hy2430Isup2.hkl            Structure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF report            Additional supplementary materials:


The Ni—N distances range from 2.0594 (12) to 2.0664 (12) Å, intra-ligand N—Ni—N angles range from 84.59 (5) to 86.06 (5)°, and adjacent inter-ligand N—Ni—N angles range between 93.94 (5) and 95.41 (5)°. In the crystal, inversion-related pyrazole rings are π–π stacked, with an interplanar spacing of 3.4494 (18) Å, forming chains that propagate parallel to the a-axis direction. Intermolecular O—H⋯O hydrogen bonds are present between water molecules and trifluoromethanesulfonate anions.In the title salt, [Ni(C DOI: 10.1107/S1600536813024252/tk5252Isup2.hklStructure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF reportAdditional supplementary materials:


The CuII atom is in a square-pyramidal coordination environment formed by four O atoms of four carboxylate groups and one water molecule, which is located in the apical position. The carboxylate groups are twisted relative to the benzene rings by 11.09 (16) and 45.55 (19)°. The nitro groups are not coplanar with the parent aromatic rings [dihedral angles = 16.2 (3)–51.45 (14)°]. O—H⋯O hydrogen bonds between the coordinated water molecules and one of the nitro groups, as well as π–π stacking interactions [centroid–centroid distance = 3.5764 (12) Å] between the benzene rings, assemble the complex molecules into a one-dimensional polymeric structure which is further extended into a three-dimensional polymeric network via O—H⋯O hydrogen bonds involving the water molecules of crystallization.The title compound, [Cu DOI: 10.1107/S1600536811000547/gk2339Isup2.hkl            Structure factors: contains datablocks I. DOI:  crystallographic information; 3D view; checkCIF report            Additional supplementary materials:


The first reported polymorph of this complex was triclinic . The present polymorph crystallized in the monoclinic space group P21/c. The CuII ion is in a square planar environment and is coordinated by one phenolate O, one imine N and one pyridine N atom of the tridentate Schiff base ligand and by one water O atom. In the crystal, molecules are linked through intermolecular O—H⋯O hydrogen bonds to form chains along the a axis.The title complex, [Cu(C al. 2010. Acta Cr For the al. 2010.13H10ClN2O)(H2O)]NO3·H2O = 0.037wR(F2) = 0.089S = 1.063410 reflections233 parameters3 restraintsH atoms treated by a mixture of independent and constrained refinementmax = 0.39 e Å−3Δρmin = −0.48 e Å−3ΔρSMART  used to solve structure: SHELXTL  I, global. DOI: 10.1107/S1600536812004564/qm2051Isup2.hklStructure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF reportAdditional supplementary materials:


The B atom deviates by 0.202 (1) Å from the least-squares plane of the mesityl ring. All of the methoxy groups are approximately coplanar with the 2,4,6-trimethoxyphenyl ring, whereas the BOH group is twisted with respect to it by 19.5°. The borinic OH group is engaged in an intramolecular O—H⋯O hydrogen bond with one of ortho-methoxy groups. The molecular structure is stabilized by weak C—H⋯O contacts. In the crystal, molecules are linked by weak C—H⋯O and C—H⋯π interactions, generating a three-dimensional network.In the title molecule, C DOI: 10.1107/S160053681002297X/pv2296Isup2.hkl            Structure factors: contains datablocks I. DOI:  crystallographic information; 3D view; checkCIF report            Additional supplementary materials:


One CdII ion is six-coordinated and exhibits a distorted octahedral geometry, while the other two CdII ions are seven-coordinated, displaying a distorted pentagonal–bipyramidal geometry. The CdII ions are bridged by two types of sulfate anions, producing inorganic chains along [100]. These chains are further connected by the H2bic ligands, leading to a three-dimensional framework. N—H⋯O and O—H⋯O hydrogen bonds and π–π interactions between the imidazole and benzene rings  further stabilize the crystal structure. The asymmetric unit of the title compound, [Cd H-benzimidazole-5-carboxylate complexes, see: Gao et al. 2(SO4)2(H2O)3] = 0.025                           wR(F                           2) = 0.067                           S = 1.06                           3935 reflections361 parameters1 restraintH-atom parameters constrainedmax = 0.56 e Å−3                        Δρmin = −0.71 e Å−3                        Δρ                                 APEX2  used to solve structure: SHELXS97  I, global. DOI: 10.1107/S1600536811034477/hy2460Isup2.hkl            Structure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF report            Additional supplementary materials:


The Ir=Ccarbene bond is strong and short and exerts a notable effect on the trans-Ir—N bond, which is about 0.10 Å longer than the two other Ir—N bonds. The chloroform solvent molecule is anchored via a weak C—H⋯Cl hydrogen bond to the Cl atom of the Ir complex molecule. In the crystal, the constituents adopt a layer-like arrangement parallel to (010) and are held together by weak intermolecular C—H⋯Cl hydrogen bonds, as well as weak Cl⋯Cl [3.498 (2) Å] and Cl⋯π [3.360 (4) Å] interactions. A weak intramolecular C—H⋯O hydrogen bond is also observed.In the title compound, [Ir(C N,N′,N′′)-iridium moiety Ir[TpMe2]. Its formation from [(TpMe2)Ir(C6H5)2(k1-N2)]  and ethoxybenzene involved multiple C—C,H,O,Cl bond transformations by the outstanding activity of the Ir[TpMe2] moiety. For general information on C—H and C—C activation, see: Lin & Yamamoto borate-moto 1999; Dyker (C8H7O)Cl]·CHCl3 = 0.028wR(F2) = 0.071S = 1.028053 reflections341 parametersH-atom parameters constrainedmax = 1.29 e Å−3Δρmin = −1.43 e Å−3ΔρSMART  used to solve structure: SHELXS97  I, global. DOI: Click here for additional data file.10.1107/S1600536813007344/lh5594Isup2.hklStructure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF reportAdditional supplementary materials:


Both the arsine and phosphine ligands are equatorial with respect to the Ru3 triangle. In addition, each Ru atom carries one equatorial and two axial terminal carbonyl ligands. In each biphenyl unit, the phenyl rings are twisted from each other, making dihedral angles of 51.22 (18), 42.94 (16) and 26.95 (16)°. The arsine-substituted phenyl rings make dihedral angles of 61.22 (15), 87.17 (15) and 83.32 (15)° with each other. The dihedral angles between the two benzene rings are 85.52 (18) and 81.77 (15)° for the two diphenylphosphanyl groups, respectively. In the crystal, molecules are linked into dimers by intermolecular C—H⋯O hydrogen bonds. Weak intermolecular C—H⋯π and π–π [centroid–centroid distance = 3.6981 (18) Å] interactions stabilize the crystal structure.In the title  DOI: 10.1107/S160053681100078X/ng5095Isup2.hkl            Structure factors: contains datablocks I. DOI:  crystallographic information; 3D view; checkCIF report            Additional supplementary materials:


The structure of the dinuclear tetracation exhibits significant distortion from planarity in the bridging 2,3,5,6-tetrakis(pyridin-2-yl)pyrazine (tppz) ligand, which has a saddle-like geometry with an average dihedral angle of 42.96 (18)° between adjacent pyridine rings. The metal–ligand coordination environment is nearly equivalent for the two RuII atoms, which have a distorted octahedral geometry due to the restricted bite angle [157.57 (13)–159.28 (12)°] of their two mer-arranged tridendate ligands  orthogonal to each other. At the peripheral tpy ligands, the average Ru—N bond distance is 2.072 (4) Å for the outer N atoms trans to each other (Nouter) and 1.984 (1) Å for the central N atoms . At the bridging tppz ligand, the average metal–ligand distances are significantly shorter [2.058 (4) Å for Ru—Nouter and 1.965 (1) Å for Ru—Ncentral] as a result of both the geometric constraints and the stronger π-acceptor ability of the pyrazine-centered bridge. The dihedral angle between the two tpy planes is 27.11 (6)°. The intramolecular linear distance between the two Ru atoms is 6.6102 (7) Å.In the title compound [Ru DOI: Click here for additional data file.10.1107/S1600536812051215/zl2523Isup2.hklStructure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF reportAdditional supplementary materials:


The binuclear complex molecules are linked together by intermolecular O—H⋯O hydrogen bonds into a layer parallel to (100). The layers are connected by C—H⋯Cl hydrogen bonds. Intramolecular O—H⋯O hydrogen bonds and π–π interactions [centroid–centroid distance = 3.5958 (16) Å] are also present.In the centrosymmetric binuclear title compound, [Cu DOI: 10.1107/S1600536811035112/hy2462Isup2.hkl            Structure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF report            Additional supplementary materials:


In the crystal, weak N—H⋯Cl hydrogen bonds link the molecules into layers, while weak π–π interactions [centroid–centroid distance = 4.2758 (18) Å] also help to stabilize the packing.In the title compound, (C DOI: 10.1107/S1600536810046817/jh2229Isup2.hkl            Structure factors: contains datablocks I. DOI:  crystallographic information; 3D view; checkCIF report            Additional supplementary materials:


The intramolecular π–π interaction [centroid–centroid distance = 3.6113 (11) Å] between two of the 4-fluorophenyl groups is complemented by both C—H⋯F and C—H⋯O interactions with distances in the range 2.51–2.60 Å, resulting in a tight head-to-tail packing. In the title complex, [Cu(NO DOI: Click here for additional data file.10.1107/S1600536812043346/mw2090Isup2.hklStructure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF reportAdditional supplementary materials:


The sixth coordination site of molybdenum is occupied by the O atom of a methanol molecule. In this complex, the NO5 coordination sphere adopts a distorted octahedral coordination geometry. The metal atom is shifted by 0.335 (1) Å from the square plane defined by the three donor atoms of the Schiff base ligand and one oxide group towards the second oxide group in the cis position. In the crystal, the complex forms inversion dimers through a pair of O—H⋯N hydrogen bonds involving the methanol –OH group and the pyridine N atom. Additional C—H⋯O contacts stack the molecules along the b axis.In the title complex, [Mo(C O2(CH4O)] = 0.026wR(F2) = 0.070S = 1.073474 reflections239 parameters13 restraintsH atoms treated by a mixture of independent and constrained refinementmax = 0.31 e Å−3Δρmin = −0.60 e Å−3ΔρSMART  used to solve structure: SHELXTL  I, global. DOI: 10.1107/S1600536813019077/sj5344Isup2.hklStructure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF reportAdditional supplementary materials:


The bridging carbonyl C—C(=O)—C plane makes dihedral angles of 47.07 (6)° with the naphthalene ring system and 24.20 (10)° with the benzene ring. A weak intermolecular C—H⋯O hydrogen bond exists between the H atom of one methoxy group and the O atom of the other methoxy group in an adjacent molecule. The crystal packing is additionally stabilized by two types of weak intermolecular interactions involving the Br atom, C—H⋯Br and Br⋯O [3.2802 (14) Å].In the title compound, C DOI: 10.1107/S160053681004016X/vm2049Isup2.hkl            Structure factors: contains datablocks I. DOI:  crystallographic information; 3D view; checkCIF report            Additional supplementary materials:


The central PbII ion has a (4 + 2) coordination by four O atoms of the two ABTC ligands and two weaker Pb—S bonding interactions (Pb—S secondary bonds) from S atoms of other two neighbouring ABTC ligands. These bonds link the metal ions into zigzag chains along the c axis, which, in turn, aggregate through π–π interactions [centroid–centroid distance = 3.7436 Å] between ABTC rings and N—H⋯O and N—H⋯N hydrogen bonds.The title complex, [Pb(C DOI: 10.1107/S1600536810049330/bg2378Isup2.hkl            Structure factors: contains datablocks I. DOI:  crystallographic information; 3D view; checkCIF report            Additional supplementary materials:


There are C—H⋯O hydrogen bonds and C—H⋯π interactions and π–π interactions [centroid–centroid distance = 3.319 (1) Å] in the crystal structure.In the title compound, [Cd(NO DOI: 10.1107/S1600536811039687/jh2323Isup2.hkl            Structure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF report            Additional supplementary materials:


The anion is a six-coordinated complex with a distorted CuN2O4 octahedral geometry around the CuII ion. N—H⋯O and C—H⋯O hydrogen bonds along with π–π contacts between the pyridine rings of the (2a4mpH)+ cations [centroid–centroid distance = 3.573 (2) Å] stabilize the crystal structure.The asymmetric unit of the title compound, (C DOI: 10.1107/S1600536811001139/bt5449Isup2.hkl            Structure factors: contains datablocks I. DOI:  crystallographic information; 3D view; checkCIF report            Additional supplementary materials:


The molecular complex has no crystallographically imposed symmetry. The coordination geometry around the metal atom is distorted square-pyramidal. The equatorial coordination around copper involves donor atoms of the bidentate chelating 2-(dimethylamino)ethanol ligand and the 2-(dimethylamino)ethanolate group, which are mutually trans to each other, with four approximately equal short Cu—O/N bond distances. The axial Cu—I bond is substantially elongated. Intermolecular hydrogen-bonding interactions involving the –OH group of the neutral 2-(dimethylamino)ethanol ligand to the O atom of the monodeprotonated 2-(dimethylamino)ethanolate group of the molecule related by the n-glide plane, as indicated by the O⋯O distance of 2.482 (12) Å, form chains of molecules propagating along [101].The title compound, [Cu(C I(C4H11NO)] = 0.058wR(F2) = 0.204S = 1.002471 reflections133 parametersH-atom parameters constrainedmax = 1.80 e Å−3Δρmin = −0.83 e Å−3ΔρAFC6S Diffractometer Control Software AFC6S Diffractometer Control Software; data reduction: TEXSAN  I, global. DOI: 10.1107/S1600536812010215/ds2178Isup2.hklStructure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF reportAdditional supplementary materials:


An intramolecular O—H⋯O hydrogen bond in the ligand generates an S(6) ring. The dihedral angle between the aromatic rings joined to the acetylacetonate unit is 6.4 (2)°. The ethanol molecule is disordered over two orientations in a 0.65 (3):0.35 (3) ratio. In the crystal, molecules are linked by O—H⋯O bonds.In the title complex, [Co(C DOI: 10.1107/S1600536810029776/hb5579Isup2.hkl            Structure factors: contains datablocks I. DOI:  crystallographic information; 3D view; checkCIF report            Additional supplementary materials:


In the ferrocenyl moiety, the unsubstituted cyclopentadienyl ring is disordered over two orientations with site occupancies of 0.64 (2) and 0.36 (2). In the pyrrolizine ring, one C atom is disordered over two positions, with site occupancies of 0.71 (1) and 0.29 (1). Intramolecular C—H⋯O interactions occur. The crystal packing is established through weak intermolecular C—H⋯O and N—H⋯O interactions.In the title compound, [Fe(C DOI: 10.1107/S1600536810045459/im2240Isup2.hkl            Structure factors: contains datablocks I. DOI:  crystallographic information; 3D view; checkCIF report            Additional supplementary materials:


The four acetamide ligands bridging the dirhodium core are arranged in a 2,2-cis manner, with two N atoms and two O atoms coordinating to the unique RhII atom cis to one another. The Neq—Rh—Rh—Oeq torsion angles on the acetamide bridges vary between 1.62 (4) and 1.78 (4)°. The Rh—Rh bond length is 2.4319 (3) Å. The axial nitrile ligand completes the distorted octahedral coordination sphere and shows a non-linear coordination with an Rh—N—C bond angle of 167.14 (15)°, while the N—C bond length is 1.135 (3) Å.The complex molecule of the title compound, [Rh DOI: Click here for additional data file.10.1107/S1600536813012828/mw2103Isup2.hklStructure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF reportAdditional supplementary materials:


The AuI atom is in a trigonal–planar geometry within an IP2 donor set with the greatest distortion seen in the P—Au—P angle [128.49 (3) °]. Close intramolecular Au⋯O interactions [3.172 (3) Å] are observed. No specific intermolecular interactions are noted in the crystal packing.In the title compound, [AuI(C DOI: 10.1107/S1600536812011609/su2394Isup2.hklStructure factors: contains datablock(s) I. DOI:  crystallographic information; 3D view; checkCIF reportAdditional supplementary materials:


The average of the four Ru—Cl bond lengths is 2.355 (15) Å, and the Ru—S and Ru—N bond lengths are 2.2853 (3) and 2.1165 (11) Å, respectively. The complex forms a chain, with a six-coordinate sodium ion bridging the ruthenium(III) units. The sodium cation is coordinated by cis-chloride ligands on ruthenium [Na—Cl = 2.9576 (7) and 2.6988 (7) Å], chloride and DMSO ligands from the ruthenium complexes related by inversion , a nitrogen ligand from the pyrimidine of the tetrachloridoruthenium(III) complex related by the twofold rotation axis [Na—N = 2.5224 (14) Å] and an oxygen-bound DMSO [Na—O = 2.3165 (12) Å]. The title complex, [NaRuCl DOI: 10.1107/S1600536811017211/om2427Isup2.hkl            Structure factors: contains datablocks I. DOI:  crystallographic information; 3D view; checkCIF report            Additional supplementary materials: