Daniela Patricia

Rojas Castro

Jean-Marie Le Gall

Christian Andreo

Stigma, discrimination and sexual (dis)satisfaction among people living with HIV: results from the

Keywords: HIV/AIDS, Sexual satisfaction, Stigma, Discrimination, Communitybased organization HIV/AIDS, Sexual satisfaction, Stigma, Discrimination, Community-based organization

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

Introduction

Stigma was defined by [START_REF] Goffman | Factors associated with unprotected anal intercourse (UAI) among men who have sex with men (MSM) in Douala, Cameroon[END_REF] as "a deeply discrediting attribute" that reduces the bearer "from a whole and usual person to a tainted, discounted one". It has been demonstrated that this circumstance impacts on people's psychological wellbeing and health [START_REF] Beals | Stigma management and well-being: the role of perceived social support, emotional processing, and suppression[END_REF]Quinn & Chaudoir, 2009). On the other hand, discrimination, defined as "any measure entailing any arbitrary distinction among persons depending on their confirmed or suspected HIV serostatus or state of health" (UNAIDS, 2000), makes reference to the enacted stigma, that is, "to the acts or omissions in which the content of stigma is applied at an individual or social level" [START_REF] Brown | Interventions to reduce HIV/AIDS stigma: what have we learned?[END_REF].

Since the beginning of the HIV/AIDS epidemic, the psycho-social well-being of the people living with HIV/AIDS (PLWHA) has certainly been mediated by the stigma and discrimination that this illness arouses [START_REF] Bos | Reducing AIDS-related stigma in developing countries: the importance of theory and evidence-based intervention[END_REF][START_REF] Logie | Meta-analysis of health and demographic correlates of stigma towards people living with HIV[END_REF]. Even more, HIV/AIDS-related stigma has been shown as strongly linked to the negative attitudes towards certain populations where the epidemic has been especially aggressive, e.g. men having sex with men -MSM- [START_REF] Herek | AIDS stigma and sexual prejudice[END_REF].

It has been demonstrated that stigma and discrimination are barriers to HIV testing (Spielberg et al., 2003;[START_REF] Genberg | A comparison of HIV/AIDS-related stigma in four countries: negative attitudes and perceived acts of discrimination towards people living with HIV/AIDS[END_REF], adequate health care [START_REF] Kinsler | The effect of perceived stigma from a health care provider on access to care among a low-income HIV-positive population[END_REF][START_REF] Maman | A comparison of HIV stigma and discrimination in five international sites: the influence of care and treatment resources in high prevalence settings[END_REF], access to work [START_REF] Anderson | HIV/AIDS-related stigma and discrimination: accounts of HIV-positive Caribbean people in the United Kingdom[END_REF]Rao et al., 2008) and so on. Therefore, it is not surprising that there exists a relationship between the experience of stigma and discrimination and the psychosocial aspects of PLWHA's quality of life [START_REF] Préau | Health related quality of life in French people living with HIV in 2003: results from the national ANRS-EN12-VESPA Study[END_REF]Subramanian et al., 2009). However, there is a lack of literature regarding sexual satisfaction among PLWHA [START_REF] Inoue | Sexual activities and social relationships of people with HIV in Japan[END_REF]Lambert et al., 2005) and, to our knowledge, its association with the HIVrelated stigma and discrimination has been barely studied [START_REF] Bouhnik | Sexual difficulties in people living with HIV in France: results from a large representative sample of outpatients attending French hospitals (ANRS-EN12-VESPA)[END_REF].

On the other hand, AIDES, the largest French HIV/AIDS community-based organization, created in 1984, has focused most of its actions and lobbying on the rights of PLWHA. Nevertheless, other activities concerning issues such as prevention and legal support have an important role. This organization (AIDES), which embraces the principles of community-based research [START_REF] Minkler | Community-based participatory research for health: from process to outcomes[END_REF], decided, as in previous community-based researches [START_REF] Bohl | Concurrent sexual partnerships and racial disparities in HIV infection among men who have sex with men[END_REF][START_REF] Goffman | Factors associated with unprotected anal intercourse (UAI) among men who have sex with men (MSM) in Douala, Cameroon[END_REF][START_REF] O'donnell | Keep it up: development of a community-based health screening and HIV prevention strategy for reaching young African American men[END_REF], to conduct a survey on the needs and the socio-economic and psychosocial conditions of the people in contact with it. The information obtained is used to develop actions and lobbying responding to the detected needs.

Based on the large experience that this community-based organization has had with PLWHA as well as on previous works [START_REF] Inoue | Sexual activities and social relationships of people with HIV in Japan[END_REF]Siegel et al., 2006;[START_REF] Bouhnik | Sexual difficulties in people living with HIV in France: results from a large representative sample of outpatients attending French hospitals (ANRS-EN12-VESPA)[END_REF], we hypothesized that feeling sexually (dis)satisfied could be Consequently, the present work aims to determine if there is a link between discrimination and stigma, and sexual (dis)satisfaction among PLWHA from the data collected by a community-based survey called "AIDES et toi".

Methods

Data collection

In 2007, AIDES carried out the fourth edition of its biannual cross-sectional nationwide survey conducted among a sample of users. They were recruited at the local offices and at outreach venues throughout France. During one week, 3,168 people in contact with the organization were asked to fill out a self-administered questionnaire, 2,434 respondents accepted. The comparison between respondents and nonrespondents showed that the latter were more likely to be younger than 25 years old (9.2% vs. 13.1% of respondents; p<0.001) and being solicited in the outreach venues rather than in the local offices (72.7% vs. 51.3%; p<0.001). No statistical differences were found concerning gender.

The questionnaire included standardized items presented in four sections: a) socio-demographics, b) health status, quality of life and discrimination, c) sexual life and d) HIV stigma, disclosure and biological markers. A fifth section concerning the use of the organization was also included but it will not be presented for the present work.

Sample

Of the whole sample, 1,098 people declared being HIV positive. The sample for the present study was drawn from the 521 HIV positive participants who answered the items concerning sexual (dis)satisfaction. We decided to include the people who reported no sexual activity during the last six months (23%) because sexual (in)activity has been shown as a sexual satisfaction determinant [START_REF] Beutel | Sexual activity, sexual and partnership satisfaction in ageing men-results from a German representative community study[END_REF].

Questionnaire

Individuals who agreed to participate answered a self-administered, 136-item questionnaire. However, in order to resolve any potential linguistic or cultural doubts about the questions, a trained interviewer was available during the whole process.

Variables

Sociodemographics

Sociodemographic characteristics included age, gender, nationality, family status (in couples/single), medical insurance, employment status and housing (stable/instable).

Health status (satisfaction), quality of life and discrimination

Participants were asked about their HIV, HBV and HVC status (positive/negative/unaware), current substance use and substitution treatment. The questionnaire also measured perceived satisfaction with their health status and quality of life. No previous validated scales were used to assess these two dimensions, instead single-items were applied. Finally, another question dealt with the fact of having being discriminated against during the last two years (yes/no) because of seven possible reasons: a) being HIV positive, b) having hepatitis, c) being a woman, d) being homosexual, e) being a migrant, f) skin colour and g) substance use. We also

Sexual life (satisfaction)

Concerning sexual life, several questions were addressed to know the kind (steady/casual) and number of sexual partners, HIV serology of the sexual partners, frequency of condom use and sexual satisfaction. This last item was formulated as follows: "In general, concerning your sexual life, you would say that you are" (Satisfied/Dissatisfied).

Disclosure, HIV-related stigma and biological markers

Disclosure to significant others, and the free will to disclose was evaluated. The French-language version of the HIV Stigma Scale (HSS; Berger et al., 2001) was used in order to measure HIV-related discrimination experienced by PLWHA. It consisted of twenty-six items (e.g.: "I have lost sexual partners when disclosing my HIV positive status", "I feel anxious about being judged because of my HIV status") with the answer scale for each item ranging from (1) "strongly disagree" to (4) "strongly agree". Participants were also asked to indicate if they were taking antiretroviral treatment, for how long, their last CD4 cell count, their viral load (detectable/undetectable) and if they had already used post-exposition prophylaxis during the last year.

Statistical analysis

The associations between the different variables of the questionnaire and the individual satisfaction or dissatisfaction with sexual life were examined using Pearson's Chi-squared tests. To identify the factors independently associated with sexual dissatisfaction, logistic models were used. A backward stepwise (likelihood

Results

Descriptive characteristics

Sociodemographics

The main results are summarized in Table 1. From the sample of PLWHA who answered the sexual satisfaction section (N=521), the mean age was 42.8 years old, men represented 63.3% of the sample and 26.5% fulfilled migration criteria.

Concerning sexual orientation, MSM accounted for 61.2% of men. In the sample, 58.7% were in couples, 52.8% had children, 39.5% were employed and 79.3% had stable housing. As to co-infection, 11% were also HBV positive and 20.5% were HCV positive. Finally, 84.6% were in treatment, 75.5% had an undetectable viral load, and 88.3% had a >200/ml CD4 cell count.

Sexual satisfaction

In relation to satisfaction with sexual life, 39% of respondents reported being dissatisfied. No significant differences were observed when MSM, heterosexual men and women were compared.

Stigma and discrimination

Concerning items about stigma, we found that 87.3% declared "I am very careful about who I disclose my HIV positive status to", 70.6% declared "I feel anxious that people will judge me when they find out that I am HIV positive" and 69.6% reported "I feel anxious that the people who know my HIV positive status will disclose it to others". Among respondents, 46.7% declared having been discriminated against during the previous two years. When asked about the reasons why this discrimination occurred, discrimination because of their HIV status was the most frequently reported reason (77.4%). As for the setting, daily life and health care (48% and 41.9% respectively) accounted for the largest percentages (for detailed results see Table 2).

Univariate analysis

The results of the cross tabulation of sexual (dis)satisfaction with each survey item will be presented following the same order as the questionnaire's sections.

Sociodemographics

Concerning sociodemographic characteristics, the variables significantly associated to sexual dissatisfaction were; being older than 40 years (p=0,002), not being in couples (p<0.001) and not having a full-time job (p=0,025). The variable "having free health care for people on low incomes" instead of private health insurance almost reached significance (p=0.05).

Health status (satisfaction), quality of life and discrimination

The variable significantly associated with being dissatisfied was "having been discriminated against in the sexual relationship setting" (p<0,001). Current substance use and being HCV positive almost reached significance. In relation to the participant's sexual life, we found that not having sex during the last month was significantly associated to being sexually dissatisfied (p<0,001). The other variables showing a significant link with sexual dissatisfaction were "not having a steady sexual partner" (p<0,001), and a lower frequency of sexual intercourse with both steady and casual sexual partners (p<0,001 and p<0,002 respectively). There was no link between HIV status of the sexual partners (steady or casual) and consistency of condom use and sexual (dis)satisfaction.

Disclosure, HIV-related stigma and biological markers

As for biological markers and disclosure of HIV positive status, no significant results were found. However, the choice of disclosing HIV status to friends and acquaintances almost reached significance.

Nevertheless, in relation to the stigma items, we found several statistically significant associations. Concretely, the items "I feel apart, isolated from the rest of the world" (p<0,001), "I am very careful about who I disclose my HIV positive status to" (p=0,032), "Some people aware of my HIV positive status have become distant" (p=0,020), "I feel anxious that the people who know my HIV positive status will disclose it to others" (p=0,045), "Some people are afraid of being rejected because they are close to me" (p=0,018), "I have lost some sexual partners when I told them I was HIV positive" (p=0,024), "Some people who know my HIV positive status tend to ignore my personal qualities" (p=0,032), "Some people seem to be afraid of me because I am HIV positive" (p=0,017) were significantly associated with sexual dissatisfaction. The item "Some sexual partners recoiled from me" almost reached significance.

Multivariate analysis

The results of the multivariate model are shown in Table 3. The variables that remained significantly associated with sexual dissatisfaction were: 1) age (>40 years old), 2) having been discriminated against in the sexual relationship setting during the last two years, 3) not having a steady sexual partner, 4) answering yes to the item "I feel apart, isolated from the rest of the world", 5) not having a full-time job and 6) a lower frequency of sexual intercourse with casual sexual partners.

Discussion

These results show that stigma and discrimination towards PLWHA responding to the survey are prevalent. We also observe that the sample who answered this survey declared being sexually dissatisfied in a larger percentage than the general French population; 39% of the respondents reported being dissatisfied versus 17% of the former [START_REF] Colson | Sexual behaviors and mental perception, satisfaction and expectations on sex life in men and women in France[END_REF]. [START_REF] Bouhnik | Sexual difficulties in people living with HIV in France: results from a large representative sample of outpatients attending French hospitals (ANRS-EN12-VESPA)[END_REF] found that 33% of respondents declared having sexual difficulties. And, another study found that as much as 60% of HIV positive respondents declared being dissatisfied with their sexual lives [START_REF] Inoue | Sexual activities and social relationships of people with HIV in Japan[END_REF]. Some limitations must be highlighted before discussing our results. Firstly, we are presenting cross-sectional data instead of longitudinal data, more appropriate to understand the association between the different factors studied. Secondly, the sample size was half of those who declared being HIV positive. We believe that the sexual life items location in the questionnaire was not the most adequate, preventing some of the respondents from answering these items. Thirdly, data proceeding from selfreported information may include a well-known desirability bias. Fourthly, no items concerning sexual dysfunction were included. Therefore, we could be missing a We can state that our results reflect two main dimensions related to sexual dissatisfaction: one includes age, full-time job and sexual activity (partner and frequency); the other one is strictly associated to HIV-stigma and discrimination in the sexual setting. Concerning the first dimension, we find a potentially obvious result: not having a sexual life, and as shown elsewhere [START_REF] Dunn | analysis of an HIV stigma scale and initial exploration of subscales[END_REF][START_REF] Beutel | Sexual activity, sexual and partnership satisfaction in ageing men-results from a German representative community study[END_REF], is linked to a greater sexual dissatisfaction. The relevance of this result arises from the fact that a non negligible percentage of the sample of PLWHA surveyed does not have a sexual life and consequently is sexually dissatisfied. The lack of sexual life in PLWHA seems to be explained, at least partially, by the second dimension mentioned before, HIV-related stigma and discrimination in the sexual setting.

The results from the present work show a significant relationship between sexual dissatisfaction and several indicators of fear of stigma and enacted stigma or discrimination. When univariate analyses were performed, nine variables reflecting experiences of rejection, detachment, fear and unfair treatment because of HIV positive status were found to predict sexual dissatisfaction. Concretely, two items made reference to the fear of stigma, mainly to the hesitation of disclosing their HIV positive status because of the dread that it would be revealed to others. Seven other items were related to enacted stigma. Moreover, the item "I have been discriminated against in the sexual relationship setting (during the previous two years)", not pertaining to the HIV Stigma Scale, was also statistically associated. Of all these variables, the latter and the HIV Stigma Scale referring to the feeling of loneliness remained significantly associated to sexual dissatisfaction. Therefore, we found both, an enacted and an affective component of stigma predicting sexual dissatisfaction.

Another interesting result makes reference to the link between sexual satisfaction and having a full-time job. On the one hand, having a full-time job is a sign of a better health status, and this better health status has been shown to be associated with a more fulfilled sexual life. On the other hand, and even if the subject has not been studied in depth, one psychosocial factor linked to sexual dissatisfaction is unemployment [START_REF] Meisler | Depressed affect and male sexual arousal[END_REF][START_REF] Abdo | The impact of psychosocial factors on the risk of erectile dysfunction and inhibition of sexual desire in a sample of the Brazilian population[END_REF]. Our results could support this association. It must also be noted that age was related to sexual dissatisfaction; another study [START_REF] Asboe | Sexual dysfunction in HIV-positive men is multi-factorial: a study of prevalence and associated factors[END_REF] has already demonstrated that this factor is also associated with sexual dysfunction in HIV-positive men.

We did not find any association between sexual dissatisfaction and biological markers or antiretroviral treatment. These results are partially supported by previous research; [START_REF] Bouhnik | Sexual difficulties in people living with HIV in France: results from a large representative sample of outpatients attending French hospitals (ANRS-EN12-VESPA)[END_REF] did not find any relationship between "sexual difficulties" and immuno-virological outcomes, however, they did find an association between HIV-treatment experience and sexual difficulties.

Current results suggest that improving PLWHA's quality of life and care do not only imply offering quality medical care, but also ensuring a global health and well-being approach, which necessarily involves the effects of stigma and discrimination in different areas. Experiencing stigma and discrimination in the sexual setting is a good example of the harmful effects these can have on the well-being of PLWHA. Besides, given that improving sexual satisfaction in HIV positive people has been demonstrated as a factor that encourages preventive attitudes (Troussier & Tourett-Turgis, 2006), we can state that PLWHA's sexual satisfaction has a potential

  experience of stigma and discrimination in sexual settings.

  setting where this discrimination occurred (work place, health care, intimate relationship, sexual relationship, daily life and own community).

  was used to select statistically significant factors in a multivariate model (entry threshold p<0.10). This procedure enables to test the statistical significance of the variables one by one, deleting those that are not significant.Statistical analyses were performed using the SPSS v17.0 software program (SPSS Inc., Chicago, IL, USA).

  sexual dissatisfaction. Finally, our sample is not a representative random sample of PLWHA but a convenience sample. Furthermore, it is possible that our sample is especially sensitive to discrimination or came to the organization because of the experience of discrimination.

  . Therefore, there is still a dramatic need to develop actions and advocacy addressed to reduce HIV-related stigma. .M. & Chaudoir, S.R.(2009). Living with a concealable stigmatized identity: the impact of anticipated stigma, centrality, salience, and cultural stigma on psychological distress and health. Journal of Personality and Social Psychology, 97(4), 634-651. Rao, D., Angell, B., Lam, C. & Corrigan, P. (2008). Stigma in the workplace: employer attitudes about people with HIV in Beijing, Hong Kong, and Chicago. Social Science & Medicine, 67(10), 1541-1549. Siegel, K., Schrimshaw, E.W. & Lekas, H.M. (2006). Diminished sexual activity, interest, and feelings of attractiveness among HIV-infected women in two eras of the AIDS epidemic. Archives of Sexual Behavior, 35(4), 437-449. Spielberg, F., Branson, B.M., Goldbaum, G.M., Lockhart, D. Kurth, A., Celum, C., Rossini, A., Critchlow, C.W. & Wood, R.W. (2003). Overcoming barriers to HIV testing: preferences for new strategies among clients of a needle exchange, a sexually transmitted disease clinic, and sex venues for men who have sex with men. Journal of Acquired Immune Deficiency Syndromes, 33, 318-328. Subramanian, T., Gupte, M.D., Dorairaj, V.S., Periannan, V. & Mathai, A.K. (2009). Psycho-social impact and quality of life of people living with HIV/AIDS in South India. AIDS Care, 21(4)4, 473-481. Troussier, T. & Tourette-Turgis, C. (2006). The quality of life from a sexual and emotional point of view has a positive effect on prevention for patients living with HIV. Sexologies, 15(3), 165-175.UNAIDS(2000). Protocol for the identification of discrimination against people living with HIV. UNAIDS: Genève.

Table 1 .

 1 Characteristics of the "AIDES et toi" survey respondents (n= 521)

	Frequency or mean
	(%)

Table 2 .

 2 Discrimination and stigma descriptive results -"AIDES et toi" survey -n= 521

	(Strongly)Agree	(Strongly)Disagree
	N (%)	N (%)

http://mc.manuscriptcentral.com/ac-phm-vcy Health Sciences

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Acknowledgements

We thank all the people who answered the "AIDES et toi" survey and all those who participated in the data collection. We thank our colleagues Joanne Otis and Martin Blais from the University of Québec, for their participation in the design of the survey and the preparation of the database, and Marie Préau from the Psychology Department of Nantes University, for her helpful comments of the draft. Finally, we thank Grace Cunnane, for her valuable help with the correction of the present article.


Matthew C H Jukes

Dr Constance A Nyamukapa
email: c.nyamukapa03@imperial.ac.uk.

S Gregson

M Wambe

P Mushore

B Lopman

Z Mupambireyi

K Nhongo

Causes and consequences of Causes and consequences of psychological psychological psychological psychological d d d distress istress istress istress among o among o among o among orphans rphans rphans rphans in e in e in e in eastern Zimbabwe astern Zimbabwe astern Zimbabwe astern Zimbabwe

Causes and consequences of psychological distress among orphans in eastern Zimbabwe

African countries with generalised epidemics [START_REF] Barnett | AIDS in the 21st Century: Disease and Globalization[END_REF]Watts et al., 2005). There is great concern, therefore, for the psychological well-being of children orphaned or otherwise made vulnerable in the context of HIV/AIDS (OVC) (Barnett and Blaikie,1992;[START_REF] Barbarin | Economic status, Community Danger and Psychological Problems among South African Children[END_REF] and substantial funds are being channelled into programmes of psychological support (UNAIDS & UNICEF, 2004;Horizon Report, 2005).

There is increasing scientific evidence that OVC, in general, suffer increased psychological distress in sub-Saharan African settings [START_REF] Makame | Psychological well-being of orphans in Dar El Salaam, Tanzania[END_REF]Atiwane et al, 2005;[START_REF] Basaza | Chapter 2: The Impact of HIV/AIDS on Children: Lights and Shadows in the "Successful Case" of Uganda. AIDS, Public Policy & Child Well-Being[END_REF][START_REF] Chatterji | The Well-Being of Children Affected by HIV/AIDS in Lusaka Zambia and Gitarama Province, Rwanda: Findings from a study[END_REF][START_REF] Foster | Factors leading to the establishment of childheaded households: the case of Zimbabwe[END_REF][START_REF] Oburu | Social adjustment of Kenyan orphaned grandchildren, perceived caregiving stresses and discipline strategies used by their fostering grandparents[END_REF][START_REF] Nampanya-Serpell | Social and Economic Risk Factors for HIV/AIDS-Affected Families in Zambia[END_REF][START_REF] Cluver | The Mental Health of Children orphaned by AIDS: A review of International and South African Research[END_REF]. However, less is known about the consequences of psychological distress in these contexts and understanding about the effectiveness of interventions remains limited [START_REF] King | Interventions for improving the psychological well-being of children affected by HIV/AIDS (Protocol)[END_REF]. There is growing recognition that not all OVC require external interventions [START_REF] Evans | Social networks, migration and care in Tanzania -caregivers' and children's resilience to coping with HIV/AIDS[END_REF]Masten 2001;[START_REF] Nyamukapa | HIV-Associated orphanhood and children's psychological distress: theoretical framework tested with data from Zimbabwe[END_REF], and that, in some instances, inappropriately targeted interventions can be harmful [START_REF] Neimeyer | Searching for the meaning of meaning: grief therapy and the process of reconstruction[END_REF] and may undermine resilience acquired through effective responses to adversity including access to community support [START_REF] Summerfield | Cross cultural perspectives on the medicalisation of human suffering, in Posttraumatic Distress Disorder[END_REF]. Therefore, a better understanding is needed of the characteristics and circumstances of children who require support (i.e. moderating factors) as well as the factors that lie on (i.e. mediating factors) the causal pathway between orphanhood and psychological distress [START_REF] Cluver | The Mental Health of Children orphaned by AIDS: A review of International and South African Research[END_REF][START_REF] Nyamukapa | HIV-Associated orphanhood and children's psychological distress: theoretical framework tested with data from Zimbabwe[END_REF].

In this paper, we address this gap in understanding through an in-depth study conducted in Manicaland, eastern Zimbabwe. We use detailed quantitative and qualitative data to test a recently published theoretical framework describing factors that moderate and mediate psychological distress amongst OVC [START_REF] Nyamukapa | HIV-Associated orphanhood and children's psychological distress: theoretical framework tested with data from Zimbabwe[END_REF] and to describe local perceptions on how these factors might be addressed.

Methods

Methods Methods Methods

Theoretical framework

The theoretical framework used in the study is shown in Figure 1. A full description of the framework and its derivation has been published [START_REF] Nyamukapa | HIV-Associated orphanhood and children's psychological distress: theoretical framework tested with data from Zimbabwe[END_REF]. In brief, the effect of orphanhood on psychosocial distress depends on the social context. Within a given social context, children may be more or less likely to suffer from psychological distress (or to develop resilience) depending on 'moderating' factors such as their sex, age, nature, social background and form and timing of parental loss. Orphanhood can result in immediate, possibly short-term, effects (e.g. trauma) as well as intermediate effects that develop over time and have a more gradual effect on psychological well-being (e.g. poor clothing). These 'mediating' factors can cause psychological distress and are more common in orphaned children. Psychological distress, in turn, can have a number of consequences including a greater propensity to engage in risky sexual behaviour.

A number of different forms of psychological distress can result from losing a parent or caregiver. However, in the current study, we focus on depression and anxiety. [START_REF] Beusenberg | A User's Guide to the Self Reporting Questionnaire (SRQ)[END_REF].

A psychological distress variable was constructed using factor analysis. Because the factor analysis suggested a single factor solution without great variability on factor loadings, an outcome score was created by summing all variables with factor loadings ≥0.3. Seventeen items with factor loadings of ≥0.3 were obtained from the 20 questions asked to children relating to psychological distress (Table 1). Based on these 17 items, the Cronbach alpha reliability coefficient was 0.73. Dichotomous variables were created for each moderating factor and immediate and intermediate effect of orphanhood. Moderating factors investigated were sex, age (12-15 years versus ≥16 years), form of orphanhood (double, maternal and paternal) and duration of parental loss (0-1 year, 2-4 years, 5-17 years, and ≥18 years). Immediate effects of orphanhood investigated were trauma from living in a household with a death in the last 3 years or a sick adult member, stigma and discrimination (being treated worse than other children in the household), frequent residence changes (> 1 move), and residence in a poorer household (poorest quintile of households based on ownership of assets).

Intermediate effects examined were care by a less closely-related caregiver (non-parent), inadequate provision of basic needs (health care, school fees and clothing by carer), inconsistent parenting (> 1 change), child labour (waged labour outside the household or > 20 hours work per week on the family land), physical abuse (beaten by an adult household member in the last month), living apart from siblings, and not being enrolled in school.

The effect of external support (targeted to the household or direct to the OVC) was investigated as a possible mitigating factor for the effect of orphanhood on psychological distress. The psychological distress scores were 'count' data and were therefore modelled using Poisson regression. Psychological distress scores were compared for orphans versus nonorphans and the possible moderating effects of sex and age on the relationship between orphanhood and psychological distress were evaluated. Multivariate models were developed to: (i) measure associations between the hypothesized moderating and mediating factors and psychological distress; and (ii) establish whether increased exposure to these determinants accounted for the greater psychological distress observed in orphaned children. Logistic regression was used to investigate associations between psychological distress and risky behaviours controlling for sex and age.

Qualitative methods

Qualitative investigations were conducted to identify locally-acceptable intervention strategies that addressed the mediating factors associated with psychological distress.

Thirteen focus group discussions (FGDs) were held with children (n=4) and caregivers (n=4), local community members (n=2), adults orphaned during childhood (n=2), and survey interviewers (n=1). Village community workers recruited 8-13 participants for each FGD with roughly equal numbers of males and females. The FGDs were held within the community and were facilitated by CN with help from another qualified social worker. The discussions were held in the local language (Shona) and were recorded on tape and flipcharts. The topics covered in the FGDs included the local understandings of psychological distress, the relevance and suitability of the study methods, the evolution and adequacy of the extended family orphan care system, and measures that might reduce children's psychological distress. Only findings on the last of these topics are presented in this paper.

The data were translated from Shona into English and analysed manually (by CN) using content theme analysis. This involved coding recurring themes and interpreting the coded

Results

Results Results Results

Associations between orphanhood and psychological distress Girls reported more psychological distress than boys (Coeff: 0.22; 95% CI 0.15-0.31).

Older children reported less psychological distress than younger children but the difference was only statistically significant for boys (Coeff: -0.27; 95% CI -0.50--0.05). After controlling for sex and age, orphans showed greater psychological distress than nonorphans (Coeff: 0.15; 95% CI 0.03-0.26; P=0.013) (Figure 2a). This was also true for girls and boys separately. For girls, the heightened psychological distress was most evident in paternal orphans. In boys, paternal and double orphans were worst affected.

For paternal orphans, greater psychological distress was seen for all durations of parental loss (Figure 2b). Maternal orphans who lost their parents >4 years ago reported less psychological distress than those whose mothers were still alive, suggesting high levels of resilience.

Causal pathways between orphanhood and psychological distress

The frequencies of experiencing the effects of orphanhood hypothesized to lie on the causal pathway between orphanhood and greater psychological are shown in Table 2, for all children in the study sample. All categories of orphan were more likely than nonorphans to live in households with a recent death (69% for all orphans vs. 5% for nonorphans; P<0.001) and to be cared for by a non-parent (61% vs. 19%; P<0.001). Paternal orphans were the most likely to live with a seriously ill household member (57%) and to experience child labour (36%). Maternal orphans were five times more likely to experience stigma than non-orphans (10% vs. 2%; P=0.05). More maternal and double orphans than non-orphans had experienced relocation (14% and 14% vs. 4%; P<0.05), changes in caregiver (23% and 28% vs. 4%; P<0.01), and separation from siblings (25% and 24% vs. 12%; P<0.05). Residence in a poorer household and child abuse were equally common in the orphan and non-orphan groups (P>0.05).

Tests for associations between immediate and intermediate effects of orphanhood and psychological distress showed strong positive associations for: (i) living in a household with a recent death, (ii) living in a household with a seriously ill adult member, (iii) suffering stigma, (iv) inadequate care, (v) child labour, (vi) physical abuse, and (vii) being out of school (Table 2). Multiple changes in residence and caregiver, residence in a poorer household, care by a non-parent, and sibling separation were not associated with greater psychological distress.

In the multivariate models of orphanhood and psychological distress, the effects of orphanhood (overall) and double orphanhood seen in the sex-and age-adjusted models became non-significant after controlling for the effects of orphanhood, suggesting that these factors do lie on the causal pathway (Table 3). For paternal orphans, the effect of orphanhood weakened but remained borderline statistically significant. Trauma, stigma, inadequate care, child labour, child abuse, and being out of school contributed to orphans' greater psychological distress. Double (45%), maternal (41%) and paternal (40%) orphans were all more likely than nonorphans (12%) to live in households that received external support (P<0.001). However, whilst residence in a household receiving support had a (non-significant) protective effect against psychological distress for maternal orphans, this was associated with higher distress amongst double and paternal orphans and had no effect for orphans overall (Table 3).

Consequences of psychological distress for early sexual risk behaviour and substance abuse in adolescence

Relatively few children in the study had started sex (8%) or taken alcohol or other drugs (7%). Psychosocial distress is a standardized variable (Mean (M) = 0, Standard deviation (SD) = 1) so the odds ratios in this analysis can be interpreted as increased odds of engaging in risk behaviour associated with a 1 SD increase in psychosocial distress.

Psychosocial distress was not associated with having engaged in sex (OR: 1.05, 95% CI 0.88-1.26; P=0.5) or having drunk alcohol or smoked cigarettes (OR: 1.16, 0.97-1.39; P=0.1).

Measures to reduce children's psychological distress (qualitative research findings)

Most of the factors associated with psychological distress in the survey data related to the nature and quality of care. In the qualitative data, concerns were frequently expressed about the characteristics of caregivers and it was suggested that more careful selection of caregivers might help to address these problems.

"A carer should be someone who volunteers ... They should be sociable, not mean, and able to guide the child morally and provide food and clothes. Ideally, they should be a relative but … they could be anybody with these qualities. Even among relatives, some do and some do not. Those who don't will ill-treat orphans by giving them hard chores or chores that are inappropriate for their age, refuse them food, or fail to send them to school or to buy them good clothes. Only those who can treat orphans well … and do things that help the child forget the pain of the loss should take in children."

Children's focus group discussion (mixed OVC and non-OVC), subsistence farming area Adults agreed with these suggestions and, generally, grandparents were preferred as caregivers for orphaned children because of their maturity, wisdom in understanding children's emotional needs, experience with raising children, and fewer responsibilities.

There was less agreement, however, about whether children themselves should be involved in selecting their caregivers.

The qualitative data also suggested that more support for caregivers might (indirectly) reduce orphans' psychological distress. Often, caregivers had also suffered the loss of close relatives and their own grief sometimes caused them to be withdrawn, irritable and insensitive. As in a number of studies now in sub-Saharan Africa, we found associations between orphanhood and psychological distress in populations in eastern Zimbabwe where HIV prevalence in adults exceeds 20% [START_REF] Gregson | HIV Decline Associated with Behaviour Change in Eastern Zimbabwe[END_REF] and orphan levels continue to rise (Watts et al., 2005). However, unlike in a larger national study in Zimbabwe [START_REF] Nyamukapa | HIV-Associated orphanhood and children's psychological distress: theoretical framework tested with data from Zimbabwe[END_REF], we did not find evidence that greater psychological distress might contribute to the earlier sexual risk behaviour reported for orphans in this population [START_REF] Gregson | HIV Infection and reproductive health in teenage women orphaned and made vulnerable by AIDS in eastern Zimbabwe[END_REF] and elsewhere [START_REF] Birdthistle | From affected to infected? Orphanhood and HIV risk among female adolescents in urban Zimbabwe[END_REF][START_REF] Kang | Maternal versus paternal orphans and HIV/STI risk among adolescent girls in Zimbabwe[END_REF][START_REF] Thurman | Sexual risk behaviour among South African adolescents: is orphan status a factor?[END_REF].

On average, boys and girls experiencing all forms of orphanhood had higher levels of psychological distress than their non-orphaned counterparts. However, a substantial minority of orphans did not exhibit higher than average distress and maternal orphans whose mothers had died more than five years previously tended to have lower levels of psychological distress than non-orphans at any given age. This finding is consistent with suggestions that orphaned children may acquire resilience over time (Masten, 2001) although a similar result was not obtained for paternal orphans.

Being out of school was associated with greater psychological distress in childhood and was more common in orphans, as has been found in Zimbabwe nationally [START_REF] Nyamukapa | HIV-Associated orphanhood and children's psychological distress: theoretical framework tested with data from Zimbabwe[END_REF] and in South Africa [START_REF] Cluver | The Mental Health of Children orphaned by AIDS: A review of International and South African Research[END_REF]. Inadequate care, in the form of basic needs not being met, was also associated with greater psychological distress; a finding which is consistent with data from a national survey in Zimbabwe showing a positive association between extreme poverty and psychological distress [START_REF] Nyamukapa | HIV-Associated orphanhood and children's psychological distress: theoretical framework tested with data from Zimbabwe[END_REF].

In addition, being cared for by someone other than a parent, child labour, physical abuse, and (less commonly reported) stigma and discrimination were associated with psychological distress and more common in orphans. After adjusting for these experiences, the statistical associations between orphanhood and psychological distress disappeared or weakened, suggesting that they contribute to the higher levels of distress observed in orphans.

The study is limited by its relatively small sample size and use of cross-sectional data.

Associations found in the data, such as those between psychological distress and risky behaviours, may be due to reverse causation. The study relied on self-reports by children; thus, we were unable to investigate psychological distress in children under 12 years of age and the data may be subject to reporting bias. Children -and orphaned children in particular -may tend to under-report (to avoid disclosure of their orphan status) or exaggerate (to obtain assistance) their levels of psychological distress. The study design did not permit investigation of the effects of community level factors that might moderate the effects of orphanhood. In a study that purposefully oversampled orphans, 37% of children lived in households receiving external OVC support. As in a national survey in Zimbabwe [START_REF] Nyamukapa | HIV-Associated orphanhood and children's psychological distress: theoretical framework tested with data from Zimbabwe[END_REF], psychological distress in children reached by external support programmes remained high even after adjusting for other factors including extreme poverty.

Longitudinal studies are needed to scientifically evaluate the impact of these programmes particularly since they typically target those in greatest need and the benefits of support may take time to show through. However, our findings could also reflect limitations in these programmes. Addressing factors that lie on the causal pathway between orphanhood and psychological distress could increase the effectiveness of these programmes. Many of these factors relate closely to the quality of care for orphaned children and focus group participants in the study suggested that this might be improved by addressing shortcomings in the selection of caregivers and the support made available to them. Thus, specific programmes might include community-based counselling and support for caregivers and courses in parenting skills and responsibilities -which, in turn, could include modules on caregiver selection and support, children's rights (e.g. in relation to child labour, abuse, basic needs and school attendance), and stigma.

  enormous increases in adult mortality and orphanhood in sub-Saharan

  1,469 children aged 0-18 years, stratified to give roughly equal numbers of paternal, maternal and double orphans and non-orphans, was drawn at random from the second round of a phased household survey in eight rural locations in Manicaland province, eastern Zimbabwe between February 2002 and March 2003. One thousand and .3%) of these children were traced and agreed to be interviewed approximately one year later in each location (December 2002 to March 2004). Interviews were conducted by qualified social workers and questions on psychological distress were asked to 551 children aged 12-18 years (272 male and 279 female); 527 (96%) children provided complete data -185 double orphans, 109 maternal orphans, 150 paternal orphans and 83 non-orphans. The questions were adapted from the World Health Organisation Self-Report Questionnaire on depression and anxiety which has been validated in Zimbabwe and 12 other African countries

  consequences of psychological distress were assessed using two variables describing risk behaviours for the 280 children aged 15 years and over -commencement of sexual activity and substance abuse (alcohol and other drugs).

  from the different groups were compared and differences and similarities were noted. The study was approved by the St. Mary's Research Ethics Committee (reference number: 04/Q0403/130), the Biomedical Research and Training Institute (reference number AP65/05), and the Medical Research Council of Zimbabwe (reference number MRCZ/A/990).

  (caregivers) need to be trained on childcare issues to prevent them from illtreating children in their care. They too are grieving and, like us, need help. They should get somebody to sit down with them and comfort them … to help them understand the consequences of their loss …and the implications of their being emotionally drained on the children they are looking after …" Female, paternal orphan, aged 16 years, Children's focus group discussion, forestry estate Regular school attendance was seen as another way of minimising orphans' psychological distress. Orphaned children viewed school as a safe haven for acquiring life skills (including handling emotional problems), for grieving (through sharing experiences with others in similar situations), and for creating social networks. The school environment offered children time to be children. "If we don't go to school, we miss the chance to learn a lot of knowledge about life and skills. You may not be good in school but just being in school opens your mind to a lot of things like how to make use of available resources (e.g. agriculture) and how to solve problems. Bible teaching and teacher instructions help mould behaviour and give direction." Male, paternal orphan, aged 17 years, Children's focus group discussion, subsistence farming area Discussion Discussion Discussion Discussion

  Figure captionsFigure captions Figure captions Figure captions

  Figure 2

Immediate / short term consequences

	Parental or caregiver death
	Father/mother/dual orphanhood, prior
	deaths, sequence of deaths
	Immediate effects	Intermediate effects
	Trauma Stigma & discrimination Relocation Poorer households Less closely-related caregiver & household head (including child heads) Loss of sole breadwinner	Inadequate care: diet, clothes, shelter, health & educational support … Inconsistent parenting Child labour Child abuse Sibling separation
	Chronic trauma, poor health (mental/physical),
	adjustment problems, absenteeism from school,
	low self-esteem, low future expectations,
	dropping out of school, street life, poor school grades

Long term / cumulative: early adulthood consequences

  Note: Adapted from[START_REF] Nyamukapa | HIV-Associated orphanhood and children's psychological distress: theoretical framework tested with data from Zimbabwe[END_REF]. Bold type indicates effects for which evidence was found in the study. Grey type indicates effects tested in the study for which no evidence was found.Standard type indicates effects not tested in the current study.

		Social context
		Moderating factors Child's nature (age/gender/child resilience), nature of illness, relationships to and sequence of prior deaths, duration of parental loss, family cohesion and functioning, social connectedness F o r
		P
		e
		e r
	F O R M S	R (All dependent on duration, severity, proximity of stressors) Psychological distress e Attention deficit/hyperactivity, depression-anxiety, conduct behaviour, eating & elimination, learning difficulties, psychosomatic, bipolar disorders v i e
		w
	C O N S U E Q	O n l Chronically traumatized adults, fewer educational qualifications & skills, low employment prospects, limited intergenerational mentoring & skills transfers, risky behaviour (sexual/drug/alcohol), poverty, unstable unions, early parenting, chronic illness/HIV, family disintegration, destroyed family networks y
	E
	N C	National level (development) consequences Increased demand for health & social services,
	E S	loss of human capital investment, erosion of economic capital, economic, political & social instability

Table 1 . Psychosocial distress variable items factor loading results: children's responses (12-18 years olds)

 1

	Question items	Factor loadings
	1 Do you cry more than usual?	0.55
	2 Do you feel tense, nervous or worried?	0.54
	3 Do you feel tired all the time?	0.54
	4 Do you have uncomfortable feelings in your stomach?	0.48
	5 Do you find it difficult to make decisions?	0.47
	6 Is your appetite poor?	0.46
	7 Do you feel more unhappy than usual?	0.45
	8 Do you feel a worthless person?	0.44
	9 Do your hands shake?	0.43
	10 Do you sleep badly?	0.43
	11 Is your digestion poor?	0.40
	12 Are you easily frightened?	0.40
	13 Do you get tired easily?	0.39
	14 Do you have trouble thinking clearly?	0.38
	15 Do find it difficult to enjoy your daily activities?	0.37
	16 Has the thought of ending your life been in your mind?	0.31
	17 Do you often have headaches?	0.31
	Question items with <0.3 factor loadings: not used
	18 Is your daily work suffering?
	19 Are you able to play a useful part in life?
	20 Have you lost interest in things?

Table 2 . Hypothesised determinants and observed effects on psychological distress in 527 children aged 12-18 years

 2

					Effect on psychosocial distress
		Information				Test for difference
	Effects of orphanhood	source	Number	%	Coeff	95% CI	P-value
	Immediate effects
	Trauma -death in household	Caregiver	312	59	0.10	0.02-0.18	0.014
	Trauma -illness in household	Caregiver	266	50	0.10	0.03-0.18	0.010
	Stigma and discrimination	Child	29	6	0.41	0.27-0.56	<0.001
	Relocation	Child & caregiver	56	11	0.10	-0.03-0.22	0.121
	Residence in poorest quintile of households	Caregiver	178	34	0.00	-0.08-0.08	0.988
	Less closely-related caregiver (non-parent)	Child & caregiver	360	68	0.04	-0.04-0.12	0.327
	Intermediate effects
	Inadequate care	Child & caregiver	417	79	0.24	0.14-0.35	<0.001
	Not enrolled in school	Child	76	14	0.26	0.14-0.38	<0.001
	Inconsistent parenting	Child & caregiver	86	16	-0.02	-0.12-0.09	0.774
	Child labour	Child	172	33	0.19	0.10-0.27	<0.001
	Physical abuse	Child	75	14	0.27	0.17-0.38	<0.001
	Sibling separation	Caregiver	102	19	-0.08	-0.19-0.02	0.114
	Mitigating factors
	Household received external support	Caregiver	196	37	0.03	-0.05-0.11	0.498

Table 3 . Multivariate Poisson regression tests for experiences on the causal pathway between orphanhood and psychological distress, by form of orphanhood, in children aged 12-18 years Model / effects of orphanhood

 3 Note: Adapted from[START_REF] Nyamukapa | HIV-Associated orphanhood and children's psychological distress: theoretical framework tested with data from Zimbabwe[END_REF]. Bold type indicates effects for which evidence was found in the study. Grey type indicates effects tested in the study for which no evidence was found. Standard type indicates effects not tested in the current study.

		Orphans (444)	Double orphans (185)	Maternal orphans (109)	Paternal orphans (150)
		Test for difference	Test for difference	Test for difference	Test for difference
		Coeff	P-value	Coeff	P-value	Coeff	P-value	Coeff	P-value
	Sex-and age-adjusted model	0.15	0.013	0.13	0.040	0.08	0.245	0.21	0.001
	Full multivariate model	0.07	0.339	-0.04	0.712	-0.02	0.873	0.17	0.044
	Immediate effects
	Trauma -death in household	0.10	0.040	0.11	0.214	0.17	0.063	0.02	0.767
	Trauma -illness in household	0.09	0.028	0.08	0.157	-0.02	0.837	0.22	0.001
	Stigma and discrimination	0.26	<0.001	0.23	0.066	0.42	0.001	0.31	0.027
	Relocation	0.10	0.151	0.14	0.167	0.17	0.192	-0.07	0.636
	Residence in poorest quintile of households	-0.08	0.090	-0.01	0.928	-0.20	0.011	-0.05	0.432
	Less closely-related caregiver (non-parent)	0.09	0.046	-	-	0.02	0.842	0.11	0.137
	Intermediate effects
	Inadequate care	0.19	0.001	0.23	0.007	0.30	0.001	0.14	0.110
	Not enrolled in school	0.17	0.009	0.24	0.009	-0.03	0.808	0.16	0.089
	Inconsistent parenting	-0.03	0.611	-0.08	0.249	0.11	0.345	0.19	0.207
	Child labour	0.13	0.006	0.16	0.015	0.14	0.122	0.13	0.061
	Physical abuse	0.21	<0.001	0.20	0.010	0.22	0.026	0.34	<0.001
	Sibling separation	-0.11	0.044	0.00	0.963	-0.24	0.018	-0.04	0.711
	Mitigating factors
	Houehold received external support	0.00	0.994	0.16	0.017	-0.13	0.140	0.17	0.044

/ short term consequences

	Chronic trauma, poor health (mental/physical),
	adjustment problems, absenteeism from school,
	low self-esteem, low future expectations,
	dropping out of school, street life, poor school grades

Long term / cumulative: early adulthood consequences

		F o r	Moderating factors	Social context
		Child's nature (age/gender/child resilience), nature of illness, relationships to and sequence of prior deaths, duration of parental loss, family cohesion and functioning, social connectedness P
		e
		e r
			R
	F O R M S	Psychological distress e (All dependent on duration, severity, proximity of stressors) Attention deficit/hyperactivity, depression-anxiety, conduct behaviour, eating & elimination, learning difficulties, psychosomatic, bipolar disorders v i e
			w
	U C O N S E Q	Chronically traumatized adults, fewer educational qualifications & skills, low employment prospects, limited intergenerational mentoring & skills transfers, risky behaviour (sexual/drug/alcohol), poverty, unstable unions, early parenting, chronic illness/HIV, family disintegration, destroyed family networks O n l y
	E
	N C	National level (development) consequences Increased demand for health & social services,
	E S		loss of human capital investment, erosion of economic capital, economic, political & social instability

Table 1 . Psychosocial distress variable items factor loading results: children's responses (12-18 years olds)

 1

	Question items	Factor loadings
	1 Do you cry more than usual?	0.55
	2 Do you feel tense, nervous or worried?	0.54
	3 Do you feel tired all the time?	0.54
	4 Do you have uncomfortable feelings in your stomach?	0.48
	5 Do you find it difficult to make decisions?	0.47
	6 Is your appetite poor?	0.46
	7 Do you feel more unhappy than usual?	0.45
	8 Do you feel a worthless person?	0.44
	9 Do your hands shake?	0.43
	10 Do you sleep badly?	0.43
	11 Is your digestion poor?	0.40
	12 Are you easily frightened?	0.40
	13 Do you get tired easily?	0.39
	14 Do you have trouble thinking clearly?	0.38
	15 Do find it difficult to enjoy your daily activities?	0.37
	16 Has the thought of ending your life been in your mind?	0.31
	17 Do you often have headaches?	0.31
	Question items with <0.3 factor loadings: not used
	18 Is your daily work suffering?
	19 Are you able to play a useful part in life?
	20 Have you lost interest in things?

Table 2 . Hypothesised determinants and observed effects on psychological distress in 527 children aged 12-18 years Information

 2

					Effect on psychosocial distress
						Test for difference
	Effects of orphanhood	source	Number	%	Coeff	95% CI	P-value
	Immediate effects
	Trauma -death in household	Caregiver	312	59	0.10	0.02-0.18	0.014
	Trauma -illness in household	Caregiver	266	50	0.10	0.03-0.18	0.010
	Stigma and discrimination	Child	29	6	0.41	0.27-0.56	<0.001
	Relocation	Child & caregiver	56	11	0.10	-0.03-0.22	0.121
	Residence in poorest quintile of households	Caregiver	178	34	0.00	-0.08-0.08	0.988
	Less closely-related caregiver (non-parent)	Child & caregiver	360	68	0.04	-0.04-0.12	0.327
	Intermediate effects
	Inadequate care	Child & caregiver	417	79	0.24	0.14-0.35	<0.001
	Not enrolled in school	Child	76	14	0.26	0.14-0.38	<0.001
	Inconsistent parenting	Child & caregiver	86	16	-0.02	-0.12-0.09	0.774
	Child labour	Child	172	33	0.19	0.10-0.27	<0.001
	Physical abuse	Child	75	14	0.27	0.17-0.38	<0.001
	Sibling separation	Caregiver	102	19	-0.08	-0.19-0.02	0.114
	Mitigating factors
	Household received external support	Caregiver	196	37	0.03	-0.05-0.11	0.498

Table 3 . Multivariate Poisson regression tests for experiences on the causal pathway between orphanhood and psychological distress, by form of orphanhood, in children aged 12-18 years Model / effects of orphanhood

 3

		Orphans (444)	Double orphans (185)	Maternal orphans (109)	Paternal orphans (150)
		Test for difference	Test for difference	Test for difference	Test for difference
		Coeff	P-value	Coeff	P-value	Coeff	P-value	Coeff	P-value
	Sex-and age-adjusted model	0.15	0.013	0.13	0.040	0.08	0.245	0.21	0.001
	Full multivariate model	0.07	0.339	-0.04	0.712	-0.02	0.873	0.17	0.044
	Immediate effects
	Trauma -death in household	0.10	0.040	0.11	0.214	0.17	0.063	0.02	0.767
	Trauma -illness in household	0.09	0.028	0.08	0.157	-0.02	0.837	0.22	0.001
	Stigma and discrimination	0.26	<0.001	0.23	0.066	0.42	0.001	0.31	0.027
	Relocation	0.10	0.151	0.14	0.167	0.17	0.192	-0.07	0.636
	Residence in poorest quintile of households	-0.08	0.090	-0.01	0.928	-0.20	0.011	-0.05	0.432
	Less closely-related caregiver (non-parent)	0.09	0.046	-	-	0.02	0.842	0.11	0.137
	Intermediate effects
	Inadequate care	0.19	0.001	0.23	0.007	0.30	0.001	0.14	0.110
	Not enrolled in school	0.17	0.009	0.24	0.009	-0.03	0.808	0.16	0.089
	Inconsistent parenting	-0.03	0.611	-0.08	0.249	0.11	0.345	0.19	0.207
	Child labour	0.13	0.006	0.16	0.015	0.14	0.122	0.13	0.061
	Physical abuse	0.21	<0.001	0.20	0.010	0.22	0.026	0.34	<0.001
	Sibling separation	-0.11	0.044	0.00	0.963	-0.24	0.018	-0.04	0.711
	Mitigating factors
	Houehold received external support	0.00	0.994	0.16	0.017	-0.13	0.140	0.17	0.044

http://mc.manuscriptcentral.com/ac-phm-vcy Health Sciences

Acknowledgements Acknowledgements Acknowledgements Acknowledgements

The study was funded by the World Bank through the Partnership for Child Development.

References References References References


Luca ; Bizzocchi
email: bizzocchi@oal.ul.pt

Caaul

Claudio Degli Esposti

Luca Dore

Submillimetre-wave spectrum of diacetylene and diacetylene-d 2

Keywords: Vibration rotation bands, Diacetylene, Hot bands, Pyrolysis, Resonances Vibration rotation bands, Diacetylene, Hot bands, Pyrolysis, Resonances

Rovibrational bands between closely lying bending vibrational states of normal diacetylene and its bideuterated variant have been recorded in the submillimetre-wave region using a source-modulation spectrometer. The two isotopologues were produced by pyrolysis (1200 • C) of benzene or benzene-d 6 vapour in a flow reactor. Measurements of the ν 8ν 6 band and of its ν 9 -associated hot band have been extended up to 615 GHz and 420 GHz, respectively. Rotational and vibrational l-type resonance were taken into account in the analysis of the ν 8 + ν 9ν 6ν 9 band; in addition the cubic anharmonic resonance existing between the v 8 = v 9 = 1 state and the v 3 = 1 stretching state has been considered explicitly in the least-squares fits to the observed frequencies. Very accurate values of the band origins and of numerous spectroscopic constants have been determined for both isotopologues.

Introduction

Diacetylene (H-C ≡ C-C ≡ C-H) and its bideuterated isotopologue are symmetric linear molecules without permanent electric dipole moment. Notwithstanding this, it has been established that the molecular vibrations through the v 6 and v 8 normal modes, involving the two apical C -H bendings, produce an appreciable vibrationally induced dipole moment [1,2]. The magnitude of this effect is quite consistent upon H-D isotopic substitution: it accounts for the small ground-state dipole moment of the asymmetric d 1 isotopologue that allowed the observation of its pure rotational spectrum [3][4][5][6]. More interestingly, it also produces large dipole moment changes with the excitation of v 6 and v 8 bending vibrations, and thus enhanced transition moments for the overtone, combination, and difference bands associated with these quanta. This phenomenon is common to many acetylene-type molecules and is caused by the large values of the second dipole moment derivatives with respect to the C ≡ C -H bending curvilinear coordinates [3,[7][8][9].

Normal diacetylene was the subject in the past of extensive high-resolution infrared investigations (see Refs. [10,11] and references therein), whereas the d 2 -variant was less studied and its vibrational fundamentals are known from low-resolution IR and liquid-phase Raman measurements [12]. In symmetric diacetylenes, the vibrational states v 6 = 1 and v 8 = 1 are located at ca. 630 cm for the normal isotopologue, and at ca. 500 cm -1 for the d 2 variant; in both cases, the energy difference between them is few wavenumber units. The vibrational band ν 8ν 6 has a band origin in the millimetre-wave (mm-wave) region below 100 GHz and, though forbidden, due to the enhanced transition moment it is well suited to be investigated with mm-wave spectroscopy. Differently, the analogous ν 5ν 4 band of the simpler acetylene molecule is placed much more higher in frequency (ν 0 ∼ 3.5 THz [13]) due to the larger separation between the relevant levels.

Earlier MW-spectroscopy studies on dyacetylene were performed by Tanaka and coworkers [14][15][16] who recorded the rotation vibration spectra of the ν 8ν 6 band, and that of the ν 9 associated hot band, in the 20-170 GHz frequency interval. Nowadays, their spectral analyses provide the sole available experimental data set for the mm-wave spectrum of symmetric diacetylenes, and its quality cannot be regarded as fully satisfactory due to the limited frequency and J coverage, and also because of the incomplete rovibrational treatment of the hot band systems.

In this work we have extended to the submillimetre-wave (submm-wave) region the investigation of the ν 8ν 6 band of HC 4 H and of the ν 6ν 8 band of DC 4 D, covering the 85-615 GHz frequency interval and reaching a J quantum number as high as 78. The ν 9 associated hot bands have also been recorded up to a frequency of 420 GHz. Rotational and vibrational l-type resonances have been taken into account in the analyses of the hot band spectra and, in addition, the cubic anharmonic interaction between the v 8 = v 9 = 1 bending combination state and the v 3 = 1 stretching state has been explicitly included in the least-squares fit to the observed transition frequencies. This analysis was supported by the results of recent high-level ab intio calculations [17,18], which provided estimates of a large set of spectroscopic parameters derived from CCSD(T) complete cubic and semi-diagonal quartic force fields. Reliable and very accurate band origins and spectroscopic parameters were obtained for each investigated band.

It should be pointed out that diacetylene, being the simplest polyyne, is an important molecule in many astrophysical environments. In the interstellar medium, the members of this family (together with cyanopolyynes) are thought to represent the main link between the observed gas phase species and the carbonaceous material responsible for the emission of the unidentified infrared bands (UIBs, see for example Refs. [19,20]). Also, they are likely to be important constituents of the C-rich planetary atmospheres, where complex hydrocarbons and nitriles form from the photolytic and catalytic dissociation of CH 4 and N 2 [21,22]. Unfortunately, the search for polyynes in extraterrestrial sources is frustrated by the absence of a permanent dipole moment, which precludes their detection in the radio domain. To date very few mid-infrared astronomical detections of diacetylene have been reported: e.g. in the proto-planetary nebula CRL 618 [20] and in Titan's atmosphere [23].

The situation is likely to change in the near future, since the forthcoming ALMA facility [24] will bring a revolution in astronomical spectroscopy at millimetre/submillimetre wavelengths, opening new perspective in the planetary research. ALMA will resolve the planetary disks down to scales of 100 km: its increased sensitivity and the ability to isolate planetary limbs (thereby increasing the line-of-sight) will allow a search for weaker spectral features and the detection of many new compounds [25]. In this context, diacetylene is a promising target as, in hot regions of planetary atmospheres, its submm-wave vibration-rotation spectrum might be strong enough to allow detection.

F

Experimental details

In the previous spectroscopic studies of normal and bideuterated diacetylenes were prepared by chemical synthesis. In the present investigation diacetylene has been generated by gas phase pyrolysis of benzene (or esadeuterated benzene for DC 4 D) at 1200 • C. The same pyrolysis apparatus previously used to produce other carbon chains (see for example Ref. [26]) was also employed to generate diacetylene. The precursors were flowed at a pressure of ca. 500 mTorr (∼ 67 Pa) through a quartz tube at 1200 • C, which was directly connected to the absorption cell of the mm-wave spectrometer, through which the reaction products were continuously pumped.

Though very weak, signals of the ν 8ν 6 band of HC 4 H could be observed during the pyrolysis process and were used to optimise to the maximum extent the reaction conditions. The spectral measurements were then performed employing a purified sample. The crude products of the pyrolysis reaction were first collected in a large liquid-N 2 -cooled trap placed between the end of the absorption cell and the pumping system, and then transferred into a sample holder by low-temperature trap-to-trap distillation. The sample holder was then placed in a acetone slush bath at a the temperature of -96.5 • C while pumping continuously over it; this allow the nearly complete removal of the more volatile side-products. The remaining material was then allowed to warm until -70 • C and the gaseous fraction, very rich in diacetylene, was readily transferred in a storing sample holder. This material was permanently stored at -25 • C in a refrigerator, and was used to record the spectra at a static pressure of ca. 10 mTorr (∼ 1.3 Pa), renewing the sample in the cell twice a day.

The rovibrational spectra of HC 4 H and DC 4 D were observed in selected frequency regions between 85 and 615 GHz using a source modulation mm-wave spectrometer, which employs four Gunn oscillators (Farran and Carlstrom) as main radiation sources to cover the fundamental frequency range 53-115 GHz. Higher frequencies were generated using three different frequency multipliers, one optimised for the 50-75 GHz band, and a quadrupler and a sextupler operating in the 85-115 GHz frequency interval. The oscillators were phase-locked to a suitable harmonic of the fundamental frequency emitted by a cm-wave solid state source (Wavetek), which was in turn locked to a computer-controlled frequency synthesiser (Schomandl). A Schottky-barrier diode (Millitech) and a liquid-helium-cooled InSb detector (QMC) were used to record the spectra below and above 200 GHz, respectively. The Gunn oscillators were frequency modulated at 16.7 kHz, and the detected signals were demodulated at 2f by a lock-in amplifier, so that the second derivative of the actual spectrum profile was displayed by the computer-controlled acquisition system. The average precision of the frequency measurements was estimated to be 15 kHz.

Observed spectra and analysis

The peculiarities of the submm-wave spectra described in the present work deserve a brief discussion of the relevant energy levels, nuclear spin statistical weights and selection rules. Figure 1, based on the experimental data reported in the literature (see Ref. [18] and references therein), shows the vibrational energy levels of HC 4 H in the 600-900 cm -1 range above the ground state; each state is also labelled with the symmetry species spanned in the D ∞h point group. We observed mm-wave lines between the two singly excited bending states v 6 = 1 and v 8 = 1, and between the bending combinations v 6 = v 9 = 1 and v 8 = v 9 = 1 (indicated with the solid arrows in the plot). Due to the perpendicular nature of these vibration rotation bands, all three P , R, and Q branches are present, and each J transition is split into a multiplet, owing to l-type resonance effects between the different l sublevels.

Symmetric diacetylenes have a set of equivalent hydrogen nuclei (H or D) and two sets of equivalent carbon nuclei which are interchanged by the C 2 symmetry operation. This produces different spin statistical weights according to the symmetry of the rovibrational wave function under the C 2 operation. Table 1 summarises the spin multiplicity for all the vibrational states of HC 4 H and DC 4 D involved in the investigated bands.

The spectra were analysed by expressing each rovibrational term using the formalism originally developed by Yamada and co-workers [27,28], and employed previously to fit the excited state rotational spectra of several carbon chains (see for example Ref. [26]). Briefly, the rovibrational Hamiltonian is first represented using the symmetric top basis functions v l6 6 , v l8 8 , v l9 9 ; J, k , with the restriction k = l 6 + l 8 + l 9 . Employing the simplified notation |l 6 , l 8 , l 9 ; k the elements of the Hamiltonian matrix which are diagonal in the quantum numbers v t and l t are:

l 6 , l 8 , l 9 ; k| Ĥ|l 6 , l 8 , l 9 ; k = G v + x L(69) l 6 l 9 + x L(89) l 8 l 9 + B v + d JL(69) l 6 l 9 + d JL(89) l 8 l 9 {J(J + 1) -k 2 } -D v {J(J + 1) -k 2 } 2 + H v {J(J + 1) -k 2 } 3 , (1)
where G v is the pure vibrational energy of the |v 6 , v 8 , v 9 state. The off-diagonal vibrational l-type doubling terms (∆l t ± 2, ∆l ′ t ∓ 2, ∆k = 0) are given by the expression:

l t ± 2, l t ′ ∓ 2; k| Ĥ|l t , l t ′ ; k = 1 4 {r tt ′ + r tt ′ J J(J + 1)} × (v t ∓ l t )(v t ± l t + 2)(v t ′ ∓ l t ′ + 2)(v t ′ ± l t ′ ) ;
(2) while the off-diagonal rotational l-type doubling terms (∆l t ± 2, |∆k| = 2) have the general form:

l t ± 2,l t ′ ; k ± 2| Ĥ|l t , l t ′ ; k = 1 4 {q t + q tJ J(J + 1)} × (v t ∓ l t )(v t ± l t + 2) × [J(J + 1) -k(k ± 1)][J(J + 1) -(k ± 1)(k ± 2)] . (3)
The resulting energy matrix is factorised into symmetric and antisymmetric blocks adopting Wang-type linear combinations of wavefunctions [27]. Any sublevel belonging to a given vibrational state can be labelled through its k value and by the '+' or '-' superscripts which designate the sign of the symmetrised linear combination or, alternatively, with the e, f parity label [29] using the correspondence + → e, -→ f for even k and vice versa for odd k.

As mentioned above, the anharmonic interaction between the vibrational states v 3 = 1 and v 8 = v 9 = 1, arising from the normal coordinate force constant φ 389 , has been considered in the present spectral analysis. The corresponding off-diagonal Submm-wave spectrum of diacetylene matrix elements in the symmetrized basis has the expression [30]:

e 1, 0 0 , 0 0 ; J, 0| Ĥ30 |0, 1 1 , 1 -1 ; J, 0 e = W 389 + W 389J J(J + 1) = 1 2 φ 389 + W 389J J(J + 1) . (4)
Over 200 new transition frequencies have been measured, and the complete list of analysed data is available as supplementary material. In the following subsections some details, dealing with the analyses performed for the various bands investigated, are given. The v 6 = 1 and the v 8 = 1 bending fundamentals are close lying states; their energy difference, |G 6 -G 8 |, is ca. 3 cm -1 in both isotopologues, but in DC 4 D the position is inverted, i.e. v 8 = 1 lies at lower energy. Rovibrational transitions occur between states with the same overall parity, thus for P and R lines (∆J = ±1) having g ↔ u, e ↔ e and f ↔ f transitions are allowed, with spin statistical weights given by Table 1.

Since the value of the rotational constant, B v , is a significant fraction of the vibrational energy separation, the rovibrational levels cross around P (10) transition, the P branch forms a band head and extends at frequency higher than band origin. This is well illustrated in Figure 2, which shows the calculated stick spectrum of the ν 8ν 6 band of HC 4 H at 300 K. It is apparent that both P -and R-type transitions reach the maximum intensity well into the submm-wave region.

These bands had been previously investigated in the 16-168 GHz frequency range by Tanaka and co-workers [14][15][16] who recorded 65 and 44 lines for HC 4 H and DC 4 D, respectively. In the present work we extended the measurements into the submm-wave region, reaching maximum frequencies of 615 GHz for HC 4 H and 550 GHz for DC 4 D. The J interval covered by the measurements was considerably increased, having achieved transitions R(59) and P (77) for both isotopic variants. Some mm-wave lines, that exhibited large residuals in the previous analyses [15,16], were also remeasured. The spectrum of the highest frequency line measured, R(61) f of HC 4 H is presented in Figure 3.

The analysis of the spectra were performed through eqs. ( 1) and (3) expressing the band origin, ν 0 , as G 8 -G 6 for HC 4 H and G 6 -G 8 for DC 4 D. All the previous mm-wave lines were included in the data sets with a reduced weighting factor (w = 1/σ 2 ), in order to take into account their lower measurement precision. Separate fits, performed on homogeneous datasets, allowed to estimate average uncertainties of σ = 15 kHz and σ = 40 kHz for the present measurements and for the literature data [14,15], respectively. The least-squares fits yielded much improved values of the band origins, rotational constants B v , quartic centrifugal distortion constants D v , and l-type doubling constants q t . Furthermore, new determinations of the sextic distortion constants H v and of the centrifugal l-type parameters q tJ were attained. The results are collected in Table 2. They exhibit a good agreement with those previously determined by Matsumura and Tanaka using more limited datasets [14,15], as they are generally coincident within the quoted uncertainties. The bending combination states ν 8 + ν 9 and ν 6 + ν 9 are placed around 850 cm -1 in diacetylene [10]; as for the the singly excited states v 6 = 1 and v 8 = 1, the energy difference between them is ca. 3 cm -1 , with the ν 6 = ν 9 = 1 being the lower level. The v 9 = 1 state is a Π u species, thus the combination with v 6 = 1 (Π u ) give rise to three substates: Σ + g and Σ - g having k = 0, and the doubly degenerate ∆ g with |k| = 2. Analogously, the v 8 = v 9 = 1 state consists of Σ + u , Σ - u , and ∆ u substates. The Σ + and Σ + states belongs to the species e and f , respectively, while the ∆ substates are split by rovibrational l-type resonances into e,f doublets. P -and R-type transitions of this band obey selection rules e ↔ e and f ↔ f , with spin statistical weights given by Table 1. The subband structure of the ν 8 + ν 9ν 6ν 9 of HC 4 H is illustrated in Figure 4.

Previous mm-wave measurements had been already performed by Matsumura et al. [15] in the 24-175 GHz frequency range. They performed first a band by band analysis, then the l-type resonance effects were considered in a coupled rovibrational fit which gave separate sets of spectroscopic parameters for Σ + , Σ - and ∆ substate, because the model employed at that time did not allow to obtain a single set of band constants. These authors noticed that the band origin of the Σ + g -Σ + u subband was red-shifted by ca. 1 cm -1 with respect to the other subbands origins. Furthermore, they found that the effective rotational constants, B, for the Σ + g (k = 0 e ) level of the v 8 = v 9 = 1 state is considerably lower than expected, giving an anomalous value of α 9 , -11.7 MHz, whereas the effective B constants of the other substates gave α 9 values very close to the known experimental value of -12.5 MHz [31]. Both anomalies were attributed to an anharmonic interaction with the v 3 = 1 (Σ + g ) C-C stretching state, ca. 26 cm -1 higher in energy, through the φ 389 normal coordinate force constant. The resonance pushes down the Σ + g sublevels of v 8 = v 9 = 1 state and produces the rotational mixing responsible for its lower effective B value. However, no accurate analysis was performed, and only rough estimates of the resonance parameters, based on reasonable assumptions, were given in Ref. [15].

In the present work we have extended the measurements of the ν 8 + ν 9ν 6ν 9 band into the submm-wave region, covering the 340-420 GHz frequency interval, in which both R and P branches of the vibration rotation spectrum of diacetylene are close to their maximum intensity (see Figure 2). The search for the new submmwave transitions has been guided by the effective subband constants of Ref. [15]. Lines belonging to the symmetry species f (i.e. those of Σ -and ∆ (f ) subbands) were found in a straightforward way, while the e symmetry transitions could not be assigned until a proper treatment of the anharmonic resonance was performed. In particular, the Σ + (k = 0 e ) lines showed displacements up to 1.2 GHz from the corresponding position predicted using the effective spectroscopic constants of Ref. [15].

Fifty-five new transition frequencies reaching R(37) and P (55) were finally assigned. They were analysed together with the previous mm-wave measurements [15] using a model which treats simultaneous all the subbands and includes explicitly the anharmonic resonance with the v 3 = 1 vibrationally excited states. The same weighting scheme used for the ν 8 -ν 6 band was adopted to account for the different precision of the previous measurements [15] and the new submm-wave lines. The rotational constant of the unobserved v 3 = 1 state has been evaluated from the theoretical value of the α 3 parameter [18], and using the experimental ground state B 0 value determined in Ref. [31]. Both off-diagonal resonance parameters W 389 and W 389J (see eq. ( 4)) were found to be important in reproducing the rotational mixing caused by the anharmonic resonance, though they are totally correlated and cannot be simultaneously determined. Therefore, we decided to fix W 389 at the value derived from the ab initio φ 389 normal coordinate cubic force constant [32], whereas W 389J was released in the least-squares fit.

The rovibrational energies were calculated through eqs. ( 1)-( 4) and expressing the band origin, ν 0 as the energy difference between the v 8 = v 9 = 1 and the v 6 = v 9 = 1 states. The fitted parameters for this band are reported in Table 3. The spectroscopic parameters determined include: very accurate values for B and D of both states, the l-type doubling constants q 6 , q 8 , and q 9 , and the vibrational parameters x L(69) , x L(89) , r 69 , and r 89 . The centrifugal corrections r 69J and r 89J could not be simultaneously determined, we thus kept r 89J constrained to zero and optimised r 69J as this latter attained the best reduction of the fit residuals.

The unperturbed vibrational energy difference between the two interacting states, v 3 = 1 and v 8 = v 9 = 1, ∆G v , could not be set free in the analysis due to large correlation between various fit parameters, then its value was optimised through a step-by-step procedure until a minimum of the residuals root mean square was achieved. The optimum fit value of 28.1 cm -1 compares favourably with the experimental one of 24 cm -1 [11].

3.3. ν 6 + ν 9 -ν 8 -ν 9 hot band of DC 4 D
In diacetylene-d 2 , the bending combination states v 6 = v 9 = 1 and v 8 = v 9 = 1 are located at ca. 700 cm -1 . As in the normal isotopologue, the energy difference between them is about 3 cm -1 , but their positions are inverted, i.e. the ν 8 = ν 9 = 1 state is placed at the lower energy. For the ν 6 + ν 9ν 8ν 9 band, mm-wave measurements had been already performed by Matsumura et al. [16] in the 30-150 GHz frequency interval.

We recorded further mm-wave transitions, reaching a maximum frequency of 205 GHz, with the aim of attaining a larger data set for the coupled rovibrational analysis. Using the band constants of Ref. [16], the identification of the 25 new lines was accomplished in a straightforward way. These frequencies were analysed together with the previous measurements adopting the same weighting scheme described in the previous subsections.

In DC 4 D, the vibrational energy difference between the v 8 = v 9 = 1 and the perturbing state v 3 = 1 is about 140 cm -1 [18], thus the resulting resonance effects on the Σ + g substate are expected to be much weaker. However, we found that this anharmonic interaction must be taken into account if one aims at obtaining a satisfactory fit of all subbands simultaneously. The v 3 = 1 state was thus included in the energy level calculation using spectroscopic parameters derived as following: the B value was evaluated from the ground state B 0 of Ref. [33] and from the ab initio α 3 constant [17], the centrifugal distortion constants D, was obtained by scaling the corresponding value of the normal isotopologue, and the φ 389 normal coordinated force constant was taken from the CCSD(T) computed force field of DC 4 D [34].

The rovibrational energies were calculated using eqs. ( 1)-( 4) and the band origin, ν 0 , is expresses as the energy difference between the v 6 = v 9 = 1 and the v 8 = v 9 = 1 states. The fitted parameters for this band are reported in Table 4, they include: accurate values for B and D, the l-type doubling constants q 6 and q 9 , and the vibrational parameters x L(69) , x L(89) , r 69 , and r 89 . The other v 6 -and v 8related l-type doubling parameters were kept fixed at the values determined for the fundamental band, whereas the centrifugal correction parameters q 9J was estimated from the value of the most abundant isotopologue by applying the scaling factor q 9 (DC 4 D)/q 9 (HC 4 H).

Conclusion

The present paper extends the study of the vibration rotation spectra of symmetric diacetylenes into the submm-wave region reaching a frequency as high as 615 GHz. HC 4 H and DC 4 D have been produced using a new method based on a high-temperature ring cleavage reaction of benzene. The bending combination bands ν 8ν 6 of HC 4 H and ν 6ν 8 of DC 4 D have been investigated over a wide frequency range, thus obtaining an improved set of spectroscopic parameters including the sextic centrifugal distortion constants H, which were determined for the first time.

New mm-wave and submm-wave measurements have been also performed for the ν 9 associated hot bands, involving vibrationally excited state up to an energy of 850 cm -1 . The rovibrational analyses of the extended data sets were performed using the linear molecule Hamiltonian developed by Yamada et al. [27], resulting in a single set of spectroscopic constants for each investigated band. The anharmonic resonance which couples the v 3 = 1 (C-C stretch, Σ + g ) state with the Σ + g (k = 0 e ) of the v 8 = v 9 = 1 state has been explicitly taken into account in the least-squares fit to the observed frequencies, assuming the relevant spectroscopic parameters from recent high level theoretical calculations [17,18].

Comparing the fit results of fundamental and hot bands, one can evaluate the value of the vibration rotation interaction constant, α 9 , from each pair of levels yielding: -12.537 MHz and -12.523 MHz for HC 4 H, and -10.103 MHz and -10.136 MHz for DC 4 D. These values compare nicely with the corresponding theoretical values [17] of -12.56 MHz and -10.13 MHz, thus confirming the validity of the present spectral analysis.

The present work complements the recently published studies on the lowest bendings of acetylene and acetylene-d 2 [35,36], whose rovibrational transitions provide a mean for detection of these non-polar molecules with microwave precision. The vibrational energy difference between the v 5 = 1 (Π u ) and v 4 = 1 (Π g ) states is 117 cm -1 in HCCH and 27 cm -1 in DCCD, thus the ν 5ν 4 difference bands occur in the terahertz and far infrared regions. In diacetylene and diacetylene-d 2 , the energy difference between the close lying v 8 = 1 and the v 6 = 1 levels is 2.40 cm -1 and -2.88 cm -1 , respectively. The maximum intensity of the corresponding difference bands is thus placed in the mm-wave region at any excitation temperature, making these molecules suitable targets for ground based observations.

F

J v 6 = 1 Πg 1 e 1 3 2 1 f 3 1 1 2 v 8 = 1 Πu 1 e 3 1 1 2 f 1 3 2 1 v 6 = v 9 = 1        Σ + u 0 e 3 1 1 2 Σ - u 0 f 1 3 2 1 ∆u 2 e 3 1 1 2 f 1 3 2 1 v 8 = v 9 = 1        Σ + g 0 e 1 3 2 1 Σ - g 0 f 3 1 1 2 ∆g 2 e 1 3 2 1 f 3

3. 1 .

 1 ν 8 -ν 6 band of HC 4 H and ν 6 -ν 8 band of DC 4 D

3 . 2 .

 32 ν 8 + ν 9 -ν 6 -ν 9 hot band of HC 4 H

1 v 6 = 1 ( 8 = v 9 Figure 1 .

 161891 Figure1. Vibrational states of diacetylene in the 600-900 cm -1 energy interval above the ground state (from Ref.[18]). The observed vibration rotation band are indicated by the arrows. The dotted line represents the anharmonic interaction considered in the present spectral analysis.

Figure 4 .

 4 Figure 4. Subband structure of the ν 8 +ν 9 -ν 6 -ν 9 band of diacetylene, calculated using the spectroscopic parameters of Table3. The arrows indicate the observed vibration rotation transitions.

Table 1 .

 1 Spin statistical weights of the rovibrational levels of HC4H and DC4D.

	o r
	P
	e
	e r
	R
	e
	v i e
	w
	O n l
	y

Table 2 .

 2 Spectroscopic parameters determined for the ν8 -ν6 band of HC4H and for the ν6 -ν8 band of DC4D a . The quantity in parentheses is one standard deviation in units of the last quoted digit. Weighted root mean square deviation of the fit.

	Molecular Physics		Page 10 of 17
	1	1	2

URL: http://mc.manuscriptcentral.com/tandf/tmph a b Fitted as a mean value for both states. c

Table 3 .

 3 Spectroscopic parameters determined for the ν8 + ν9 -ν6 -ν9 hot band of HC4H a . The quantity in parentheses is one standard deviation in units of the last quoted digit.

	Parameter		v6 = v9 = 1	v8 = v9 = 1	v3 = 1
	ν0	/ MHz	80130.928(25)
	x L(t9)	/ GHz	15.9292(25)	13.3719(24)
	rt9	/ GHz	0.3408(44)	9.6168(44)
	rt9J	/ kHz	-6.129(63)
	Bv	/ MHz	4403.86468(12)	4403.72458(12)	4379.9094 b
	d JL(t9)	/ kHz	-5.12(12)	-14.38(13)
	Dv	/ kHz	0.490455(46)	0.490433(50)	0.47 c
	qt	/ MHz	2.50157(59)	2.44806(54)
	qtJ	/ Hz	-1.188 d	-1.302 d
	q9	/ MHz	6.17893(76)	6.19055(85)
	q9J	/ Hz	-16.04 e	-16.04 e
	∆G f v	/ cm -1		28.1 g
	W389	/ cm -1		6.746 b
	W389J	/ MHz		-0.78907(28)
	σ h w		0.762
	no. of lines	158

a b Assumed value, see text. c Ground state value, from Ref.

[31]

. d Fixed to the ν8 -ν6 band value. e v9 = 2 state value, from Ref.

[31]

. f Vibrational energy difference between the v3 = 1 and the v8 = v9 = 1 states. g Optimised through step-by-step procedure. h Weighted root mean square deviation of the fit.

Table 4 .

 4 Spectroscopic parameters determined for the ν6 + ν9 -ν8 -ν9 hot band of DC4D a . The quantity in parentheses is one standard deviation in units of the last quoted digit.

	Parameter		v6 = v9 = 1	v8 = v9 = 1	v3 = 1
	ν0	/ MHz	84723.340(16)
	x L(t9)	/ GHz	15.2159(54)	14.1230(54)
	rt9	/ GHz	2.0423(93)	2.4263(93)
	rt9J	/ kHz	-36.60(19)
	Bv	/ MHz	3824.38760(32)	3823.05282(35)	3801.9443 b
	d JL(t9)	/ kHz	-11.24(31)	-8.12(36)
	Dv	/ kHz	0.34785(67)	0.34827(63)	0.33 b
	qt	/ MHz	2.2914(14)	2.27713 c
	qtJ	/ Hz	-0.872 c	-1.248 c
	q9	/ MHz	5.0762(65) d	5.0762(65) d
	q9J	/ Hz	-12.8 e	-12.8 e
	∆G f v	/ cm -1		140.0 b
	W389	/ cm -1		11.512 b
	W389J	/ MHz		-0.6070(22)
	σ g w			0.699
	no. of lines		94

a b Assumed value, see text. c Fixed to the ν6 -ν8 band value. d Fitted as a mean value for both states. e Scaled value, see text. f Vibrational energy difference between the v3 = 1 and the v8 = v9 = 1 states. g Weighted root mean square deviation of the fit.

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  Figure 2. Calculated stick spectrum of the ν 8ν 6 band of diacetylene at 300 K. The apparent large line separations is due to the 3:1 intensity alternation due to spin statistical weights. The vertical grey stick at 71.9 GHz indicates the band origin position.Figure 3. Spectrum of the R(61) f line of the ν 8ν 6 band of diacetylene. Six scans with time constant of 0.3 s coadded (total integration time 180 s).

	March 11, 2010 12:44 Molecular Physics diac˙rev March 11, 2010 12:44 Molecular Physics diac˙rev March 11, 2010 12:44 Molecular Physics diac˙rev
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	16		Molecular Physics Taylor & Francis and I.T. Consultant Molecular Physics				15 17
				Diacetylene, ν 8 -ν 6 band
		Band Origin 71.9 GHz	HC 4 H ν 8 -ν 6 band R(61)
	Intensity (a.u.) Intensity (a.u.)
		P branch			R branch
		F o r F o r F o r
	0 615444	100	P 200 300 P 615445 P	400 Frequency (GHz) 500 600 615446 615447 Frequency (GHz)	700	800 615448	900	1000 615449
			e e e
			e r e r e r
				R R R
				e e e
				v i e v i e v i e
				w w w
					O n l O n l O n l
							y y y

: http://mc.manuscriptcentral.com/tandf/tmph URL: http://mc.manuscriptcentral.com/tandf/tmph f URL: http://mc.manuscriptcentral.com/tandf/tmph

Taylor & Francis and I.T. Consultant

Acknowledgements

Support from MIUR (PRIN 2007 funds, project "Trasferimenti di energia, carica e molecole in sistemi complessi") and from the University of Bologna (RFO funds) is gratefully acknowledged.