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Friday, January 14, 2022

Anorexia nervosa

From Wikipedia, the free encyclopedia

Anorexia nervosa
Other namesAnorexia
Gull - Anorexia Miss A.jpg
"Miss A—" depicted in 1866 and in 1870 after treatment. She was one of the earliest case studies of anorexia. From the published medical papers of Sir William Gull.

SpecialtyPsychiatry, Clinical psychology
SymptomsLow weight, fear of gaining weight, strong desire to be thin, food restrictions body image disturbance
ComplicationsOsteoporosis, infertility, heart damage, suicide
Usual onsetTeen years to young adulthood
CausesUnknown
Risk factorsFamily history, high-level athletics, modelling, substance use disorder, dancing
Differential diagnosisBody dysmorphic disorder, bulimia nervosa, hyperthyroidism, inflammatory bowel disease, dysphagia, cancer
TreatmentCognitive behavioral therapy, hospitalisation to restore weight
Prognosis5% risk of death over 10 years
Frequency2.9 million (2015)
Deaths600 (2015)

Why do anorexia patients feel fat? - Anouk Keizer (Utrecht University)

Anorexia nervosa, often referred to simply as anorexia, is an eating disorder characterized by low weight, food restriction, body image disturbance, fear of gaining weight, and an overpowering desire to be thin. Anorexia is a term of Greek origin: an- (ἀν-, prefix denoting negation) and orexis (ὄρεξις, "appetite"), translating literally to "a loss of appetite"; the adjective nervosa indicating the functional and non-organic nature of the disorder. Anorexia nervosa was coined by Gull in 1873 but, despite literal translation, the symptom of hunger is frequently present and the pathological control of this instinct is a source of satisfaction for the patients.

Individuals with anorexia nervosa commonly see themselves as overweight, although they are in fact underweight. The DSM-5 describes this perceptual symptom as "disturbance in the way in which one's body weight or shape is experienced". In research and clinical settings, this symptom is called "body image disturbance". Individuals with anorexia nervosa also often deny that they have a problem with low weight. They may weigh themselves frequently, eat small amounts, and only eat certain foods. Some exercise excessively, force themselves to vomit (in the "anorexia purging" subtype), or use laxatives to lose weight and control body shapes. Medical complications may include osteoporosis, infertility, and heart damage, among others. Women will often stop having menstrual periods. In extreme cases, patients with anorexia nervosa who continually refuse significant dietary intake and weight restoration interventions, and are declared incompetent to make decisions by a psychiatrist, may be fed by force under restraint via nasogastric tube after asking their parents or proxies to make the decision for them.

The cause of anorexia is currently unknown. There appear to be some genetic components with identical twins more often affected than fraternal twins. Cultural factors also appear to play a role, with societies that value thinness having higher rates of the disease. Additionally, it occurs more commonly among those involved in activities that value thinness, such as high-level athletics, modeling, and dancing. Anorexia often begins following a major life-change or stress-inducing event. The diagnosis requires a significantly low weight and the severity of disease is based on body mass index (BMI) in adults with mild disease having a BMI of greater than 17, moderate a BMI of 16 to 17, severe a BMI of 15 to 16, and extreme a BMI less than 15. In children, a BMI for age percentile of less than the 5th percentile is often used.

Treatment of anorexia involves restoring the patient back to a healthy weight, treating their underlying psychological problems, and addressing behaviors that promote the problem. While medications do not help with weight gain, they may be used to help with associated anxiety or depression. Different therapy methods may be useful, such as cognitive behavioral therapy or an approach where parents assume responsibility for feeding their child, known as Maudsley family therapy. Sometimes people require admission to a hospital to restore weight. Evidence for benefit from nasogastric tube feeding is unclear; such an intervention may be highly distressing for both anorexia patients and healthcare staff when administered against the patient's will under restraint. Some people with anorexia will have a single episode and recover while others may have recurring episodes over years. Many complications improve or resolve with the regaining of weight.

Globally, anorexia is estimated to affect 2.9 million people as of 2015. It is estimated to occur in 0.9% to 4.3% of women and 0.2% to 0.3% of men in Western countries at some point in their life. About 0.4% of young women are affected in a given year and it is estimated to occur ten times more commonly among women than men. Rates in most of the developing world are unclear. Often it begins during the teen years or young adulthood. While anorexia became more commonly diagnosed during the 20th century it is unclear if this was due to an increase in its frequency or simply better diagnosis. In 2013, it directly resulted in about 600 deaths globally, up from 400 deaths in 1990. Eating disorders also increase a person's risk of death from a wide range of other causes, including suicide. About 5% of people with anorexia die from complications over a ten-year period, a nearly six times increased risk. The term "anorexia nervosa" was first used in 1873 by William Gull to describe this condition.

In recent years, evolutionary psychiatry as an emerging scientific discipline has been studying mental disorders from an evolutionary perspective. It is still debated whether eating disorders such as anorexia have evolutionary functions or if they are problems resulting from a modern lifestyle.

Signs and symptoms

The back of a person with anorexia

Anorexia nervosa is an eating disorder characterized by attempts to lose weight to the point of starvation. A person with anorexia nervosa may exhibit a number of signs and symptoms, the type and severity of which may vary and be present but not readily apparent.

Anorexia nervosa, and the associated malnutrition that results from self-imposed starvation, can cause complications in every major organ system in the body. Hypokalaemia, a drop in the level of potassium in the blood, is a sign of anorexia nervosa. A significant drop in potassium can cause abnormal heart rhythms, constipation, fatigue, muscle damage, and paralysis.

Signs and symptoms may be classified in physical, cognitive, affective, behavioral and perceptual:

Physical symptoms

Cognitive symptoms

  • An obsession with counting calories and monitoring fat contents of food.
  • Preoccupation with food, recipes, or cooking; may cook elaborate dinners for others, but not eat the food themselves or consume a very small portion.
  • Admiration of thinner people.
  • Thoughts of being fat or not thin enough
  • An altered mental representation of one's body
  • Difficulty in abstract thinking and problem solving
  • Rigid and inflexible thinking
  • Poor self-esteem
  • Hypercriticism and clinical perfectionism

Affective symptoms

Behavioral symptoms

  • Food restrictions despite being underweight or at a healthy weight.
  • Food rituals, such as cutting food into tiny pieces, refusing to eat around others, and hiding or discarding of food.
  • Purging (only in the anorexia purging subtype) with laxatives, diet pills, ipecac syrup, or diuretics to flush food out of their system after eating or engage in self-induced vomiting.
  • Excessive exercise, including micro-exercising, for example making small persistent movements of fingers or toes.
  • Self harming or self-loathing.
  • Solitude: may avoid friends and family and become more withdrawn and secretive.

Perceptual symptoms

  • Perception of self as overweight, in contradiction to an underweight reality (namely "body image disturbance" )
  • Intolerance to cold and frequent complaints of being cold; body temperature may lower (hypothermia) in an effort to conserve energy due to malnutrition.
  • Altered body schema (i.e. an implicit representation of the body evoked by acting)
  • Altered interoception

Interoception

Interoception involves the conscious and unconscious sense of the internal state of the body, and it has an important role in homeostasis and regulation of emotions. Aside from noticeable physiological dysfunction, interoceptive deficits also prompt individuals with anorexia to concentrate on distorted perceptions of multiple elements of their body image. This exists in both people with anorexia and in healthy individuals due to impairment in interoceptive sensitivity and interoceptive awareness.

Aside from weight gain and outer appearance, people with anorexia also report abnormal bodily functions such as indistinct feelings of fullness. This provides an example of miscommunication between internal signals of the body and the brain. Due to impaired interoceptive sensitivity, powerful cues of fullness may be detected prematurely in highly sensitive individuals, which can result in decreased calorie consumption and generate anxiety surrounding food intake in anorexia patients. People with anorexia also report difficulty identifying and describing their emotional feelings and the inability to distinguish emotions from bodily sensations in general, called alexithymia.

Interoceptive awareness and emotion are deeply intertwined, and could mutually impact each other in abnormalities. Anorexia patients also exhibit emotional regulation difficulties that ignite emotionally-cued eating behaviors, such as restricting food or excessive exercising. Impaired interoceptive sensitivity and interoceptive awareness can lead anorexia patients to adapt distorted interpretations of weight gain that are cued by physical sensations related to digestion (e.g., fullness). Combined, these interoceptive and emotional elements could together trigger maladaptive and negatively reinforced behavioral responses that assist in the maintenance of anorexia. In addition to metacognition, people with anorexia also have difficulty with social cognition including interpreting others’ emotions, and demonstrating empathy. Abnormal interoceptive awareness and interoceptive sensitivity shown through all of these examples have been observed so frequently in anorexia that they have become key characteristics of the illness.

Comorbidity

Other psychological issues may factor into anorexia nervosa. Some people have a previous disorder which may increase their vulnerability to developing an eating disorder and some develop them afterwards. The presence of psychiatric comorbidity has been shown to affect the severity and type of anorexia nervosa symptoms in both adolescents and adults.

Obsessive-compulsive disorder (OCD) and obsessive-compulsive personality disorder (OCPD) are highly comorbid with AN. OCD is linked with more severe symptomatology and worse prognosis. The causality between personality disorders and eating disorders has yet to be fully established. Other comorbid conditions include depression, alcoholism, borderline and other personality disorders, anxiety disorders, attention deficit hyperactivity disorder, and body dysmorphic disorder (BDD). Depression and anxiety are the most common comorbidities, and depression is associated with a worse outcome. Autism spectrum disorders occur more commonly among people with eating disorders than in the general population. Zucker et al. (2007) proposed that conditions on the autism spectrum make up the cognitive endophenotype underlying anorexia nervosa and appealed for increased interdisciplinary collaboration.

Causes

Dysregulation of the serotonin pathways has been implicated in the cause and mechanism of anorexia.

There is evidence for biological, psychological, developmental, and sociocultural risk factors, but the exact cause of eating disorders is unknown.

Genetic

Genetic correlations of anorexia with psychiatric and metabolic traits.

Anorexia nervosa is highly heritable. Twin studies have shown a heritability rate of between 28 and 58%. First-degree relatives of those with anorexia have roughly 12 times the risk of developing anorexia. Association studies have been performed, studying 128 different polymorphisms related to 43 genes including genes involved in regulation of eating behavior, motivation and reward mechanics, personality traits and emotion. Consistent associations have been identified for polymorphisms associated with agouti-related peptide, brain derived neurotrophic factor, catechol-o-methyl transferase, SK3 and opioid receptor delta-1. Epigenetic modifications, such as DNA methylation, may contribute to the development or maintenance of anorexia nervosa, though clinical research in this area is in its infancy.

A 2019 study found a genetic relationship with mental disorders, such as schizophrenia, obsessive–compulsive disorder, anxiety disorder and depression; and metabolic functioning with a negative correlation with fat mass, type 2 diabetes and leptin.

Environmental

Obstetric complications: prenatal and perinatal complications may factor into the development of anorexia nervosa, such as preterm birth, maternal anemia, diabetes mellitus, preeclampsia, placental infarction, and neonatal heart abnormalities. Neonatal complications may also have an influence on harm avoidance, one of the personality traits associated with the development of AN.

Neuroendocrine dysregulation: altered signalling of peptides that facilitate communication between the gut, brain and adipose tissue, such as ghrelin, leptin, neuropeptide Y and orexin, may contribute to the pathogenesis of anorexia nervosa by disrupting regulation of hunger and satiety.

Gastrointestinal diseases: people with gastrointestinal disorders may be more at risk of developing disorders of eating practices than the general population, principally restrictive eating disturbances. An association of anorexia nervosa with celiac disease has been found. The role that gastrointestinal symptoms play in the development of eating disorders seems rather complex. Some authors report that unresolved symptoms prior to gastrointestinal disease diagnosis may create a food aversion in these persons, causing alterations to their eating patterns. Other authors report that greater symptoms throughout their diagnosis led to greater risk. It has been documented that some people with celiac disease, irritable bowel syndrome or inflammatory bowel disease who are not conscious about the importance of strictly following their diet, choose to consume their trigger foods to promote weight loss. On the other hand, individuals with good dietary management may develop anxiety, food aversion and eating disorders because of concerns around cross contamination of their foods. Some authors suggest that medical professionals should evaluate the presence of an unrecognized celiac disease in all people with eating disorder, especially if they present any gastrointestinal symptom (such as decreased appetite, abdominal pain, bloating, distension, vomiting, diarrhea or constipation), weight loss, or growth failure; and also routinely ask celiac patients about weight or body shape concerns, dieting or vomiting for weight control, to evaluate the possible presence of eating disorders, especially in women.

Studies have hypothesized the continuance of disordered eating patterns may be epiphenomena of starvation. The results of the Minnesota Starvation Experiment showed normal controls exhibit many of the behavioral patterns of AN when subjected to starvation. This may be due to the numerous changes in the neuroendocrine system, which results in a self-perpetuating cycle.

Anorexia nervosa is more likely to occur in a person's pubertal years. Some explanatory hypotheses for the rising prevalence of eating disorders in adolescence are "increase of adipose tissue in girls, hormonal changes of puberty, societal expectations of increased independence and autonomy that are particularly difficult for anorexic adolescents to meet; [and] increased influence of the peer group and its values."

Psychological

Early theories of the cause of anorexia linked it to childhood sexual abuse or dysfunctional families; evidence is conflicting, and well-designed research is needed. The fear of food is known as sitiophobia  or cibophobia, and is part of the differential diagnosis. Other psychological causes of anorexia include low self-esteem, feeling like there is lack of control, depression, anxiety, and loneliness. Anorexic people are, in general, highly perfectionistic and most have obsessive compulsive personality traits which may facilitate sticking to a restricted diet. It has been suggested that anorexic patients are rigid in their thought patterns, and place a high level of importance upon being thin.

A risk factor for anorexia is trauma. Although the prevalence rates vary greatly, between 37% and 100%, there appears to be a link between traumatic events and eating disorder diagnosis. Approximately 72% of individuals with anorexia report experiencing a traumatic event prior to the onset of eating disorder symptoms, with binge-purge subtype reporting the highest rates. There are many traumatic events that may be risk factors for development of anorexia, the first identified traumatic event predicting anorexia was childhood sexual abuse. However, other traumatic events, such as physical and emotional abuse have also been found to be risk factors. Interpersonal, as opposed to non-interpersonal trauma, has been seen as the most common type of traumatic event, which can encompass sexual, physical, and emotional abuse. Individuals who experience repeated trauma, like those who experience trauma perpetrated by a caregiver or loved one, have increased symptom severity of anorexia and a greater prevalence of comorbid psychiatric diagnoses. In individuals with anorexia, the prevalence rates for those who also qualify for a PTSD diagnosis ranges from 4% to 52% in non-clinical samples to 10% to 47% in clinical samples. A complicated symptom profile develops when trauma and anorexia meld; the bodily experience of the individual is changed and intrusive thoughts and sensations may be experienced. Traumatic events can lead to intrusive and obsessive thoughts, and the symptom of anorexia that has been most closely linked to a PTSD diagnosis is increased obsessive thoughts pertaining to food. Similarly, impulsivity is linked to the purge and binge-purge subtypes of anorexia, trauma, and PTSD. Emotional trauma (e.g., invalidation, chaotic family environment in childhood) may lead to difficulty with emotions, particularly the identification of and how physical sensations contribute to the emotional response. Trauma and traumatic events can disturb an individual’s sense of self and affect their ability to thrive, especially within their bodies. When trauma is perpetrated on an individual, it can lead to feelings of not being safe within their own body; that their body is for others to use and not theirs alone. Individuals may experience a feeling of disconnection from their body after a traumatic experience, leading to a desire to distance themselves from the body. Trauma overwhelms individuals emotionally, physically, and psychologically. Both physical and sexual abuse can lead to an individual seeing their body as belonging to an “other” and not to the “self”. Individuals who feel as though they have no control over their bodies due to trauma may use food as a means of control because the choice to eat is an unmatched expression of control. By exerting control over food, individuals can choose when to eat and how much to eat. Individuals, particularly children experiencing abuse, may feel a loss of control over their life, circumstances, and their own bodies. Particularly sexual abuse, but also physical abuse, individuals may feel that the body is not a safe place and an object over which another has control. Starvation, in the case of anorexia, may also lead to reduction in the body as a sexual object, making starvation a solution. Restriction may also be a means by which the pain an individual is experiencing can be communicated.

Sociological

Anorexia nervosa has been increasingly diagnosed since 1950; the increase has been linked to vulnerability and internalization of body ideals. People in professions where there is a particular social pressure to be thin (such as models and dancers) were more likely to develop anorexia, and those with anorexia have much higher contact with cultural sources that promote weight loss. This trend can also be observed for people who partake in certain sports, such as jockeys and wrestlers. There is a higher incidence and prevalence of anorexia nervosa in sports with an emphasis on aesthetics, where low body fat is advantageous, and sports in which one has to make weight for competition. Family group dynamics can play a role in the cause of anorexia including negative expressed emotion in overprotective families where blame is frequently experienced among its members. When there is a constant pressure from people to be thin, teasing and bullying can cause low self-esteem and other psychological symptoms.

Media effects

Persistent exposure to media that present body ideals may constitute a risk factor for body dissatisfaction and anorexia nervosa. The cultural ideal for body shape for men versus women continues to favor slender women and athletic, V-shaped muscular men. A 2002 review found that, of the magazines most popular among people aged 18 to 24 years, those read by men, unlike those read by women, were more likely to feature ads and articles on shape than on diet. Body dissatisfaction and internalization of body ideals are risk factors for anorexia nervosa that threaten the health of both male and female populations.

Websites that stress the importance of attainment of body ideals extol and promote anorexia nervosa through the use of religious metaphors, lifestyle descriptions, "thinspiration" or "fitspiration" (inspirational photo galleries and quotes that aim to serve as motivators for attainment of body ideals). Pro-anorexia websites reinforce internalization of body ideals and the importance of their attainment.

The media portray a false view of what people truly look like. In magazines and movies and even on billboards most of the actors/models are digitally altered in multiple ways. People then strive to look like these "perfect" role models when in reality they are not near perfection themselves.

Mechanisms

Evidence from physiological, pharmacological and neuroimaging studies suggest serotonin (also called 5-HT) may play a role in anorexia. While acutely ill, metabolic changes may produce a number of biological findings in people with anorexia that are not necessarily causative of the anorexic behavior. For example, abnormal hormonal responses to challenges with serotonergic agents have been observed during acute illness, but not recovery. Nevertheless, increased cerebrospinal fluid concentrations of 5-hydroxyindoleacetic acid (a metabolite of serotonin), and changes in anorectic behavior in response to acute tryptophan depletion (tryptophan is a metabolic precursor to serotonin) support a role in anorexia. The activity of the 5-HT2A receptors has been reported to be lower in patients with anorexia in a number of cortical regions, evidenced by lower binding potential of this receptor as measured by PET or SPECT, independent of the state of illness. While these findings may be confounded by comorbid psychiatric disorders, taken as a whole they indicate serotonin in anorexia. These alterations in serotonin have been linked to traits characteristic of anorexia such as obsessiveness, anxiety, and appetite dysregulation.

Neuroimaging studies investigating the functional connectivity between brain regions have observed a number of alterations in networks related to cognitive control, introspection, and sensory function. Alterations in networks related to the dorsal anterior cingulate cortex may be related to excessive cognitive control of eating related behaviors. Similarly, altered somatosensory integration and introspection may relate to abnormal body image. A review of functional neuroimaging studies reported reduced activations in "bottom up" limbic region and increased activations in "top down" cortical regions which may play a role in restrictive eating.

Compared to controls, recovered anorexics show reduced activation in the reward system in response to food, and reduced correlation between self reported liking of a sugary drink and activity in the striatum and anterior cingulate cortex. Increased binding potential of 11C radiolabelled raclopride in the striatum, interpreted as reflecting decreased endogenous dopamine due to competitive displacement, has also been observed.

Structural neuroimaging studies have found global reductions in both gray matter and white matter, as well as increased cerebrospinal fluid volumes. Regional decreases in the left hypothalamus, left inferior parietal lobe, right lentiform nucleus and right caudate have also been reported in acutely ill patients. However, these alterations seem to be associated with acute malnutrition and largely reversible with weight restoration, at least in nonchronic cases in younger people. In contrast, some studies have reported increased orbitofrontal cortex volume in currently ill and  in recovered patients, although findings are inconsistent. Reduced white matter integrity in the fornix has also been reported.

Diagnosis

A diagnostic assessment includes the person's current circumstances, biographical history, current symptoms, and family history. The assessment also includes a mental state examination, which is an assessment of the person's current mood and thought content, focusing on views on weight and patterns of eating.

DSM-5

Anorexia nervosa is classified under the Feeding and Eating Disorders in the latest revision of the Diagnostic and Statistical Manual of Mental Disorders (DSM 5). There is no specific BMI cut-off that defines low weight required for the diagnosis of anorexia nervosa.

The diagnostic criteria for anorexia nervosa (all of which needing to be met for diagnosis) are:

  • Restriction of energy intake relative to requirements leading to a low body weight. (Criterion A)
  • Intense fear of gaining weight or persistent behaviors that interfere with gaining weight. (Criterion B)
  • Disturbance in the way a person's weight or body shape is experienced or a lack of recognition about the risks of the low body weight. (Criterion C)

Relative to the previous version of the DSM (DSM-IV-TR), the 2013 revision (DSM5) reflects changes in the criteria for anorexia nervosa. Most notably, the amenorrhea (absent period) criterion was removed. Amenorrhea was removed for several reasons: it does not apply to males, it is not applicable for females before or after the age of menstruation or taking birth control pills, and some women who meet the other criteria for AN still report some menstrual activity.

Subtypes

There are two subtypes of AN:

  • Binge-eating/purging type: patients with anorexia could show binge eating and purging behavior. It is different from bulimia nervosa in terms of the individual's weight. An individual with binge-eating/purging type anorexia is usually significantly underweight. People with bulimia nervosa on the other hand can sometimes be normal-weight or overweight.
  • Restricting type: the individual uses restricting food intake, fasting, diet pills, or exercise as a means for losing weight; they may exercise excessively to keep off weight or prevent weight gain, and some individuals eat only enough to stay alive. In the restrictive type, there are no recurrent episodes of binge-eating or purging present.

Levels of severity

Body mass index (BMI) is used by the DSM-5 as an indicator of the level of severity of anorexia nervosa. The DSM-5 states these as follows:

  • Mild: BMI of greater than 17
  • Moderate: BMI of 16–16.99
  • Severe: BMI of 15–15.99
  • Extreme: BMI of less than 15

Investigations

Medical tests to check for signs of physical deterioration in anorexia nervosa may be performed by a general physician or psychiatrist, including:

Differential diagnoses

A variety of medical and psychological conditions have been misdiagnosed as anorexia nervosa; in some cases the correct diagnosis was not made for more than ten years.

The distinction between binge purging anorexia, bulimia nervosa and Other Specified Feeding or Eating Disorders (ORFED) is often difficult for non-specialist clinicians. A main factor differentiating binge-purge anorexia from bulimia is the gap in physical weight. Patients with bulimia nervosa are ordinarily at a healthy weight, or slightly overweight. Patients with binge-purge anorexia are commonly underweight. Moreover, patients with the binge-purging subtype may be significantly underweight and typically do not binge-eat large amounts of food. In contrast, those with bulimia nervosa tend to binge large amounts of food. It is not unusual for patients with an eating disorder to "move through" various diagnoses as their behavior and beliefs change over time.

Treatment

There is no conclusive evidence that any particular treatment for anorexia nervosa works better than others.

Treatment for anorexia nervosa tries to address three main areas.

  • Restoring the person to a healthy weight;
  • Treating the psychological disorders related to the illness;
  • Reducing or eliminating behaviors or thoughts that originally led to the disordered eating.

In some clinical settings a specific body image intervention is performed to reduce body dissatisfaction and body image disturbance. Although restoring the person's weight is the primary task at hand, optimal treatment also includes and monitors behavioral change in the individual as well. There is some evidence that hospitalization might adversely affect long term outcome, but sometimes is necessary. Psychotherapy for individuals with AN is challenging as they may value being thin and may seek to maintain control and resist change. Initially, developing a desire to change is fundamental. Despite no evidence for better treatment in adults patients, research stated that family based therapy is the primary choice for adolescents with AN.

Therapy

Family-based treatment (FBT) has been shown to be more successful than individual therapy for adolescents with AN. Various forms of family-based treatment have been proven to work in the treatment of adolescent AN including conjoint family therapy (CFT), in which the parents and child are seen together by the same therapist, and separated family therapy (SFT) in which the parents and child attend therapy separately with different therapists. Proponents of family therapy for adolescents with AN assert that it is important to include parents in the adolescent's treatment.

A four- to five-year follow up study of the Maudsley family therapy, an evidence-based manualized model, showed full recovery at rates up to 90%. Although this model is recommended by the NIMH, critics claim that it has the potential to create power struggles in an intimate relationship and may disrupt equal partnerships. Cognitive behavioral therapy (CBT) is useful in adolescents and adults with anorexia nervosa. One of the most known psychotherapy in the field is CBT-E, an enhanced cognitive-behavior therapy specifically focus to eating disorder psychopatology. Acceptance and commitment therapy is a third-wave cognitive-behavioral therapy which has shown promise in the treatment of AN. Cognitive remediation therapy (CRT) is also used in treating anorexia nervosa. Schema-Focused Therapy (a form of CBT) was developed by Dr. Jeffrey Young and is effective in helping patients identify origins and triggers for disordered eating. https://www.tandfonline.com/doi/pdf/10.1080/20797222.2017.1326728

Diet

Diet is the most essential factor to work on in people with anorexia nervosa, and must be tailored to each person's needs. Food variety is important when establishing meal plans as well as foods that are higher in energy density. People must consume adequate calories, starting slowly, and increasing at a measured pace. Evidence of a role for zinc supplementation during refeeding is unclear.

Medication

Pharmaceuticals have limited benefit for anorexia itself. There is a lack of good information from which to make recommendations concerning the effectiveness of antidepressants in treating anorexia. Administration of olanzapine has been shown to result in a modest but statistically significant increase in body weight of anorexia nervosa patients.

Admission to hospital

AN has a high mortality and patients admitted in a severely ill state to medical units are at particularly high risk. Diagnosis can be challenging, risk assessment may not be performed accurately, consent and the need for compulsion may not be assessed appropriately, refeeding syndrome may be missed or poorly treated and the behavioural and family problems in AN may be missed or poorly managed. Guidelines published by the Royal College of Psychiatrists recommend that medical and psychiatric experts work together in managing severely ill people with AN.

Refeeding syndrome

The rate of refeeding can be difficult to establish, because the fear of refeeding syndrome (RFS) can lead to underfeeding. It is thought that RFS, with falling phosphate and potassium levels, is more likely to occur when BMI is very low, and when medical comorbidities such as infection or cardiac failure, are present. In those circumstances, it is recommended to start refeeding slowly but to build up rapidly as long as RFS does not occur. Recommendations on energy requirements vary, from 5–10 kcal/kg/day in the most medically compromised patients, who appear to have the highest risk of RFS, to 1900 kcal/day.

Prognosis

Deaths due to eating disorders per million persons in 2012
  0–1
  1–2
  2–3
  3–4
  4–25

AN has the highest mortality rate of any psychological disorder. The mortality rate is 11 to 12 times greater than in the general population, and the suicide risk is 56 times higher. Half of women with AN achieve a full recovery, while an additional 20–30% may partially recover. Not all people with anorexia recover completely: about 20% develop anorexia nervosa as a chronic disorder. If anorexia nervosa is not treated, serious complications such as heart conditions and kidney failure can arise and eventually lead to death. The average number of years from onset to remission of AN is seven for women and three for men. After ten to fifteen years, 70% of people no longer meet the diagnostic criteria, but many still continue to have eating-related problems.

Alexithymia influences treatment outcome. Recovery is also viewed on a spectrum rather than black and white. According to the Morgan-Russell criteria, individuals can have a good, intermediate, or poor outcome. Even when a person is classified as having a "good" outcome, weight only has to be within 15% of average, and normal menstruation must be present in females. The good outcome also excludes psychological health. Recovery for people with anorexia nervosa is undeniably positive, but recovery does not mean a return to normal.

Complications

Anorexia nervosa can have serious implications if its duration and severity are significant and if onset occurs before the completion of growth, pubertal maturation, or the attainment of peak bone mass. Complications specific to adolescents and children with anorexia nervosa can include the following: Growth retardation may occur, as height gain may slow and can stop completely with severe weight loss or chronic malnutrition. In such cases, provided that growth potential is preserved, height increase can resume and reach full potential after normal intake is resumed. Height potential is normally preserved if the duration and severity of illness are not significant or if the illness is accompanied by delayed bone age (especially prior to a bone age of approximately 15 years), as hypogonadism may partially counteract the effects of undernutrition on height by allowing for a longer duration of growth compared to controls. Appropriate early treatment can preserve height potential, and may even help to increase it in some post-anorexic subjects, due to factors such as long-term reduced estrogen-producing adipose tissue levels compared to premorbid levels. In some cases, especially where onset is before puberty, complications such as stunted growth and pubertal delay are usually reversible.

Anorexia nervosa causes alterations in the female reproductive system; significant weight loss, as well as psychological stress and intense exercise, typically results in a cessation of menstruation in women who are past puberty. In patients with anorexia nervosa, there is a reduction of the secretion of gonadotropin releasing hormone in the central nervous system, preventing ovulation. Anorexia nervosa can also result in pubertal delay or arrest. Both height gain and pubertal development are dependent on the release of growth hormone and gonadotropins (LH and FSH) from the pituitary gland. Suppression of gonadotropins in people with anorexia nervosa has been documented. Typically, growth hormone (GH) levels are high, but levels of IGF-1, the downstream hormone that should be released in response to GH are low; this indicates a state of “resistance” to GH due to chronic starvation. IGF-1 is necessary for bone formation, and decreased levels in anorexia nervosa contribute to a loss of bone density and potentially contribute to osteopenia or osteoporosis. Anorexia nervosa can also result in reduction of peak bone mass. Buildup of bone is greatest during adolescence, and if onset of anorexia nervosa occurs during this time and stalls puberty, low bone mass may be permanent.

Hepatic steatosis, or fatty infiltration of the liver, can also occur, and is an indicator of malnutrition in children. Neurological disorders that may occur as complications include seizures and tremors. Wernicke encephalopathy, which results from vitamin B1 deficiency, has been reported in patients who are extremely malnourished; symptoms include confusion, problems with the muscles responsible for eye movements and abnormalities in walking gait.

The most common gastrointestinal complications of anorexia nervosa are delayed stomach emptying and constipation, but also include elevated liver function tests, diarrhea, acute pancreatitis, heartburn, difficulty swallowing, and, rarely, superior mesenteric artery syndrome. Delayed stomach emptying, or gastroparesis, often develops following food restriction and weight loss; the most common symptom is bloating with gas and abdominal distension, and often occurs after eating. Other symptoms of gastroparesis include early satiety, fullness, nausea, and vomiting. The symptoms may inhibit efforts at eating and recovery, but can be managed by limiting high-fiber foods, using liquid nutritional supplements, or using metoclopramide to increase emptying of food from the stomach. Gastroparesis generally resolves when weight is regained.

Cardiac complications

Anorexia nervosa increases the risk of sudden cardiac death, though the precise cause is unknown. Cardiac complications include structural and functional changes to the heart. Some of these cardiovascular changes are mild and are reversible with treatment, while others may be life-threatening. Cardiac complications can include arrhythmias, abnormally slow heart beat, low blood pressure, decreased size of the heart muscle, reduced heart volume, mitral valve prolapse, myocardial fibrosis, and pericardial effusion.

Abnormalities in conduction and repolarization of the heart that can result from anorexia nervosa include QT prolongation, increased QT dispersion, conduction delays, and junctional escape rhythms.[162] Electrolyte abnormalities, particularly hypokalemia and hypomagnesemia, can cause anomalies in the electrical activity of the heart, and result in life-threatening arrhythmias. Hypokalemia most commonly results in anorexic patients when restricting is accompanied by purging (induced vomiting or laxative use). Hypotension (low blood pressure) is common, and symptoms include fatigue and weakness. Orthostatic hypotension, a marked decrease in blood pressure when standing from a supine position, may also occur. Symptoms include lightheadedness upon standing, weakness, and cognitive impairment, and may result in fainting or near-fainting. Orthostasis in anorexia nervosa indicates worsening cardiac function and may indicate a need for hospitalization. Hypotension and orthostasis generally resolve upon recovery to a normal weight. The weight loss in anorexia nervosa also causes atrophy of cardiac muscle. This leads to decreased ability to pump blood, a reduction in the ability to sustain exercise, a diminished ability to increase blood pressure in response to exercise, and a subjective feeling of fatigue.

Some individuals may also have a decrease in cardiac contractility. Cardiac complications can be life-threatening, but the heart muscle generally improves with weight gain, and the heart normalizes in size over weeks to months, with recovery. Atrophy of the heart muscle is a marker of the severity of the disease, and while it is reversible with treatment and refeeding, it is possible that it may cause permanent, microscopic changes to the heart muscle that increase the risk of sudden cardiac death. Individuals with anorexia nervosa may experience chest pain or palpitations; these can be a result of mitral valve prolapse. Mitral valve prolapse occurs because the size of the heart muscle decreases while the tissue of the mitral valve remains the same size. Studies have shown rates of mitral valve prolapse of around 20 percent in those with anorexia nervosa, while the rate in the general population is estimated at 2–4 percent. It has been suggested that there is an association between mitral valve prolapse and sudden cardiac death, but it has not been proven to be causative, either in patients with anorexia nervosa or in the general population.

Relapse

Rates of relapse after treatment range from 9–52% with many studies reporting a relapse rate of at least 25%. Relapse occurs in approximately a third of people in hospital, and is greatest in the first six to eighteen months after release from an institution.

Epidemiology

Anorexia is estimated to occur in 0.9% to 4.3% of women and 0.2% to 0.3% of men in Western countries at some point in their life. About 0.4% of young females are affected in a given year and it is estimated to occur three to ten times less commonly in males. Rates in most of the developing world are unclear. Often it begins during the teen years or young adulthood.

The lifetime rate of atypical anorexia nervosa, a form of ED-NOS in which the person loses a significant amount of weight and is at risk for serious medical complications despite having a higher body-mass index, is much higher, at 5–12%.

While anorexia became more commonly diagnosed during the 20th century it is unclear if this was due to an increase in its frequency or simply better diagnosis. Most studies show that since at least 1970 the incidence of AN in adult women is fairly constant, while there is some indication that the incidence may have been increasing for girls aged between 14 and 20.

Underrepresentation

Eating disorders are less reported in preindustrial, non-westernized countries than in Western countries. In Africa, not including South Africa, the only data presenting information about eating disorders occurs in case reports and isolated studies, not studies investigating prevalence. Data shows in research that in westernized civilizations, ethnic minorities have very similar rates of eating disorders, contrary to the belief that eating disorders predominantly occur in white people.

Men (and women) who might otherwise be diagnosed with anorexia may not meet the DSM IV criteria for BMI since they have muscle weight, but have very little fat. Male and female athletes are often overlooked as anorexic. Research emphasizes the importance to take athletes' diet, weight and symptoms into account when diagnosing anorexia, instead of just looking at weight and BMI. For athletes, ritualized activities such as weigh-ins place emphasis on gaining and losing large amounts of weight, which may promote the development of eating disorders among them. While women use diet pills, which is an indicator of unhealthy behavior and an eating disorder, men use steroids, which contextualizes the beauty ideals for genders. In a Canadian study, 4% of boys in grade nine used anabolic steroids. Anorexic men are sometimes referred to as manorexic.

Anorexia Nervosa and gender

Despite the stereotypes around eating disorders with women, one in three people with an eating disorder is male. This statistic may represent a minimum estimation. Due to the feminine stigma attached to anorexia, many men are hesitant to seek help and remain undiagnosed. Additionally, assessment tests are geared towards how anorexia is experienced in women, leading to misconceptions around how men experience anorexia. Some reports note a rise in men developing anorexia, however this may be explained by men feeling better able to seek help and wider recognition of the fact men experience eating disorders.

History

Two images of an anorexic woman published in 1900 in "Nouvelle Iconographie de la Salpêtrière". The case was titled "Un cas d'anorexie hysterique" (A case of hysteric anorexia).

The history of anorexia nervosa begins with descriptions of religious fasting dating from the Hellenistic era and continuing into the medieval period. The medieval practice of self-starvation by women, including some young women, in the name of religious piety and purity also concerns anorexia nervosa; it is sometimes referred to as anorexia mirabilis. The earliest medical descriptions of anorexic illnesses are generally credited to English physician Richard Morton in 1689. Case descriptions fitting anorexic illnesses continued throughout the 17th, 18th, and 19th centuries.

The term "anorexia nervosa" was coined in 1873 by Sir William Gull, one of Queen Victoria's personal physicians. Gull published a seminal paper providing a number of detailed case descriptions of patients with anorexia nervosa. In the same year, French physician Ernest-Charles Lasègue similarly published details of a number of cases in a paper entitled De l'Anorexie hystérique.

In the late 19th century anorexia nervosa became widely accepted by the medical profession as a recognized condition. Awareness of the condition was largely limited to the medical profession until the latter part of the 20th century, when German-American psychoanalyst Hilde Bruch published The Golden Cage: the Enigma of Anorexia Nervosa in 1978. Despite major advances in neuroscience, Bruch's theories tend to dominate popular thinking. A further important event was the death of the popular singer and drummer Karen Carpenter in 1983, which prompted widespread ongoing media coverage of eating disorders.

Computational chemistry

From Wikipedia, the free encyclopedia

Computational chemistry is a branch of chemistry that uses computer simulation to assist in solving chemical problems. It uses methods of theoretical chemistry, incorporated into computer programs, to calculate the structures and properties of molecules, groups of molecules, and solids. It is necessary because, apart from relatively recent results concerning the hydrogen molecular ion (dihydrogen cation, see references therein for more details), the quantum many-body problem cannot be solved analytically, much less in closed form. While computational results normally complement the information obtained by chemical experiments, it can in some cases predict hitherto unobserved chemical phenomena. It is widely used in the design of new drugs and materials.

Examples of such properties are structure (i.e., the expected positions of the constituent atoms), absolute and relative (interaction) energies, electronic charge density distributions, dipoles and higher multipole moments, vibrational frequencies, reactivity, or other spectroscopic quantities, and cross sections for collision with other particles.

The methods used cover both static and dynamic situations. In all cases, the computer time and other resources (such as memory and disk space) increase rapidly with the size of the system being studied. That system can be one molecule, a group of molecules, or a solid. Computational chemistry methods range from very approximate to highly accurate; the latter are usually feasible for small systems only. Ab initio methods are based entirely on quantum mechanics and basic physical constants. Other methods are called empirical or semi-empirical because they use additional empirical parameters.

Both ab initio and semi-empirical approaches involve approximations. These range from simplified forms of the first-principles equations that are easier or faster to solve, to approximations limiting the size of the system (for example, periodic boundary conditions), to fundamental approximations to the underlying equations that are required to achieve any solution to them at all. For example, most ab initio calculations make the Born–Oppenheimer approximation, which greatly simplifies the underlying Schrödinger equation by assuming that the nuclei remain in place during the calculation. In principle, ab initio methods eventually converge to the exact solution of the underlying equations as the number of approximations is reduced. In practice, however, it is impossible to eliminate all approximations, and residual error inevitably remains. The goal of computational chemistry is to minimize this residual error while keeping the calculations tractable.

In some cases, the details of electronic structure are less important than the long-time phase space behavior of molecules. This is the case in conformational studies of proteins and protein-ligand binding thermodynamics. Classical approximations to the potential energy surface are used, typically with molecular mechanics force fields, as they are computationally less intensive than electronic calculations, to enable longer simulations of molecular dynamics. Furthermore, cheminformatics uses even more empirical (and computationally cheaper) methods like machine learning based on physicochemical properties. One typical problem in cheminformatics is to predict the binding affinity of drug molecules to a given target. Other problems include predicting binding specificity, off-target effects, toxicity, and pharmacokinetic properties.

History

Building on the founding discoveries and theories in the history of quantum mechanics, the first theoretical calculations in chemistry were those of Walter Heitler and Fritz London in 1927, using valence bond theory. The books that were influential in the early development of computational quantum chemistry include Linus Pauling and E. Bright Wilson's 1935 Introduction to Quantum Mechanics – with Applications to Chemistry, Eyring, Walter and Kimball's 1944 Quantum Chemistry, Heitler's 1945 Elementary Wave Mechanics – with Applications to Quantum Chemistry, and later Coulson's 1952 textbook Valence, each of which served as primary references for chemists in the decades to follow.

With the development of efficient computer technology in the 1940s, the solutions of elaborate wave equations for complex atomic systems began to be a realizable objective. In the early 1950s, the first semi-empirical atomic orbital calculations were performed. Theoretical chemists became extensive users of the early digital computers. One major advance came with the 1951 paper in Reviews of Modern Physics by Clemens C. J. Roothaan in 1951, largely on the "LCAO MO" approach (Linear Combination of Atomic Orbitals Molecular Orbitals), for many years the second-most cited paper in that journal. A very detailed account of such use in the United Kingdom is given by Smith and Sutcliffe. The first ab initio Hartree–Fock method calculations on diatomic molecules were performed in 1956 at MIT, using a basis set of Slater orbitals. For diatomic molecules, a systematic study using a minimum basis set and the first calculation with a larger basis set were published by Ransil and Nesbet respectively in 1960. The first polyatomic calculations using Gaussian orbitals were performed in the late 1950s. The first configuration interaction calculations were performed in Cambridge on the EDSAC computer in the 1950s using Gaussian orbitals by Boys and coworkers. By 1971, when a bibliography of ab initio calculations was published, the largest molecules included were naphthalene and azulene. Abstracts of many earlier developments in ab initio theory have been published by Schaefer.

In 1964, Hückel method calculations (using a simple linear combination of atomic orbitals (LCAO) method to determine electron energies of molecular orbitals of π electrons in conjugated hydrocarbon systems) of molecules, ranging in complexity from butadiene and benzene to ovalene, were generated on computers at Berkeley and Oxford. These empirical methods were replaced in the 1960s by semi-empirical methods such as CNDO.

In the early 1970s, efficient ab initio computer programs such as ATMOL, Gaussian, IBMOL, and POLYAYTOM, began to be used to speed ab initio calculations of molecular orbitals. Of these four programs, only Gaussian, now vastly expanded, is still in use, but many other programs are now in use. At the same time, the methods of molecular mechanics, such as MM2 force field, were developed, primarily by Norman Allinger.

One of the first mentions of the term computational chemistry can be found in the 1970 book Computers and Their Role in the Physical Sciences by Sidney Fernbach and Abraham Haskell Taub, where they state "It seems, therefore, that 'computational chemistry' can finally be more and more of a reality." During the 1970s, widely different methods began to be seen as part of a new emerging discipline of computational chemistry. The Journal of Computational Chemistry was first published in 1980.

Computational chemistry has featured in several Nobel Prize awards, most notably in 1998 and 2013. Walter Kohn, "for his development of the density-functional theory", and John Pople, "for his development of computational methods in quantum chemistry", received the 1998 Nobel Prize in Chemistry. Martin Karplus, Michael Levitt and Arieh Warshel received the 2013 Nobel Prize in Chemistry for "the development of multiscale models for complex chemical systems".

Fields of application

The term theoretical chemistry may be defined as a mathematical description of chemistry, whereas computational chemistry is usually used when a mathematical method is sufficiently well developed that it can be automated for implementation on a computer. In theoretical chemistry, chemists, physicists, and mathematicians develop algorithms and computer programs to predict atomic and molecular properties and reaction paths for chemical reactions. Computational chemists, in contrast, may simply apply existing computer programs and methodologies to specific chemical questions.

Computational chemistry has two different aspects:

  • Computational studies, used to find a starting point for a laboratory synthesis, or to assist in understanding experimental data, such as the position and source of spectroscopic peaks.
  • Computational studies, used to predict the possibility of so far entirely unknown molecules or to explore reaction mechanisms not readily studied via experiments.

Thus, computational chemistry can assist the experimental chemist or it can challenge the experimental chemist to find entirely new chemical objects.

Several major areas may be distinguished within computational chemistry:

  • The prediction of the molecular structure of molecules by the use of the simulation of forces, or more accurate quantum chemical methods, to find stationary points on the energy surface as the position of the nuclei is varied.
  • Storing and searching for data on chemical entities (see chemical databases).
  • Identifying correlations between chemical structures and properties (see quantitative structure–property relationship (QSPR) and quantitative structure–activity relationship (QSAR)).
  • Computational approaches to help in the efficient synthesis of compounds.
  • Computational approaches to design molecules that interact in specific ways with other molecules (e.g. drug design and catalysis).

Accuracy

Computational chemistry is not an exact description of real-life chemistry, as our mathematical models of the physical laws of nature can only provide us with an approximation. However, the majority of chemical phenomena can be described to a certain degree in a qualitative or approximate quantitative computational scheme.

Molecules consist of nuclei and electrons, so the methods of quantum mechanics apply. Computational chemists often attempt to solve the non-relativistic Schrödinger equation, with relativistic corrections added, although some progress has been made in solving the fully relativistic Dirac equation. In principle, it is possible to solve the Schrödinger equation in either its time-dependent or time-independent form, as appropriate for the problem in hand; in practice, this is not possible except for very small systems. Therefore, a great number of approximate methods strive to achieve the best trade-off between accuracy and computational cost.

Accuracy can always be improved with greater computational cost. Significant errors can present themselves in ab initio models comprising many electrons, due to the computational cost of full relativistic-inclusive methods. This complicates the study of molecules interacting with high atomic mass unit atoms, such as transitional metals and their catalytic properties. Present algorithms in computational chemistry can routinely calculate the properties of small molecules that contain up to about 40 electrons with errors for energies less than a few kJ/mol. For geometries, bond lengths can be predicted within a few picometers and bond angles within 0.5 degrees. The treatment of larger molecules that contain a few dozen atoms is computationally tractable by more approximate methods such as density functional theory (DFT).

There is some dispute within the field whether or not the latter methods are sufficient to describe complex chemical reactions, such as those in biochemistry. Large molecules can be studied by semi-empirical approximate methods. Even larger molecules are treated by classical mechanics methods that use what are called molecular mechanics (MM). In QM-MM methods, small parts of large complexes are treated quantum mechanically (QM), and the remainder is treated approximately (MM).

Methods

One molecular formula can represent more than one molecular isomer: a set of isomers. Each isomer is a local minimum on the energy surface (called the potential energy surface) created from the total energy (i.e., the electronic energy, plus the repulsion energy between the nuclei) as a function of the coordinates of all the nuclei. A stationary point is a geometry such that the derivative of the energy with respect to all displacements of the nuclei is zero. A local (energy) minimum is a stationary point where all such displacements lead to an increase in energy. The local minimum that is lowest is called the global minimum and corresponds to the most stable isomer. If there is one particular coordinate change that leads to a decrease in the total energy in both directions, the stationary point is a transition structure and the coordinate is the reaction coordinate. This process of determining stationary points is called geometry optimization.

The determination of molecular structure by geometry optimization became routine only after efficient methods for calculating the first derivatives of the energy with respect to all atomic coordinates became available. Evaluation of the related second derivatives allows the prediction of vibrational frequencies if harmonic motion is estimated. More importantly, it allows for the characterization of stationary points. The frequencies are related to the eigenvalues of the Hessian matrix, which contains second derivatives. If the eigenvalues are all positive, then the frequencies are all real and the stationary point is a local minimum. If one eigenvalue is negative (i.e., an imaginary frequency), then the stationary point is a transition structure. If more than one eigenvalue is negative, then the stationary point is a more complex one, and is usually of little interest. When one of these is found, it is necessary to move the search away from it if the experimenter is looking solely for local minima and transition structures.

The total energy is determined by approximate solutions of the time-dependent Schrödinger equation, usually with no relativistic terms included, and by making use of the Born–Oppenheimer approximation, which allows for the separation of electronic and nuclear motions, thereby simplifying the Schrödinger equation. This leads to the evaluation of the total energy as a sum of the electronic energy at fixed nuclei positions and the repulsion energy of the nuclei. A notable exception are certain approaches called direct quantum chemistry, which treat electrons and nuclei on a common footing. Density functional methods and semi-empirical methods are variants on the major theme. For very large systems, the relative total energies can be compared using molecular mechanics. The ways of determining the total energy to predict molecular structures are:

Ab initio methods

The programs used in computational chemistry are based on many different quantum-chemical methods that solve the molecular Schrödinger equation associated with the molecular Hamiltonian. Methods that do not include any empirical or semi-empirical parameters in their equations – being derived directly from theoretical principles, with no inclusion of experimental data – are called ab initio methods. This does not imply that the solution is an exact one; they are all approximate quantum mechanical calculations. It means that a particular approximation is rigorously defined on first principles (quantum theory) and then solved within an error margin that is qualitatively known beforehand. If numerical iterative methods must be used, the aim is to iterate until full machine accuracy is obtained (the best that is possible with a finite word length on the computer, and within the mathematical and/or physical approximations made).

Diagram illustrating various ab initio electronic structure methods in terms of energy. Spacings are not to scale.

The simplest type of ab initio electronic structure calculation is the Hartree–Fock method (HF), an extension of molecular orbital theory, in which the correlated electron-electron repulsion is not specifically taken into account; only its average effect is included in the calculation. As the basis set size is increased, the energy and wave function tend towards a limit called the Hartree–Fock limit. Many types of calculations (termed post-Hartree–Fock methods) begin with a Hartree–Fock calculation and subsequently correct for electron-electron repulsion, referred to also as electronic correlation. As these methods are pushed to the limit, they approach the exact solution of the non-relativistic Schrödinger equation. To obtain exact agreement with experiment, it is necessary to include relativistic and spin orbit terms, both of which are far more important for heavy atoms. In all of these approaches, along with choice of method, it is necessary to choose a basis set. This is a set of functions, usually centered on the different atoms in the molecule, which are used to expand the molecular orbitals with the linear combination of atomic orbitals (LCAO) molecular orbital method ansatz. Ab initio methods need to define a level of theory (the method) and a basis set.

The Hartree–Fock wave function is a single configuration or determinant. In some cases, particularly for bond breaking processes, this is inadequate, and several configurations must be used. Here, the coefficients of the configurations, and of the basis functions, are optimized together.

The total molecular energy can be evaluated as a function of the molecular geometry; in other words, the potential energy surface. Such a surface can be used for reaction dynamics. The stationary points of the surface lead to predictions of different isomers and the transition structures for conversion between isomers, but these can be determined without a full knowledge of the complete surface.

A particularly important objective, called computational thermochemistry, is to calculate thermochemical quantities such as the enthalpy of formation to chemical accuracy. Chemical accuracy is the accuracy required to make realistic chemical predictions and is generally considered to be 1 kcal/mol or 4 kJ/mol. To reach that accuracy in an economic way it is necessary to use a series of post-Hartree–Fock methods and combine the results. These methods are called quantum chemistry composite methods.

Density functional methods

Density functional theory (DFT) methods are often considered to be ab initio methods for determining the molecular electronic structure, even though many of the most common functionals use parameters derived from empirical data, or from more complex calculations. In DFT, the total energy is expressed in terms of the total one-electron density rather than the wave function. In this type of calculation, there is an approximate Hamiltonian and an approximate expression for the total electron density. DFT methods can be very accurate for little computational cost. Some methods combine the density functional exchange functional with the Hartree–Fock exchange term and are termed hybrid functional methods.

Semi-empirical methods

Semi-empirical quantum chemistry methods are based on the Hartree–Fock method formalism, but make many approximations and obtain some parameters from empirical data. They were very important in computational chemistry from the 60s to the 90s, especially for treating large molecules where the full Hartree–Fock method without the approximations were too costly. The use of empirical parameters appears to allow some inclusion of correlation effects into the methods.

Primitive semi-empirical methods were designed even before, where the two-electron part of the Hamiltonian is not explicitly included. For π-electron systems, this was the Hückel method proposed by Erich Hückel, and for all valence electron systems, the extended Hückel method proposed by Roald Hoffmann. Sometimes, Hückel methods are referred to as "completely emprirical" because they do not derive from a Hamiltonian.Yet, the term "empirical methods", or "empirical force fields" is usually used to describe Molecular Mechanics.

Molecular mechanics

In many cases, large molecular systems can be modeled successfully while avoiding quantum mechanical calculations entirely. Molecular mechanics simulations, for example, use one classical expression for the energy of a compound, for instance the harmonic oscillator. All constants appearing in the equations must be obtained beforehand from experimental data or ab initio calculations.

The database of compounds used for parameterization, i.e., the resulting set of parameters and functions is called the force field, is crucial to the success of molecular mechanics calculations. A force field parameterized against a specific class of molecules, for instance proteins, would be expected to only have any relevance when describing other molecules of the same class.

These methods can be applied to proteins and other large biological molecules, and allow studies of the approach and interaction (docking) of potential drug molecules.

Methods for solids

Computational chemical methods can be applied to solid state physics problems. The electronic structure of a crystal is in general described by a band structure, which defines the energies of electron orbitals for each point in the Brillouin zone. Ab initio and semi-empirical calculations yield orbital energies; therefore, they can be applied to band structure calculations. Since it is time-consuming to calculate the energy for a molecule, it is even more time-consuming to calculate them for the entire list of points in the Brillouin zone.

Chemical dynamics

Once the electronic and nuclear variables are separated (within the Born–Oppenheimer representation), in the time-dependent approach, the wave packet corresponding to the nuclear degrees of freedom is propagated via the time evolution operator (physics) associated to the time-dependent Schrödinger equation (for the full molecular Hamiltonian). In the complementary energy-dependent approach, the time-independent Schrödinger equation is solved using the scattering theory formalism. The potential representing the interatomic interaction is given by the potential energy surfaces. In general, the potential energy surfaces are coupled via the vibronic coupling terms.

The most popular methods for propagating the wave packet associated to the molecular geometry are:

Molecular dynamics

Molecular dynamics (MD) use either quantum mechanics, molecular mechanics or a mixture of both to calculate forces which are then used to solve Newton's laws of motion to examine the time-dependent behaviour of systems. The result of a molecular dynamics simulation is a trajectory that describes how the position and velocity of particles varies with time. The phase point of a system described by the positions and momenta of all its particles on a previous time point, will determine the next phase point in time by integrating over Newton's laws of motion.

Monte Carlo

Monte Carlo (MC) generates configurations of a system by making random changes to the positions of its particles, together with their orientations and conformations where appropriate. It is a random sampling method, which makes use of the so-called importance sampling. Importance sampling methods are able to generate low energy states, as this enables properties to be calculated accurately. The potential energy of each configuration of the system can be calculated, together with the values of other properties, from the positions of the atoms.

Quantum mechanics/Molecular mechanics (QM/MM)

QM/MM is a hybrid method that attempts to combine the accuracy of quantum mechanics with the speed of molecular mechanics. It is useful for simulating very large molecules such as enzymes.

Interpreting molecular wave functions

The atoms in molecules (QTAIM) model of Richard Bader was developed to effectively link the quantum mechanical model of a molecule, as an electronic wavefunction, to chemically useful concepts such as atoms in molecules, functional groups, bonding, the theory of Lewis pairs, and the valence bond model. Bader has demonstrated that these empirically useful chemistry concepts can be related to the topology of the observable charge density distribution, whether measured or calculated from a quantum mechanical wavefunction. QTAIM analysis of molecular wavefunctions is implemented, for example, in the AIMAll software package.

Software packages

Many self-sufficient computational chemistry software packages exist. Some include many methods covering a wide range, while others concentrate on a very specific range or even on one method. Details of most of them can be found in:

Inequality (mathematics)

From Wikipedia, the free encyclopedia https://en.wikipedia.org/wiki/Inequality...