title: Alcoholics Anonymous

text: The same survey showed that AA received 32% of its membership from other members, another 32% from treatment facilities, 30% were self-motivated to attend AA, 12% of its membership from court-ordered attendance, and only 1% of AA members decided to join based on information obtained from the Internet. People taking the survey were allowed to select multiple answers for what motivated them to join AA.


title: Alcoholics Anonymous

text: Many AA meetings take place in treatment facilities. Carrying the message of AA into hospitals was how the co-founders of AA first remained sober. They discovered great value in working with alcoholics who are still suffering, and that even if the alcoholic they were working with did not stay sober, they did. Bill Wilson wrote, "Practical experience shows that nothing will so much insure immunity from drinking as intensive work with other alcoholics". Bill Wilson visited Towns Hospital in New York City in an attempt to help the alcoholics who were patients there in 1934. At St. Thomas Hospital in Akron, Ohio, Smith worked with still more alcoholics. In 1939, a New York mental institution, Rockland State Hospital, was one of the first institutions to allow AA hospital groups. Service to corrections and treatment facilities used to be combined until the General Service Conference, in 1977, voted to dissolve its Institutions Committee and form two separate committees, one for treatment facilities, and one for correctional facilities.


title: Alcoholics Anonymous

text: In the United States and Canada, AA meetings are held in hundreds of correctional facilities. The AA General Service Office has published a workbook with detailed recommendations for methods of approaching correctional-facility officials with the intent of developing an in-prison AA program. In addition, AA publishes a variety of pamphlets specifically for the incarcerated alcoholic. Additionally, the AA General Service Office provides a pamphlet with guidelines for members working with incarcerated alcoholics.


title: Alcoholics Anonymous

text: United States courts have ruled that inmates, parolees, and probationers cannot be ordered to attend AA. Though AA itself was not deemed a religion, it was ruled that it contained "enough" religious components (variously described in "Griffin v. Coughlin" below as, inter alia, "religion", "religious activity", "religious exercise") to make coerced attendance at AA meetings a violation of the Establishment Clause of the First Amendment of the constitution. In 2007, the Ninth Circuit of the U.S. Court of Appeals stated that a parolee who was ordered to attend AA had standing to sue his parole office.


title: Alcoholics Anonymous

text: In 1939, High Watch Recovery Center in Kent, Connecticut, was founded by Bill Wilson and Marty Mann. Sister Francis who owned the farm tried to gift the spiritual retreat for alcoholics to Alcoholics Anonymous, however citing the sixth tradition Bill W. turned down the gift but agreed to have a separate non-profit board run the facility composed of AA members. Bill Wilson and Marty Mann served on the High Watch board of directors for many years. High Watch was the first and therefore the oldest 12-step-based treatment center in the world still operating today.


title: Alcoholics Anonymous

text: In 1949, the Hazelden treatment center was founded and staffed by AA members, and since then many alcoholic rehabilitation clinics have incorporated AA's precepts into their treatment programs. 32% of AA's membership was introduced to it through a treatment facility.


title: Alcoholics Anonymous

text: There are several ways one can determine whether AA works and numerous ways of measuring if AA is successful, such as looking at abstinence, reduced drinking intensity, reduced alcohol-related consequences, alcohol addiction severity, and healthcare cost.


title: Alcoholics Anonymous

text: The effectiveness of AA (compared to other methods and treatments) has been challenged throughout the years, but recent high quality clinical meta-studies using randomized trials show that AA costs less than other treatments and results in increased abstinence.


title: Alcoholics Anonymous

text: Because of the anonymous and voluntary nature of AA meetings, it has been difficult to perform random trials with them; the research suggests that AA can help alcoholics make positive changes.


title: Alcoholics Anonymous

text: A 2020 Cochrane review concluded that "compared to other well-established treatments, clinical linkage using well-articulated Twelve-Step Facilitation (TSF) manualized interventions intended to increase Alcoholics Anonymous (AA) participation" are more effective than other established treatments, such as motivational enhancement therapy (MET) and cognitive-behavioral therapy (CBT), as measured by abstinence rates. Manualized TSF probably achieves additional desirable outcomes—such as fewer drinks per drinking day and less severe alcohol-related problems—at equivalent rates as other treatments, although evidence for such a conclusion comes from low to moderate certainty evidence "so should be regarded with caution".


title: Alcoholics Anonymous

text: In response to a concern expressed by another addiction researcher that "those more strongly committed to total abstinence after receiving AA/TSF were likely to experience more protracted 'slips' if they did for any reason drink", the Cochrane review authors stated that subjects who did not achieve abstinence did not have worse drinking outcomes overall.


title: Alcoholics Anonymous

text: A 2006 study by Rudolf H. Moos and Bernice S. Moos saw a 67% success rate 16 years later for the 24.9% of alcoholics who ended up, on their own, undergoing a lot of AA treatment. The study's results may be skewed by self-selection bias.


title: Alcoholics Anonymous

text: Project MATCH was a 1990s 8-year, multi-site, $27-million investigation that studied which types of alcoholics respond best to which forms of treatment.


title: Alcoholics Anonymous

text: In 2001–2002, the National Institute on Alcohol Abuse and Alcoholism (NIAAA) conducted the National Epidemiological Survey on Alcoholism and Related Conditions (NESARC). Similarly structured to the NLAES, the survey conducted in-person interviews with 43,093 individuals. Respondents were asked if they had ever attended a twelve-step meeting for an alcohol problem in their lifetime (the question was not AA-specific). 1441 (3.4%) of respondents answered the question affirmatively. Answers were further broken down into three categories: disengaged, those who started attending at some point in the past but had ceased attending at some point in the past year (988); continued engagement, those who started attending at some point in the past and continued to attend during the past year (348); and newcomers, those who started attending during the past year (105). In their discussion of the findings, Kaskautas et al. (2008) state that to study disengagement, only the disengaged and continued engagement should be utilized (pg. 270).


title: Alcoholics Anonymous

text: American psychiatrist Lance Dodes, in "The Sober Truth", says that research indicates that only five to eight percent of the people who go to one or more AA meetings achieve sobriety.


title: Alcoholics Anonymous

text: The 5–8% figure put forward by Dodes is controversial; other doctors say that the book uses "three separate, questionable, calculations that arrive at the 5–8% figure." Addiction specialists state that the book's conclusion that "[12-step] approaches are almost completely ineffective and even harmful in treating substance use disorders" is wrong. One review called Dodes' reasoning against AA success a "pseudostatistical polemic."


title: Alcoholics Anonymous

text: Dodes has not, as of March 2020, read the 2020 Cochrane review showing AA efficacy, but opposes the idea that a social network is needed to overcome substance abuse.


title: Alcoholics Anonymous

text: In a 2015 article for "The Atlantic", Gabrielle Glaser criticized the dominance of AA in the treatment of addiction in the United States. Her article uses Lance Dodes's figures and an outdated Cochrane report to state that AA has a low success rate, but those figures have been criticized by experts in the addiction treatment field. The Glaser article incorrectly conflates the efficacy of treatment centers with the efficacy of Alcoholics Anonymous. The Glaser article says that "nothing about the 12-step approach draws on modern science", but a large amount of scientific research has been done with AA, showing that AA increases abstinence rates. The Glaser article criticizes 12-step programs for being "faith-based", but 12-step programs allow for a very wide diversity of spiritual beliefs, and there are a growing number of secular 12-step meetings.


title: Alcoholics Anonymous

text: "Thirteenth-stepping" is a pejorative term for AA members approaching new members for dates. A study in the "Journal of Addiction Nursing" sampled 55 women in AA and found that 35% of these women had experienced a "pass" and 29% had felt seduced at least once in AA settings. This has also happened with new male members who received guidance from older female AA members pursuing sexual company. The authors suggest that both men and women must be prepared for this behavior or find male or female-only groups. Women-only meetings are a very prevalent part of AA culture, and AA has become more welcoming for women. AA's pamphlet on sponsorship suggests that men be sponsored by men and women be sponsored by women.


title: Alcoholics Anonymous

text: Alcoholics Anonymous World Services has a safety flier which states that "Unwanted sexual advances and predatory behaviors are in conflict with carrying the A.A. message of recovery."


title: Alcoholics Anonymous

text: Stanton Peele argued that some AA groups apply the disease model to all problem drinkers, whether or not they are "full-blown" alcoholics. Along with Nancy Shute, Peele has advocated that besides AA, other options should be readily available to those problem drinkers who can manage their drinking with the right treatment. The Big Book says "moderate drinkers" and "a certain type of hard drinker" can stop or moderate their drinking. The Big Book suggests no program for these drinkers, but instead seeks to help drinkers without "power of choice in drink."


title: Alcoholics Anonymous

text: In 1983, a review stated that the AA program's focus on admission of having a problem increases deviant stigma and strips members of their previous cultural identity, replacing it with the deviant identity. A 1985 study based on observations of AA meetings warned of detrimental iatrogenic effects of the twelve-step philosophy and concluded that AA uses many methods that are also used by cults. A later review disagreed, stating that AA's program bore little resemblance to religious cult practices. In 2014, Vaillant published a paper making the case that Alcoholics Anonymous is not a cult.


title: Alcoholics Anonymous

text: Alcoholics Anonymous publishes several books, reports, pamphlets, and other media, including a periodical known as the "AA Grapevine". Two books are used primarily: "Alcoholics Anonymous" (the "Big Book") and "Twelve Steps and Twelve Traditions", the latter explaining AA's fundamental principles in depth. The full text of each of these two books is available on the AA website at no charge.


title: The Ones Who Walk Away from Omelas

text: "The Ones Who Walk Away from Omelas" is a 1973 work of short philosophical fiction by American writer Ursula K. Le Guin. With deliberately both vague and vivid descriptions, the narrator depicts a summer festival in the utopian city of Omelas, whose prosperity depends on the perpetual misery of a single child. "The Ones Who Walk Away from Omelas" was nominated for the Locus Award for Best Short Fiction in 1974 and won the Hugo Award for Best Short Story in 1974.


title: The Ones Who Walk Away from Omelas

text: The only chronological element of the work is that it begins by describing the first day of summer in Omelas, a shimmering city of unbelievable happiness and delight. In Omelas, the summer solstice is celebrated with a glorious festival and a race featuring young people on horseback. The vibrant festival atmosphere, however, seems to be an everyday characteristic of the blissful community, whose citizens, though limited in their technology and resources, are still intelligent, sophisticated, and cultured. Omelas has no kings, soldiers, priests, or slaves. The specific socio-politico-economic setup of the community is not mentioned; the narrator merely claims not to be sure of every particular.


title: The Ones Who Walk Away from Omelas

text: The narrator reflects that "Omelas sounds in my words like a city in a fairy tale, long ago and far away, once upon a time. Perhaps it would be best if you imagined it as your own fancy bids, assuming it will rise to the occasion, for certainly I cannot suit you all." Everything about Omelas is so abundantly pleasing that the narrator decides the reader is not yet truly convinced of its existence and so elaborates upon the final element of the city: its one atrocity. The city's constant state of serenity and splendor requires that a single unfortunate child be kept in perpetual filth, darkness, and misery.


title: The Ones Who Walk Away from Omelas

text: Once citizens are old enough to know the truth, most, though initially shocked and disgusted, ultimately acquiesce to this one injustice that secures the happiness of the rest of the city. However, some citizens, young and old, walk away from the city after seeing the child. Each is alone, and no one knows where they go, but none come back. The story ends with "The place they go towards is a place even less imaginable to most of us than the city of happiness. I cannot describe it at all. It is possible it does not exist. But they seem to know where they are going, the ones who walk away from Omelas."


title: The Ones Who Walk Away from Omelas

text: Le Guin stated that the city's name is pronounced ""OH-meh-lahss"". Le Guin hit upon the name of the town on seeing a road sign for Salem, Oregon, in a car mirror. "[… People ask me] 'Where "do" you get your ideas from, Ms. Le Guin?' From forgetting Dostoyevsky and reading road signs backwards, naturally. Where else?"


title: The Ones Who Walk Away from Omelas

text: "The central idea of this psychomyth, the scapegoat", writes Le Guin, "turns up in Dostoyevsky's "Brothers Karamazov", and several people have asked me, rather suspiciously, why I gave the credit to William James. The fact is, I haven't been able to re-read Dostoyevsky, much as I loved him, since I was twenty-five, and I'd simply forgotten he used the idea. But when I met it in James' 'The Moral Philosopher and the Moral Life', it was with a shock of recognition."


title: The Ones Who Walk Away from Omelas

text: Le Guin's piece was originally published in "New Dimensions 3", a hardcover science fiction anthology edited by Robert Silverberg, in October 1973. It was reprinted in Le Guin's "The Wind's Twelve Quarters" in 1975, and has been frequently anthologized elsewhere. It has also appeared as an independently published, 31-page hardcover book for young adults in 1993.


title: The Ones Who Walk Away from Omelas

text: It was republished in the second volume of the short-story anthology "The Unreal and the Real" in 2014. Introducing the short work in her 2012 collection "The Unreal and the Real, Volume Two", Le Guin noted that "The Ones Who Walk Away from Omelas" "has a long and happy career of being used by teachers to upset students and make them argue fiercely about morality."


title: The Ones Who Walk Away from Omelas

text: Game Designers Ricardo Bare and Harvey Smith drew upon "The Ones Who Walk Away from Omelas" as inspiration for the supernatural being of the Outsider in the Dishonored video game series.


title: The Ones Who Walk Away from Omelas

text: In "", artist and author Andrew DeGraff illustrated a map visualizing Le Guin's story. DeGraff wrote that: "Le Guin provides us with the building blocks to construct the city of Omelas, but if we want to forsake it afterward, then we too have to strike out alone."


title: The Ones Who Walk Away from Omelas

text: The 2017 music video for "Spring Day" by South Korean band BTS references Le Guin's short story, both thematically and in displaying a hotel named 'Omelas'.


title: The Ones Who Walk Away from Omelas

text: N. K. Jemisin's 2018 anthology "How Long 'til Black Future Month?" opens with a piece titled "The Ones Who Stay and Fight", which is a direct response to Le Guin's story. In an interview with "The Paris Review", the writer stated that many readers misunderstand Le Guin as arguing that the only way to create a better society is to leave, and that in fact Le Guin was arguing that one has to "fix" their society, "especially when there's nowhere to walk away to." Jemisin's 2022 novel "The World We Make" makes allusion to the story as well, using the descriptor "Omelasian" in reference to children being captive in a basement.


title: The Ones Who Walk Away from Omelas

text: In a 2019 Tor.com article, Joe George argued that the 2019 film "Us" was influenced by both Le Guin's short story as well as Octavia E. Butler's "Speech Sounds".


title: The Ones Who Walk Away from Omelas

text: Catherine Lacey's 2020 novel "Pew" begins with an epigraph from "The Ones Who Walk Away from Omelas", quoting the last paragraph of the story. The novel itself is heavily tied to Le Guin's work, with several key similarities present.


title: The Ones Who Walk Away from Omelas

text: Executive Producers and co-showrunners Michelle Paradise and Alex Kurtzman cited Le Guin's short story as inspiration for the plot line of the third season of , with Kurtzman noting that both creators were interested in the central dilemma being solely caused by a child. Several reviewers also noted a strong similarity between the story and the episode "Lift Us Where Suffering Cannot Reach" of "." One such was Anthony Pascale, who called the episode "almost a beat-for-beat recreation" of Le Guin's work. On the satirical website Cracked, JM McNab pointed out the long history of Le Guin's influence on the Star Trek franchise and that while the writers of "Star Trek: Discovery" did name a ship after her, the honor is "still not as good as being credited".


title: American University

text: The American University (AU or American) is a private federally chartered research university in Washington, D.C. Its main campus spans 90 acres (36 ha) on Ward Circle, mostly in the Spring Valley neighborhood of Northwest D.C. AU was chartered by an Act of Congress in 1893 at the urging of Methodist bishop John Fletcher Hurst, who sought to create an institution that would promote public service, internationalism, and pragmatic idealism. AU broke ground in 1902, opened as a graduate education institution in 1914, and admitted its first undergraduates in 1925. Although affiliated with the United Methodist Church, religious affiliation is not a criterion for admission.


title: American University

text: American University has eight schools and colleges: the School of International Service, College of Arts and Sciences, Kogod School of Business, School of Communication, School of Professional and Extended Studies, School of Public Affairs, School of Education, and the Washington College of Law (WCL). It has over 160 programs, including 71 bachelor's degrees, 87 master's degrees, and 10 doctoral degrees, as well as JD, LLM, and SJD programs. AU's student body numbers over 13,000 and represents all 50 U.S. states and 141 countries; around a fifth of students are international. It is classified among "".


title: American University

text: American University's alumni, faculty, and staff have included two Pulitzer Prize winners, two Nobel Prize winners, one United States Senator, 25 United States Representatives, 18 Ambassadors of the United States, and several foreign heads of state. American University is one of the top five feeder schools to the U.S. Foreign Service, Congressional staff, and other governmental agencies.


title: American University

text: The university owns National Public Radio's flagship capital affiliate, WAMU, which has been a source of nationally and internationally distributed programming such as "The Diane Rehm Show" and the more recent "1A", styled as "the 1A", as in "the 1st Amendment".


title: American University

text: The American University was established in the District of Columbia by an Act of Congress on December 5, 1892, primarily due to the efforts of Methodist bishop John Fletcher Hurst, who aimed to create an institution that could train future public servants. Hurst also chose the university's site, which was in the rural periphery of the District. After more than three decades devoted principally to securing financial support, the university was officially dedicated on May 15, 1914, with its first instructions beginning October of that year when 28 students were enrolled, 19 of whom were graduates and the remainder special students not candidates for a degree. The First Commencement, at which no degrees were awarded, was held on June 2, 1915. The Second Annual Commencement was held the following year and saw the awarding of the first degrees: one master's degree and two doctor's degrees. AU admitted both women and African Americans, which was uncommon in higher education at the time. Among its first 28 students were five women, while an African American doctoral student was admitted in 1915.


title: American University

text: Shortly after these early commencement ceremonies, classes were interrupted by war. During World War I, the university allowed the U.S. military to use some of its grounds for testing. In 1917, the U.S. military divided American University into two segments, Camp American University and Camp Leach. Camp American University became the birthplace of the United States' chemical weapons program and the site of chemical weapons testing; this required a major cleanup effort in the 1990s. Camp Leach was home to advanced research, development, and testing of modern camouflage techniques. , the Army Corps of Engineers was still removing ordnance including mustard gas and mortar shells.


title: American University

text: Instruction was first offered only at the graduate level, in accordance with the plan of the founders. This changed in 1925 with the establishment of the College of Liberal Arts (subsequently named the College of Arts and Sciences), which offered the first undergraduate degrees and programs. What is now the School of Public Affairs was founded in 1934, partly to educate future federal employees in new approaches to public administration introduced by the New Deal; during the event commemorating its launch, President Franklin D. Roosevelt stressed cooperation between the school and his administration.


title: American University

text: AU's relationship with the U.S. government continued during World War II, when the campus hosted the U.S. Navy Bomb Disposal School and a WAVE barracks. For AU's role in these wartime efforts, the Victory ship SS "American Victory" was named in its honor.


title: American University

text: The post-war period saw considerable growth and restructuring of AU. In 1947, the Washington Semester Program was established, pioneering the concept of


title: American University

text: semester-long internships in the nation's capital. In 1949, the university merged with the Washington College of Law, which began in 1896 as the first law school founded by women and the first coeducational institution for the professional study of law in the District. Shortly after that, three departments were reorganized as schools: the School of Business Administration in 1955 (subsequently named the Robert P. and Arlene R. Kogod College of Business Administration and in 1999 renamed the Kogod School of Business); the School of Government and Public Administration in 1957; and the School of International Service in 1958.


title: American University

text: In the early 1960s, the Department of Defense and the Central Intelligence Agency operated the FFRDC Special Operations Research Office as a think tank at American University. The government abandoned the think tank after its research was criticized as imperialistic by the general public. AU's political involvement was furthered by President John F. Kennedy's Spring 1963 commencement address. In the speech, Kennedy called on the Soviet Union to work with the United States to achieve a nuclear test ban treaty and to reduce the considerable international tensions and the specter of nuclear war during that juncture of the Cold War.


title: American University

text: From 1965 to 1977, the College of Continuing Education existed as a degree-granting college responsible for on- and off-campus adult education programs. The Lucy Webb Hayes School of Nursing provided an undergraduate study in Nursing from 1965 until 1988. In 1972, the School of Government and Public Administration, the School of International Service, the Center for Technology and Administration, and the Center for the Administration of Justice (subsequently named the School of Justice) were incorporated into the College of Public and International Affairs.


title: American University

text: The university bought the Immaculata Campus in 1986 to alleviate space problems. This would later become Tenley Campus.


title: American University

text: In 1986, construction on the Adnan Khashoggi Sports and Convocation Center began. Financed with $5 million from and named for Saudi Arabian Trustee Adnan Khashoggi, the building was intended to update athletics facilities and provide a new arena, as well as a parking garage and office space for administrative services. Costing an estimated $19 million, the building represented the largest construction project to date but met protest by both faculty and students to the university's use of Khashoggi's name on the building due to his involvement in the international arms trade.


title: American University

text: In 1988, the College of Public and International Affairs was reorganized to create two free-standing schools: the School of International Service and the School of Public Affairs, incorporating the School of Government and Public Administration and the School of Justice. That same year, construction on the Adnan Khashoggi Sports Center was completed while the Iran–Contra Affair controversy was at its height, although his name remained on the building until after Khashoggi defaulted on his donation obligation in the mid to late 1990s.


title: American University

text: In 1997, American University of Sharjah, the only coeducational, liberal arts university in the United Arab Emirates, signed a two-year contract with AU to provide academic management. This contract has since been extended multiple times through August 2009. A team of senior AU administrators relocated to Sharjah to assist in the establishment of the university and guide it through the Middle States Association of Colleges and Schools accreditation process.


title: American University

text: Benjamin Ladner was suspended from his position as president of the university on August 24, 2005, pending an investigation into possible misuse of university funds for his personal expenses. University faculty passed votes of no confidence in President Ladner on September 26. On October 10, 2005, the board of trustees of American University decided that Ladner would not return to American University as its president. Dr. Cornelius M. Kerwin, a long-time AU administrator, served as interim president and was appointed to the position permanently on September 1, 2007, after two outsiders declined an offer from the board of trustees. According to "The Chronicle of Higher Education", Ladner received a total compensation of $4,270,665 in his final year of service, the second highest of any university president in the United States.


title: American University

text: Ground was broken for the new School of International Service building on November 14, 2007, and completed in 2010. A speech was given by Senator Daniel K. Inouye (D-HI).


title: American University

text: Neil Kerwin retired as AU's president at the end of May 2017. The current president is Sylvia Mathews Burwell whose tenure officially began on June 1, 2017.


title: American University

text: As of the 2017–2018 academic year, a female tuxedo feral cat took up residence on the campus grounds near the McKinley School of Communications building. School students and staff maintain the cat's small shelter and feeding station and dubbed her "Wonk Cat". Wonk Cat has been adopted by the campus community at large, including in university social media postings and her own student-run social media sites. During the COVID-19 pandemic, Wonk cat went missing and has not been found to this day. Given the harsh winter conditions, abundance of drivers in the District of Columbia and general lifespan of cats, Wonk cat is believed to have passed away.


title: American University

text: In 2017, Taylor Dumpson became AU's first female black student body president. In her first full day in office, bananas were found at three places on campus, hanging from noose-like ropes, and marked with the initials "AKA", which are also the initials of the Alpha Kappa Alpha sorority. The university considered the incident to be racist, and then-president Neil Kerwin called it a "cowardly, despicable act." In May 2018, the school said it had exhausted "all credible leads" about who had perpetrated the incident.


title: American University

text: Also in May 2018, Dumpson filed a lawsuit against several people, including Andrew Anglin, the founder of the neo-Nazi website "The Daily Stormer". She accused Anglin of organizing a racist and sexist trolling campaign against her. She alleged that Anglin posted her name, her picture, links to her Facebook page, and the Twitter page of the university's student government, and urged his readers to "troll storm" her, which resulted in many hate-filled and racist online messages directed at her. A federal judge ordered the defendants to pay more than $101,000 in compensatory damages, $500,000 in punitive damages, and more than $124,000 in attorney's fees. Dumpson also entered a restraining order against him. Although Dumpson and Anglin have not settled, she settled in December 2018 with one of the people who harassed her, a man from Oregon who was required to apologize, to renounce white supremacy, to stop trolling and doxing online, and to provide information to and cooperate with authorities in the prosecution of white supremacists.


title: American University

text: In 2019, the School of Education (SOE) split from the College of Arts and Sciences. According to Cheryl Holcomb-McCoy (Dean of SOE) the move was made to "encourage more students to pursue careers in education". Areas of study that students can pursue within the school include: teacher education, special education, education policy, and leadership and international education. The school is home to the Institute for Innovation in Education and the newly created Center for Postsecondary Readiness and Success.


title: American University

text: On April 22, 2020, AU announced that it had divested its endowment of fossil fuels, becoming one of the first universities in the United States to completely divest of both direct and indirect fossil fuel holdings. Following a student referendum in favor of divestment, the AU board of trustees voted against divesting the endowment in 2014. The decision to divest in 2020 came after extensive student campaigning from groups like Fossil Free AU and the undergraduate student government. In 2020, Fossil Free AU pushed for a second student referendum on the subject, and the student government released a report on divestment, presented to the board of trustees by student comptroller Robert Zitzmann.


title: American University

text: American University has two contiguous campuses for academics and student housing: the main campus on Massachusetts Avenue and the East Campus on Nebraska Avenue. The Washington College of Law has since been moved to the site of the Tenley Campus located in Tenleytown. Additionally, AU owns several other buildings in the Tenleytown, Spring Valley, the East Campus in Wesley Heights, and American University Park areas.


title: American University

text: The first design for the campus was done by Frederick Law Olmsted. However, it was significantly modified over time due to financial constraints. The campus occupies adjacent to Ward Circle, the intersection of Nebraska and Massachusetts Avenues. AU's campus is predominantly surrounded by the affluent residential neighborhoods characteristic of the Northwest quadrant of Washington, D.C. The campus includes a main quadrangle surrounded by academic buildings, nine residential halls, a 5,000-seat arena, and an outdoor amphitheater. The campus has been designated a public garden and arboretum by the American Public Gardens Association, with many foreign and exotic plants and trees dotting the landscape.


title: American University

text: Housing is guaranteed for two years. Most freshman and sophomore students choose to live on campus. First-year students are not required to live on campus.


title: American University

text: The university recently added 590 beds in 2017 with the opening of East Campus. Residence halls on the main campus are grouped into three "campuses".


title: American University

text: Formerly the Immaculata School, Tenley Campus is located half a mile east of the main campus and was purchased by American University in 1987 specifically for the Washington Semester program. Tenley Campus used to be home to the Washington Semester and Washington Mentorship Program students, which featured housing primarily for international and transfer students. Before the construction of the new Washington College of Law, Tenley Campus was home to the main offices of: the School of Professional & Extended Studies, including the Washington Semester Program, University Marketing and Publications, and the Osher Lifelong Learning Institute. During the summer, the residence halls were used to house students in the Washington Semester - Summer Internship Program.


title: American University

text: Since 2016, Tenley Campus has been home to American University's law school, the Washington College of Law. Over several years, former dormitory halls and academic buildings were torn down and replaced with many newer, more contemporary academic buildings that now house the Washington College of Law. The law school's reputation has fallen since construction began on the new campus. Graduates are reportedly saddled with enormous amounts of debt, and in 2014 only 42% of graduates held jobs that required they pass the Bar.


title: American University

text: The university is composed of eight divisions, referred to as colleges or schools, which house its academic programs. Except for WCL, undergraduate and graduate courses are housed within the same division, although organized into different programs.


title: American University

text: American University is also home to a unique program known as the Washington Semester Program. This program partners with institutions around the world to bring students to AU for a semester. The program operates as part of the School of Professional & Extended Studies. The program combines two seminar courses three days a week with a two-day-per-week internship that gives students a unique look at Washington, D.C. The program is unique because the courses are not typical lecture courses; instead, speakers from various sectors of a particular field are invited to address the class, often from different perspectives.


title: American University

text: In the "Chronicle of Higher Education" survey of college presidents' salaries for 2007–08, President Cornelius M. Kerwin was fifth highest in the nation with a compensation of $1.4 million.


title: American University

text: Admission to American is considered to be "more selective" by the "U.S. News & World Report". For the Class of 2023 (enrolling fall 2019), AU received 18,545 freshmen applications; 6,691 were admitted (36%) and 1,755 enrolled. The middle 50% range of SAT scores were 590–690 for Evidence-Based Reading and Writing and 590–690 for Math. The middle 50% range of the ACT Composite score was 27–31.


title: American University

text: "The U.S. News & World Report" has ranked American University 7th in Study Abroad programs. American University operates three premier programs in Brussels, Belgium; Madrid, Spain; and Nairobi, Kenya but, also partners with universities across the globe. Students can study abroad for a semester or a year or with programs available at the London School of Economics, Peking University, University of Warwick, Freie University Berlin, Yonsei University, Sorbonne University, Sciences Po and the Balsillie School of International Affairs.


title: American University

text: American University's undergraduate program was tied for 76th overall among "national universities" in "U.S. News & World Report" 2021 rankings, tied for 25th in "Best Undergraduate Teaching", tied for 35th in "Most Innovative Schools", and 82nd in "Best Value Schools".


title: American University

text: In 2008, 2010, 2012, and 2018, American University was named the most politically active school in the nation by "The Princeton Review"'s annual survey of college students. In 2006, the "Fiske Guide to Colleges" ranked AU as a "Best Buy" college for the quality of academic offerings in relation to the cost of attendance. However, in 2013, the Daily Beast listed the school in their list of "20 Least Affordable Colleges". For two years in a row, American University has had more students chosen to receive Presidential Management Fellowships than any other college or university in the country. In spring 2006, 34 graduate and law students were chosen for the honor. American University routinely ranks among the top mid-sized universities for producing Peace Corps volunteers.


title: American University

text: Among The Association of Professional Schools of International Affairs (APSIA) schools, AU School of International Service has the largest number of minority students and female students. It is ranked 6th among APSIA schools in numbers of international students. A review in "Foreign Policy Magazine" ranked the school 8th in the country for preparing future foreign policy professionals and 25th for academic careers. SIS's undergraduate programs earned a spot at number 11, and its graduate programs were ranked number 8. Because the field of international relations is not evaluated by "U.S. News & World Report", the College of William and Mary recently published the results of their survey, which ranked the AU international relations master's degree in the top 10 in the United States and the doctoral degree in the top 25. The School of Communication is among the top 25 in the nation, and it graduates the third-largest number of communication professionals among U.S. colleges and universities. The School of Public Affairs is ranked 13th in the U.S. by "U.S. News & World Report" for 2020.


title: American University

text: The cross-campus American University Center for Innovation (AUCI) was recognized the Association to Advance Collegiate Schools of Business (AACSB) as one of the world's top twenty entrepreneurship centers in April 2017. At the undergraduate level, AUCI offers an entrepreneurship minor for all university majors and a specialization for business school students.


title: American University

text: "Folio" is a literary magazine founded in 1984 and based at American University. It publishes fiction, poetry, and creative nonfiction twice each year. "Folio" is also known for interviews with prominent writers, most recently Ann Beattie, Alice Fulton, Leslie Pietrzyk, Gregory Orr, and Adam Haslett. Work that has appeared in "Folio" was short-listed for the Pushcart Prize multiple time in the 1980s. Among the notable stories that first appeared in "Folio" are Jacob M. Appel's "Fata Morgana" and "Becoming Coretta Davis" by I. Bennett Capers.


title: American University

text: On September 24, 2018, AU President Sylvia M. Burwell announced the Sine Institute of Policy and Politics. Taking advantage of AU's location in the nation's capital, the institute will bring together scholars, journalists, and experts from the public, private, and nonprofit sectors to find common ground and bipartisan policy solutions to the nation's problems. The Sine Institute launched with a conversation between Burwell and Republican Senator Bob Corker of Tennessee. Amy K. Dacey is the first and current executive director of the Sine Institute.


title: American University

text: The Jack I. and Dorothy G. Bender Library and Learning Resources Center is the main library facility for the campus. A branch Music Library is located in the Katzen Art Center. The Pence Law Library, part of AU's Washington College of Law, operates separately from the main library system. The University Library is part of the Washington Research Library Consortium (WRLC), which includes seven other libraries. The WRLC operates a consortium loan service between member institutions and has a shared collections site in Upper Marlboro, Maryland.


title: American University

text: The Bender Library provides various individual and group study spaces. It includes a Curriculum Materials Center, a New Media Center, Graduate Research Center, classrooms, and a café. About 160 public computer workstations are available throughout the Bender building. Researchers also may borrow laptops, chargers, tablets, and other electronic devices. In October 2012, the library acquired a large poster printer which researchers may use for presentations and other academic purposes.


title: American University

text: The Library's Archives and Special Collections houses unique and rare materials and information on the institution's history. The University Archives is the repository for papers and other documents, including sound recordings and photographs, spanning more than a century of the university's history. Special Collections houses rare materials. Among the more important holdings are the Artemas Martin collection of mathematical texts, the Charles Nelson Spinks collection of artistic and historical works of Japan, the Irwin M. Heine collection of literary works, and Christopher Johnson collection of William Faulkner books. Playbills form a significant set of the collections, with the James Carroll and Iris Lipkowitz collections most notable among them. Other significant collections include the Barlett & Steele Archive, the John R. Hickman Collection, the Friends of Colombia Archives, the Records of the National Peace Corps Association, the Records of the National Commission on the Public Service, the Sally L. Smith Papers, and the Records of Women Strike for Peace.


title: American University

text: AU has over 240 recognized organizations on campus, ranging from political and social. The Student Union Board (SUB), a part of the Student Government, is AU's oldest student-run organization. Since 1963, the SUB has arranged big name concerts and live entertainment for AU. Acts have ranged from the Grateful Dead to Ben Folds. Past acts include Chance The Rapper, Lupe Fiasco, Bob Dylan, Nirvana, Red Hot Chili Peppers, Andrew W.K., Phantom Planet, Everclear, Ben Kweller, Jimmy Eat World, Paramore, Stephen Lynch, Jim Gaffigan, Snow Patrol, Ghostface Killah, Ted Leo and the Pharmacists, Blackalicious, Metro Boomin, and Hayley Kiyoko. SUB also screens free second-run movies for the AU community, known as SUB Cinema.


title: American University

text: American University also has an internationally top-ranked Model United Nations team (ranking 1st in North America following the 2021-2022 academic year). The team competes actively at intercollegiate tournaments, and also hosts "AmeriMUNC" (American Model United Nations Conference) a yearly High School Model UN competition on campus.


title: American University

text: AU has eight student-run university-recognized media organizations, including "The Eagle" newspaper, radio station WVAU, the Second District Records record label, the American Literary Magazine (AmLit), and several magazines. These media organizations are governed by a Student Media Board and are funded through the university's undergraduate student activity fee:


title: American University

text: American University's feminist student-run clubs include AUSG Women's Initiative (WI), the first-generation women student-run organization which "advocates for AU by creating responsive programming addressing gender & sexuality based issues." Another is Sister Sister AU. The mission is described as "building a community for women of the African Diaspora at American University." Black Girls Vote is "dedicated to the engagement, education, and empowerment of collegiate women through the electoral process."


title: American University

text: American University's institutional feminist organizations include the Women and Politics Institute in the School of Public Affairs. The institute announces its mission on its website as "to close the gender gap in political leadership and provide young women with academic and practical training that encourages them to become involved in the political process and facilitates research by faculty and students that enhances their understanding of the challenges and opportunities women face in the political arena." The department of Women's, Gender, and Sexuality Studies (WGSS) within the College of Arts and Sciences is "an interdisciplinary program encompassing feminist studies, masculinity studies, and sexuality studies. The program is committed to a multicultural curriculum that sustains and integrates diverse perspectives." Students who major or minor in WGSS gain experience off-campus through an internship placement in an organization or agency whose mission embraces some aspect of women's/gender/sexuality studies. WGSS has both undergraduate programs and graduate programs.


title: American University

text: American University's discrimination and sexual harassment policy regarding Title IX rights is "to prohibit sex- or gender-based harassment and discrimination, sexual violence, relationship violence, and stalking. American University is committed to creating an accessible and inclusive environment for all students and employees." AU's Office of Advocacy Services for Interpersonal and Sexual Violence (OASIS) "provides free and confidential victim advocacy services for American University students who are impacted by all forms of sexual violence either directly or indirectly." The Center for Diversity and Inclusion (CDI) is dedicated to enhancing LGBTQ, multicultural, first-generation, and women's experiences on campus.


title: American University

text: AU is also home to several women suffragist alumni such as Alice Paul, one of the prominent leaders and strategists of the suffrage campaign. In 1896, The Washington College of Law was founded for women. In 1915, 5 of AU's first 28 students were women.


title: American University

text: While AU is affiliated with the United Methodist Church and hosts the AU United Methodist Community, AU has a variety of other religious life groups, including Catholic, Chabad Lubavitch of the AU Community, American University Hillel, and the Jewish Student Association.


title: American University

text: American University has a Panhellenic Association (PHA), Interfraternity Council (IFC), National Pan-Hellenic Council (NPHC), and Multicultural Greek Council (MGC). There are also several independent organizations.


title: American University

text: In 2008, American University joined more than 500 other US universities in signing the American College and University Presidents Climate Commitment, demonstrating the university's commitment to environmental responsibility. Within a year, American University's Office of Sustainability was established. In 2010, American University adopted a zero-waste policy and released its first climate action plan, with the goal of achieving carbon neutrality by 2020.


title: American University

text: An environmental science class at American conducted a study from February to April 2009 to measure the amount of food waste avoided by eliminating trays from one of the college's dining halls. The class found that trayless dinners resulted in 47.1% less solid waste than dinners during which trays were used, spurring a student-driven campaign to go trayless across campus.


title: American University

text: In 2011, the Association for the Advancement of Sustainability in Higher Education (AASHE) awarded American University a gold rating, the highest possible, on their STARS scale for sustainability. Since then, American University has earned five consecutive gold ratings, the most recent in 2020.


title: American University

text: Also in 2011, American University's School of International Service building earned Leadership in Energy and Environmental Design (LEED) Gold certification for its 70,000 square foot building renowned for sustainable design and "cradle-to-cradle" philosophy.


title: American University

text: In 2014, the university announced an ambitious project to build a solar farm in partnership with George Washington University. , the completed solar farm provides an equivalent of 50% of the university's electricity.


title: American University

text: In 2018, American University became the first university in the United States to achieve carbon-neutral status.


title: American University

text: In 2020, American University announced that it had eliminated all public fossil fuel investments from its endowment.


title: American University

text: A member of the Patriot League, AU has several sports teams including men's and women's basketball, soccer, cross-country, swimming and diving, track, women's volleyball, field hockey, and lacrosse, and men's wrestling. Club sports, such as tennis, rugby, rowing, ice hockey, field hockey, equestrian and ultimate frisbee also have teams. AU's football team had their last season in 1941.


title: American University

text: Bender Arena, a multi-purpose facility, hosts many of American's athletic competitions. Bender Arena opened on January 23, 1988, when AU's women's basketball team hosted James Madison University.


title: American University

text: Reeves Field, home to AU's soccer team, earned the 2002 College Soccer Field of the Year by the Sports Turf Managers Association, hosted its fifth NCAA Tournament game, and served as the training site for the Uruguayan national football team. Reeves Field features a six-lane track to accommodate the track and field programs at AU and functions as a multi-purpose event site.


title: American University

text: American University has seven tennis courts and two basketball courts in the outdoor recreational facility located next to Reeves Field and behind Bender Arena. AU has hosted Patriot League tennis team championships three times since joining the league. Both the men's and women's tennis teams have been cut from the athletics program.


title: American University

text: On March 14, 2008, AU earned its first NCAA tournament berth in men's basketball by defeating Colgate University in the Patriot League Championship Game. However, AU lost its first-round NCAA tournament game against the University of Tennessee. On March 13, 2009, AU's men's basketball team repeated as Patriot League Champion by defeating Holy Cross 73–57, earning an automatic bid to the NCAA Men's Division I Basketball Championship. They ultimately lost to Villanova University in the first round on March 19, 2009, with a final score of 80–67.


title: American University

text: William I Jacobs Recreational Complex is also located on campus, containing an AstroTurf surface, a softball diamond, and two sand volleyball courts.


title: American University

text: Off-campus facilities include the Massachusetts Ave. Field, which hosts intramural and varsity athletic practices for both the Men's and Women's soccer teams.


title: American University

text: The Marilyn Meltzer Wrestling Room is located within Jacobs Fitness Center, and hosts practices for the Men's Varsity Wrestling Team at American University.


title: Atomic orbital

text: In atomic theory and quantum mechanics, an atomic orbital is a function describing the location and wave-like behavior of an electron in an atom. This function can be used to calculate the probability of finding any electron of an atom in any specific region around the atom's nucleus. The term "atomic orbital" may also refer to the physical region or space where the electron can be calculated to be present, as predicted by the particular mathematical form of the orbital.


title: Atomic orbital

text: Each orbital in an atom is characterized by a set of values of the three quantum numbers , , and , which respectively correspond to the electron's energy, angular momentum, and an angular momentum vector component (magnetic quantum number). Alternative to the magnetic quantum number, the orbitals are often labeled by the associated harmonic polynomials (e.g., "xy", ). Each such orbital can be occupied by a maximum of two electrons, each with its own projection of spin formula_1. The simple names s orbital, p orbital, d orbital, and f orbital refer to orbitals with angular momentum quantum number and respectively. These names, together with the value of , are used to describe the electron configurations of atoms. They are derived from the description by early spectroscopists of certain series of alkali metal spectroscopic lines as sharp, principal, diffuse, and fundamental. Orbitals for > 3 continue alphabetically (g, h, i, k, ...), omitting j because some languages do not distinguish between the letters "i" and "j".


title: Atomic orbital

text: Atomic orbitals are the basic building blocks of the atomic orbital model (or electron cloud or wave mechanics model), a modern framework for visualizing the submicroscopic behavior of electrons in matter. In this model the electron cloud of an atom may be seen as being built up (in approximation) in an electron configuration that is a product of simpler hydrogen-like atomic orbitals. The repeating "periodicity" of blocks of 2, 6, 10, and 14 elements within sections of the periodic table arises naturally from the total number of electrons that occupy a complete set of s, p, d, and f orbitals, respectively, though for higher values of quantum number , particularly when the atom bears a positive charge, the energies of certain sub-shells become very similar and so the order in which they are said to be populated by electrons (e.g., Cr = [Ar]4s3d and Cr = [Ar]3d) can be rationalized only somewhat arbitrarily.


title: Atomic orbital

text: With the development of quantum mechanics and experimental findings (such as the two slit diffraction of electrons), it was found that the electrons orbiting a nucleus could not be fully described as particles, but needed to be explained by wave–particle duality. In this sense, electrons have the following properties:


title: Atomic orbital

text: Thus, electrons cannot be described simply as solid particles. An analogy might be that of a large and often oddly shaped "atmosphere" (the electron), distributed around a relatively tiny planet (the nucleus). Atomic orbitals exactly describe the shape of this "atmosphere" only when one electron is present. When more electrons are added, the additional electrons tend to more evenly fill in a volume of space around the nucleus so that the resulting collection ("electron cloud") tends toward a generally spherical zone of probability describing the electron's location, because of the uncertainty principle.


title: Atomic orbital

text: Atomic orbitals may be defined more precisely in formal quantum mechanical language. They are approximate solutions to the Schrödinger equation for the electrons bound to the atom by the electric field of the atom's nucleus. Specifically, in quantum mechanics, the state of an atom, i.e., an eigenstate of the atomic Hamiltonian, is approximated by an expansion (see configuration interaction expansion and basis set) into linear combinations of anti-symmetrized products (Slater determinants) of one-electron functions. The spatial components of these one-electron functions are called atomic orbitals. (When one considers also their spin component, one speaks of atomic spin orbitals.) A state is actually a function of the coordinates of all the electrons, so that their motion is correlated, but this is often approximated by this independent-particle model of products of single electron wave functions. (The London dispersion force, for example, depends on the correlations of the motion of the electrons.)


title: Atomic orbital

text: In atomic physics, the atomic spectral lines correspond to transitions (quantum leaps) between quantum states of an atom. These states are labeled by a set of quantum numbers summarized in the term symbol and usually associated with particular electron configurations, i.e., by occupation schemes of atomic orbitals (for example, 1s 2s 2p for the ground state of neon-term symbol: S).


title: Atomic orbital

text: This notation means that the corresponding Slater determinants have a clear higher weight in the configuration interaction expansion. The atomic orbital concept is therefore a key concept for visualizing the excitation process associated with a given transition. For example, one can say for a given transition that it corresponds to the excitation of an electron from an occupied orbital to a given unoccupied orbital. Nevertheless, one has to keep in mind that electrons are fermions ruled by the Pauli exclusion principle and cannot be distinguished from each other. Moreover, it sometimes happens that the configuration interaction expansion converges very slowly and that one cannot speak about simple one-determinant wave function at all. This is the case when electron correlation is large.


title: Atomic orbital

text: Fundamentally, an atomic orbital is a one-electron wave function, even though many electrons are not in one-electron atoms, and so the one-electron view is an approximation. When thinking about orbitals, we are often given an orbital visualization heavily influenced by the Hartree–Fock approximation, which is one way to reduce the complexities of molecular orbital theory.


title: Atomic orbital

text: Atomic orbitals can be the hydrogen-like "orbitals" which are exact solutions to the Schrödinger equation for a hydrogen-like "atom" (i.e., atom with one electron). Alternatively, atomic orbitals refer to functions that depend on the coordinates of one electron (i.e., orbitals) but are used as starting points for approximating wave functions that depend on the simultaneous coordinates of all the electrons in an atom or molecule. The coordinate systems chosen for orbitals are usually spherical coordinates in atoms and Cartesian in polyatomic molecules. The advantage of spherical coordinates here is that an orbital wave function is a product of three factors each dependent on a single coordinate: . The angular factors of atomic orbitals generate s, p, d, etc. functions as real combinations of spherical harmonics (where and are quantum numbers). There are typically three mathematical forms for the radial functions  which can be chosen as a starting point for the calculation of the properties of atoms and molecules with many electrons:


title: Atomic orbital

text: Although hydrogen-like orbitals are still used as pedagogical tools, the advent of computers has made STOs preferable for atoms and diatomic molecules since combinations of STOs can replace the nodes in hydrogen-like orbitals. Gaussians are typically used in molecules with three or more atoms. Although not as accurate by themselves as STOs, combinations of many Gaussians can attain the accuracy of hydrogen-like orbitals.


title: Atomic orbital

text: The term "orbital" was coined by Robert Mulliken in 1932 as short for "one-electron orbital wave function". Niels Bohr explained around 1913 that electrons might revolve around a compact nucleus with definite angular momentum. Bohr's model was an improvement on the 1911 explanations of Ernest Rutherford, that of the electron moving around a nucleus. Japanese physicist Hantaro Nagaoka published an orbit-based hypothesis for electron behavior as early as 1904. These theories were each built upon new observations starting with simple understanding and becoming more correct and complex. Explaining the behavior of these electron "orbits" was one of the driving forces behind the development of quantum mechanics.


title: Atomic orbital

text: With J. J. Thomson's discovery of the electron in 1897, it became clear that atoms were not the smallest building blocks of nature, but were rather composite particles. The newly discovered structure within atoms tempted many to imagine how the atom's constituent parts might interact with each other. Thomson theorized that multiple electrons revolve in orbit-like rings within a positively charged jelly-like substance, and between the electron's discovery and 1909, this "plum pudding model" was the most widely accepted explanation of atomic structure.


title: Atomic orbital

text: Shortly after Thomson's discovery, Hantaro Nagaoka predicted a different model for electronic structure. Unlike the plum pudding model, the positive charge in Nagaoka's "Saturnian Model" was concentrated into a central core, pulling the electrons into circular orbits reminiscent of Saturn's rings. Few people took notice of Nagaoka's work at the time, and Nagaoka himself recognized a fundamental defect in the theory even at its conception, namely that a classical charged object cannot sustain orbital motion because it is accelerating and therefore loses energy due to electromagnetic radiation. Nevertheless, the Saturnian model turned out to have more in common with modern theory than any of its contemporaries.


title: Atomic orbital

text: In 1909, Ernest Rutherford discovered that the bulk of the atomic mass was tightly condensed into a nucleus, which was also found to be positively charged. It became clear from his analysis in 1911 that the plum pudding model could not explain atomic structure. In 1913, Rutherford's post-doctoral student, Niels Bohr, proposed a new model of the atom, wherein electrons orbited the nucleus with classical periods, but were permitted to have only discrete values of angular momentum, quantized in units ħ. This constraint automatically allowed only certain electron energies. The Bohr model of the atom fixed the problem of energy loss from radiation from a ground state (by declaring that there was no state below this), and more importantly explained the origin of spectral lines.


title: Atomic orbital

text: After Bohr's use of Einstein's explanation of the photoelectric effect to relate energy levels in atoms with the wavelength of emitted light, the connection between the structure of electrons in atoms and the emission and absorption spectra of atoms became an increasingly useful tool in the understanding of electrons in atoms. The most prominent feature of emission and absorption spectra (known experimentally since the middle of the 19th century), was that these atomic spectra contained discrete lines. The significance of the Bohr model was that it related the lines in emission and absorption spectra to the energy differences between the orbits that electrons could take around an atom. This was, however, "not" achieved by Bohr through giving the electrons some kind of wave-like properties, since the idea that electrons could behave as matter waves was not suggested until eleven years later. Still, the Bohr model's use of quantized angular momenta and therefore quantized energy levels was a significant step toward the understanding of electrons in atoms, and also a significant step towards the development of quantum mechanics in suggesting that quantized restraints must account for all discontinuous energy levels and spectra in atoms.


title: Atomic orbital

text: With de Broglie's suggestion of the existence of electron matter waves in 1924, and for a short time before the full 1926 Schrödinger equation treatment of hydrogen-like atoms, a Bohr electron "wavelength" could be seen to be a function of its momentum; so a Bohr orbiting electron was seen to orbit in a circle at a multiple of its half-wavelength. The Bohr model for a short time could be seen as a classical model with an additional constraint provided by the 'wavelength' argument. However, this period was immediately superseded by the full three-dimensional wave mechanics of 1926. In our current understanding of physics, the Bohr model is called a semi-classical model because of its quantization of angular momentum, not primarily because of its relationship with electron wavelength, which appeared in hindsight a dozen years after the Bohr model was proposed.


title: Atomic orbital

text: The Bohr model was able to explain the emission and absorption spectra of hydrogen. The energies of electrons in the "n" = 1, 2, 3, etc. states in the Bohr model match those of current physics. However, this did not explain similarities between different atoms, as expressed by the periodic table, such as the fact that helium (two electrons), neon (10 electrons), and argon (18 electrons) exhibit similar chemical inertness. Modern quantum mechanics explains this in terms of electron shells and subshells which can each hold a number of electrons determined by the Pauli exclusion principle. Thus the "n" = 1 state can hold one or two electrons, while the "n" = 2 state can hold up to eight electrons in 2s and 2p subshells. In helium, all "n" = 1 states are fully occupied; the same is true for "n" = 1 and "n" = 2 in neon. In argon, the 3s and 3p subshells are similarly fully occupied by eight electrons; quantum mechanics also allows a 3d subshell but this is at higher energy than the 3s and 3p in argon (contrary to the situation for hydrogen) and remains empty.


title: Atomic orbital

text: Immediately after Heisenberg discovered his uncertainty principle, Bohr noted that the existence of any sort of wave packet implies uncertainty in the wave frequency and wavelength, since a spread of frequencies is needed to create the packet itself. In quantum mechanics, where all particle momenta are associated with waves, it is the formation of such a wave packet which localizes the wave, and thus the particle, in space. In states where a quantum mechanical particle is bound, it must be localized as a wave packet, and the existence of the packet and its minimum size implies a spread and minimal value in particle wavelength, and thus also momentum and energy. In quantum mechanics, as a particle is localized to a smaller region in space, the associated compressed wave packet requires a larger and larger range of momenta, and thus larger kinetic energy. Thus the binding energy to contain or trap a particle in a smaller region of space increases without bound as the region of space grows smaller. Particles cannot be restricted to a geometric point in space, since this would require infinite particle momentum.


title: Atomic orbital

text: In chemistry, Schrödinger, Pauling, Mulliken and others noted that the consequence of Heisenberg's relation was that the electron, as a wave packet, could not be considered to have an exact location in its orbital. Max Born suggested that the electron's position needed to be described by a probability distribution which was connected with finding the electron at some point in the wave-function which described its associated wave packet. The new quantum mechanics did not give exact results, but only the probabilities for the occurrence of a variety of possible such results. Heisenberg held that the path of a moving particle has no meaning if we cannot observe it, as we cannot with electrons in an atom.


title: Atomic orbital

text: In the quantum picture of Heisenberg, Schrödinger and others, the Bohr atom number "n" for each orbital became known as an "n-sphere" in a three-dimensional atom and was pictured as the most probable energy of the probability cloud of the electron's wave packet which surrounded the atom.


title: Atomic orbital

text: where "X" is the energy level corresponding to the principal quantum number ; type is a lower-case letter denoting the shape or subshell of the orbital, corresponding to the angular momentum quantum number .


title: Atomic orbital

text: For example, the orbital 1s (pronounced as the individual numbers and letters: "'one' 'ess'") is the lowest energy level () and has an angular quantum number of , denoted as s. Orbitals with are denoted as p, d and f respectively.


title: Atomic orbital

text: The exponent y shows the number of electrons in the subshell. For example, the notation 2p indicates that the 2p subshell of an atom contains 4 electrons. This subshell has 3 orbitals, each with n = 2 and = 1.


title: Atomic orbital

text: There is also another, less common system still used in X-ray science known as X-ray notation, which is a continuation of the notations used before orbital theory was well understood. In this system, the principal quantum number is given a letter associated with it. For , the letters associated with those numbers are K, L, M, N, O, ... respectively.


title: Atomic orbital

text: The simplest atomic orbitals are those that are calculated for systems with a single electron, such as the hydrogen atom. An atom of any other element ionized down to a single electron is very similar to hydrogen, and the orbitals take the same form. In the Schrödinger equation for this system of one negative and one positive particle, the atomic orbitals are the eigenstates of the Hamiltonian operator for the energy. They can be obtained analytically, meaning that the resulting orbitals are products of a polynomial series, and exponential and trigonometric functions. (see hydrogen atom).


title: Atomic orbital

text: For atoms with two or more electrons, the governing equations can be solved only with the use of methods of iterative approximation. Orbitals of multi-electron atoms are "qualitatively" similar to those of hydrogen, and in the simplest models, they are taken to have the same form. For more rigorous and precise analysis, numerical approximations must be used.


title: Atomic orbital

text: A given (hydrogen-like) atomic orbital is identified by unique values of three quantum numbers: , , and . The rules restricting the values of the quantum numbers, and their energies (see below), explain the electron configuration of the atoms and the periodic table.


title: Atomic orbital

text: The stationary states (quantum states) of the hydrogen-like atoms are its atomic orbitals. However, in general, an electron's behavior is not fully described by a single orbital. Electron states are best represented by time-depending "mixtures" (linear combinations) of multiple orbitals. See Linear combination of atomic orbitals molecular orbital method.


title: Atomic orbital

text: The quantum number first appeared in the Bohr model where it determines the radius of each circular electron orbit. In modern quantum mechanics however, determines the mean distance of the electron from the nucleus; all electrons with the same value of "n" lie at the same average distance. For this reason, orbitals with the same value of "n" are said to comprise a "shell". Orbitals with the same value of "n" and also the same value of  are even more closely related, and are said to comprise a "subshell".


title: Atomic orbital

text: Because of the quantum mechanical nature of the electrons around a nucleus, atomic orbitals can be uniquely defined by a set of integers known as quantum numbers. These quantum numbers occur only in certain combinations of values, and their physical interpretation changes depending on whether real or complex versions of the atomic orbitals are employed.


title: Atomic orbital

text: In physics, the most common orbital descriptions are based on the solutions to the hydrogen atom, where orbitals are given by the product between a radial function and a pure spherical harmonic. The quantum numbers, together with the rules governing their possible values, are as follows:


title: Atomic orbital

text: The principal quantum number describes the energy of the electron and is always a positive integer. In fact, it can be any positive integer, but for reasons discussed below, large numbers are seldom encountered. Each atom has, in general, many orbitals associated with each value of "n"; these orbitals together are sometimes called "electron shells".


title: Atomic orbital

text: The azimuthal quantum number describes the orbital angular momentum of each electron and is a non-negative integer. Within a shell where is some integer , ranges across all (integer) values satisfying the relation formula_5. For instance, the  shell has only orbitals with formula_6, and the  shell has only orbitals with formula_6, and formula_8. The set of orbitals associated with a particular value of  are sometimes collectively called a "subshell".


title: Atomic orbital

text: The magnetic quantum number, formula_9, describes the magnetic moment of an electron in an arbitrary direction, and is also always an integer. Within a subshell where formula_10 is some integer formula_11, formula_9 ranges thus: formula_13.


title: Atomic orbital

text: The above results may be summarized in the following table. Each cell represents a subshell, and lists the values of formula_9 available in that subshell. Empty cells represent subshells that do not exist.


title: Atomic orbital

text: Subshells are usually identified by their formula_15- and formula_10-values. formula_15 is represented by its numerical value, but formula_10 is represented by a letter as follows: 0 is represented by 's', 1 by 'p', 2 by 'd', 3 by 'f', and 4 by 'g'. For instance, one may speak of the subshell with formula_19 and formula_6 as a '2s subshell'.


title: Atomic orbital

text: Each electron also has a spin quantum number, "s", which describes the spin of each electron (spin up or spin down). The number "s" can be + or −.


title: Atomic orbital

text: The Pauli exclusion principle states that no two electrons in an atom can have the same values of all four quantum numbers. If there are two electrons in an orbital with given values for three quantum numbers, (, , ), these two electrons must differ in their spin.


title: Atomic orbital

text: The above conventions imply a preferred axis (for example, the "z" direction in Cartesian coordinates), and they also imply a preferred direction along this preferred axis. Otherwise there would be no sense in distinguishing from . As such, the model is most useful when applied to physical systems that share these symmetries. The Stern–Gerlach experiment — where an atom is exposed to a magnetic field — provides one such example.


title: Atomic orbital

text: In addition to the complex orbitals described above, it is common, especially in the chemistry literature, to utilize "real" atomic orbitals. These real orbitals arise from simple linear combinations of complex orbitals. Using the Condon–Shortley phase convention, real orbitals are related to complex orbitals in the same way that the real spherical harmonics are related to complex spherical harmonics. Letting formula_21 denote a complex orbital with quantum numbers formula_15, formula_23, and formula_24, the real orbitals formula_25 may be defined by


title: Atomic orbital

text: If formula_27, with formula_28 the radial part of the orbital, this definition is equivalent to formula_29 where formula_30 is the real spherical harmonic related to either the real or imaginary part of the complex spherical harmonic formula_31.


title: Atomic orbital

text: Real spherical harmonics are physically relevant when an atom is embedded in a crystalline solid, in which case there are multiple preferred symmetry axes but no single preferred direction. Real atomic orbitals are also more frequently encountered in introductory chemistry textbooks and shown in common orbital visualizations. In real hydrogen-like orbitals, quantum numbers formula_15 and formula_10 have the same interpretation and significance as their complex counterparts, but formula_24 is no longer a good quantum number (but its absolute value is).


title: Atomic orbital

text: Some real orbitals are given specific names beyond the simple formula_35 designation. Orbitals with quantum number formula_10 equal to formula_37 are called formula_38 orbitals. With this one can already assign names to complex orbitals such as formula_39; the first symbol is the formula_15 quantum number, the second number is the symbol for that particular formula_10 quantum number and the subscript is the formula_24 quantum number.


title: Atomic orbital

text: As an example of how the full orbital names are generated for real orbitals, one may calculate formula_43. From the table of spherical harmonics, formula_44 with formula_45. Then


title: Atomic orbital

text: In all these cases we generate a Cartesian label for the orbital by examining, and abbreviating, the polynomial in formula_49, formula_50, and formula_51 appearing in the numerator. We ignore any terms in the formula_52 polynomial except for the term with the highest exponent in formula_51.


title: Atomic orbital

text: We then use the abbreviated polynomial as a subscript label for the atomic state, using the same nomenclature as above to indicate the formula_15 and formula_10 quantum numbers.


title: Atomic orbital

text: The expression above all use the Condon–Shortley phase convention which is favored by quantum physicists. Other conventions for the phase of the spherical harmonics exists. Under these different conventions the formula_57 and formula_58 orbitals may appear, for example, as the sum and difference of formula_59 and formula_60, contrary to what is shown above.


title: Atomic orbital

text: Below is a list of these Cartesian polynomial names for the atomic orbitals. Note that there does not seem to be reference in the literature as to how to abbreviate the long Cartesian spherical harmonic polynomials for formula_61 so there does not seem be consensus on the naming of formula_62 orbitals or higher according to this nomenclature.


title: Atomic orbital

text: Simple pictures showing orbital shapes are intended to describe the angular forms of regions in space where the electrons occupying the orbital are likely to be found. The diagrams cannot show the entire region where an electron can be found, since according to quantum mechanics there is a non-zero probability of finding the electron (almost) anywhere in space. Instead the diagrams are approximate representations of boundary or contour surfaces where the probability density has a constant value, chosen so that there is a certain probability (for example 90%) of finding the electron within the contour. Although as the square of an absolute value is everywhere non-negative, the sign of the wave function is often indicated in each subregion of the orbital picture.


title: Atomic orbital

text: Sometimes the function is graphed to show its phases, rather than which shows probability density but has no phase (which is lost when taking absolute value, since is a complex number). orbital graphs tend to have less spherical, thinner lobes than graphs, but have the same number of lobes in the same places, and otherwise are recognizable. This article, in order to show wave function phase, shows mostly graphs.


title: Atomic orbital

text: The lobes can be seen as standing wave interference patterns between the two counter rotating, ring resonant traveling wave and modes; the projection of the orbital onto the xy plane has a resonant wavelength around the circumference. Alhough rarely shown, the traveling wave solutions can be seen as rotating banded tori; the bands represent phase information. For each there are two standing wave solutions and . If , the orbital is vertical, counter rotating information is unknown, and the orbital is "z"-axis symmetric. If there are no counter rotating modes. There are only radial modes and the shape is spherically symmetric. For any given , the smaller is, the more radial nodes there are. For any given , the smaller is, the fewer radial nodes there are (zero for whichever first has that orbital). Loosely speaking, is energy, is analogous to eccentricity, and is orientation. In the classical case, a ring resonant traveling wave, for example in a circular transmission line, unless actively forced, spontaneously decays into a ring resonant standing wave because reflections build up over time at even the smallest imperfection or discontinuity.


title: Atomic orbital

text: In general, determines size and energy of the orbital for a given nucleus; as increases, the size of the orbital increases. The higher nuclear charge of heavier elements causes their orbitals to contract by comparison to lighter ones, so that the size of the atom remains very roughly constant, even as the number of electrons increases.


title: Atomic orbital

text: Also in general terms, determines an orbital's shape, and its orientation. However, since some orbitals are described by equations in complex numbers, the shape sometimes depends on also. Together, the whole set of orbitals for a given and fill space as symmetrically as possible, though with increasingly complex sets of lobes and nodes.


title: Atomic orbital

text: The single s-orbitals (formula_6) are shaped like spheres. For it is roughly a solid ball (densest at center and fades outward exponentially), but for , each single s-orbital is made of spherically symmetric surfaces which are nested shells (i.e., the "wave-structure" is radial, following a sinusoidal radial component as well). See illustration of a cross-section of these nested shells, at right. The s-orbitals for all numbers are the only orbitals with an anti-node (a region of high wave function density) at the center of the nucleus. All other orbitals (p, d, f, etc.) have angular momentum, and thus avoid the nucleus (having a wave node "at" the nucleus). Recently, there has been an effort to experimentally image the 1s and 2p orbitals in a SrTiO crystal using scanning transmission electron microscopy with energy dispersive x-ray spectroscopy. Because the imaging was conducted using an electron beam, Coulombic beam-orbital interaction that is often termed as the impact parameter effect is included in the final outcome (see the figure at right).


title: Atomic orbital

text: The shapes of p, d and f-orbitals are described verbally here and shown graphically in the "Orbitals table" below. The three p-orbitals for have the form of two ellipsoids with a point of tangency at the nucleus (the two-lobed shape is sometimes referred to as a "dumbbell"—there are two lobes pointing in opposite directions from each other). The three p-orbitals in each shell are oriented at right angles to each other, as determined by their respective linear combination of values of . The overall result is a lobe pointing along each direction of the primary axes.


title: Atomic orbital

text: Four of the five d-orbitals for look similar, each with four pear-shaped lobes, each lobe tangent at right angles to two others, and the centers of all four lying in one plane. Three of these planes are the xy-, xz-, and yz-planes—the lobes are between the pairs of primary axes—and the fourth has the centre along the x and y axes themselves. The fifth and final d-orbital consists of three regions of high probability density: a torus in between two pear-shaped regions placed symmetrically on its z axis. The overall total of 18 directional lobes point in every primary axis direction and between every pair.


title: Atomic orbital

text: Additionally, as is the case with the s orbitals, individual p, d, f and g orbitals with values higher than the lowest possible value, exhibit an additional radial node structure which is reminiscent of harmonic waves of the same type, as compared with the lowest (or fundamental) mode of the wave. As with s orbitals, this phenomenon provides p, d, f, and g orbitals at the next higher possible value of (for example, 3p orbitals vs. the fundamental 2p), an additional node in each lobe. Still higher values of further increase the number of radial nodes, for each type of orbital.


title: Atomic orbital

text: The shapes of atomic orbitals in one-electron atom are related to 3-dimensional spherical harmonics. These shapes are not unique, and any linear combination is valid, like a transformation to cubic harmonics, in fact it is possible to generate sets where all the d's are the same shape, just like the and are the same shape.


title: Atomic orbital

text: Although individual orbitals are most often shown independent of each other, the orbitals coexist around the nucleus at the same time. Also, in 1927, Albrecht Unsöld proved that if one sums the electron density of all orbitals of a particular azimuthal quantum number of the same shell (e.g., all three 2p orbitals, or all five 3d orbitals) where each orbital is occupied by an electron or each is occupied by an electron pair, then all angular dependence disappears; that is, the resulting total density of all the atomic orbitals in that subshell (those with the same ) is spherical. This is known as Unsöld's theorem.


title: Atomic orbital

text: This table shows the real hydrogen-like wave functions for all atomic orbitals up to 7s, and therefore covers the occupied orbitals in the ground state of all elements in the periodic table up to radium and some beyond. "ψ" graphs are shown with − and + wave function phases shown in two different colors (arbitrarily red and blue). The orbital is the same as the orbital, but the and are formed by taking linear combinations of the and orbitals (which is why they are listed under the label). Also, the and are not the same shape as the , since they are pure spherical harmonics.


title: Atomic orbital

text: † "Elements with 7p electrons have been discovered, but their electronic configurations are only predicted."


title: Atomic orbital

text: ‡ "For the elements whose highest occupied orbital is a 6d orbital, only some electronic configurations have been confirmed." (Ds, Rg and Cn are still missing).


title: Atomic orbital

text: These are the real-valued orbitals commonly used in chemistry. Only the formula_64 orbitals where are eigenstates of the orbital angular momentum operator, formula_65. The columns with formula_66 are combinations of two eigenstates. See :


title: Atomic orbital

text: The shapes of atomic orbitals can be qualitatively understood by considering the analogous case of standing waves on a circular drum. To see the analogy, the mean vibrational displacement of each bit of drum membrane from the equilibrium point over many cycles (a measure of average drum membrane velocity and momentum at that point) must be considered relative to that point's distance from the center of the drum head. If this displacement is taken as being analogous to the probability of finding an electron at a given distance from the nucleus, then it will be seen that the many modes of the vibrating disk form patterns that trace the various shapes of atomic orbitals. The basic reason for this correspondence lies in the fact that the distribution of kinetic energy and momentum in a matter-wave is predictive of where the particle associated with the wave will be. That is, the probability of finding an electron at a given place is also a function of the electron's average momentum at that point, since high electron momentum at a given position tends to "localize" the electron in that position, via the properties of electron wave-packets (see the Heisenberg uncertainty principle for details of the mechanism).


title: Atomic orbital

text: This relationship means that certain key features can be observed in both drum membrane modes and atomic orbitals. For example, in all of the modes analogous to s orbitals (the top row in the animated illustration below), it can be seen that the very center of the drum membrane vibrates most strongly, corresponding to the antinode in all s orbitals in an atom. This antinode means the electron is most likely to be at the physical position of the nucleus (which it passes straight through without scattering or striking it), since it is moving (on average) most rapidly at that point, giving it maximal momentum.


title: Atomic orbital

text: A mental "planetary orbit" picture closest to the behavior of electrons in s orbitals, all of which have no angular momentum, might perhaps be that of a Keplerian orbit with the orbital eccentricity of 1 but a finite major axis, not physically possible (because particles were to collide), but can be imagined as a limit of orbits with equal major axes but increasing eccentricity.


title: Atomic orbital

text: Below, a number of drum membrane vibration modes and the respective wave functions of the hydrogen atom are shown. A correspondence can be considered where the wave functions of a vibrating drum head are for a two-coordinate system and the wave functions for a vibrating sphere are three-coordinate .


title: Atomic orbital

text: None of the other sets of modes in a drum membrane have a central antinode, and in all of them the center of the drum does not move. These correspond to a node at the nucleus for all non-s orbitals in an atom. These orbitals all have some angular momentum, and in the planetary model, they correspond to particles in orbit with eccentricity less than 1.0, so that they do not pass straight through the center of the primary body, but keep somewhat away from it.


title: Atomic orbital

text: In addition, the drum modes analogous to p and d modes in an atom show spatial irregularity along the different radial directions from the center of the drum, whereas all of the modes analogous to s modes are perfectly symmetrical in radial direction. The non radial-symmetry properties of non-s orbitals are necessary to localize a particle with angular momentum and a wave nature in an orbital where it must tend to stay away from the central attraction force, since any particle localized at the point of central attraction could have no angular momentum. For these modes, waves in the drum head tend to avoid the central point. Such features again emphasize that the shapes of atomic orbitals are a direct consequence of the wave nature of electrons.


title: Atomic orbital

text: In atoms with one electron (hydrogen-like atom), the energy of an orbital (and, consequently, any electron in the orbital) is determined mainly by formula_15. The formula_68 orbital has the lowest possible energy in the atom. Each successively higher value of formula_15 has a higher energy, but the difference decreases as formula_15 increases. For high formula_15, the energy becomes so high that the electron can easily escape the atom. In single electron atoms, all levels with different formula_10 within a given formula_15 are degenerate in the Schrödinger approximation, and have the same energy. This approximation is broken slightly in the solution to the Dirac equation (where energy depends on and another quantum number ), and by the effect of the magnetic field of the nucleus and quantum electrodynamics effects. The latter induce tiny binding energy differences especially for s electrons that go nearer the nucleus, since these feel a very slightly different nuclear charge, even in one-electron atoms; see Lamb shift.


title: Atomic orbital

text: In atoms with multiple electrons, the energy of an electron depends not only on its orbital, but also on its interactions with other electrons. These interactions depend on the detail of its spatial probability distribution, and so the energy levels of orbitals depend not only on formula_15 but also on formula_10. Higher values of formula_10 are associated with higher values of energy; for instance, the 2p state is higher than the 2s state. When formula_77, the increase in energy of the orbital becomes so large as to push the energy of orbital above the energy of the s-orbital in the next higher shell; when formula_78 the energy is pushed into the shell two steps higher. The filling of the 3d orbitals does not occur until the 4s orbitals have been filled.


title: Atomic orbital

text: The increase in energy for subshells of increasing angular momentum in larger atoms is due to electron–electron interaction effects, and it is specifically related to the ability of low angular momentum electrons to penetrate more effectively toward the nucleus, where they are subject to less screening from the charge of intervening electrons. Thus, in atoms with higher atomic number, the formula_10 of electrons becomes more and more of a determining factor in their energy, and the principal quantum numbers formula_15 of electrons becomes less and less important in their energy placement.


title: Atomic orbital

text: The energy sequence of the first 35 subshells (e.g., 1s, 2p, 3d, etc.) is given in the following table. Each cell represents a subshell with formula_15 and formula_10 given by its row and column indices, respectively. The number in the cell is the subshell's position in the sequence. For a linear listing of the subshells in terms of increasing energies in multielectron atoms, see the section below.


title: Atomic orbital

text: "Note: empty cells indicate non-existent sublevels, while numbers in italics indicate sublevels that could (potentially) exist, but which do not hold electrons in any element currently known."


title: Atomic orbital

text: Several rules govern the placement of electrons in orbitals ("electron configuration"). The first dictates that no two electrons in an atom may have the same set of values of quantum numbers (this is the Pauli exclusion principle). These quantum numbers include the three that define orbitals, as well as , or spin quantum number. Thus, two electrons may occupy a single orbital, so long as they have different values of . However, "only" two electrons, because of their spin, can be associated with each orbital.


title: Atomic orbital

text: Additionally, an electron always tends to fall to the lowest possible energy state. It is possible for it to occupy any orbital so long as it does not violate the Pauli exclusion principle, but if lower-energy orbitals are available, this condition is unstable. The electron will eventually lose energy (by releasing a photon) and drop into the lower orbital. Thus, electrons fill orbitals in the order specified by the energy sequence given above.


title: Atomic orbital

text: This behavior is responsible for the structure of the periodic table. The table may be divided into several rows (called 'periods'), numbered starting with 1 at the top. The presently known elements occupy seven periods. If a certain period has number "i", it consists of elements whose outermost electrons fall in the "i"th shell. Niels Bohr was the first to propose (1923) that the periodicity in the properties of the elements might be explained by the periodic filling of the electron energy levels, resulting in the electronic structure of the atom.


title: Atomic orbital

text: The periodic table may also be divided into several numbered rectangular 'blocks'. The elements belonging to a given block have this common feature: their highest-energy electrons all belong to the same -state (but the associated with that -state depends upon the period). For instance, the leftmost two columns constitute the 's-block'. The outermost electrons of Li and Be respectively belong to the 2s subshell, and those of Na and Mg to the 3s subshell.


title: Atomic orbital

text: The following is the order for filling the "subshell" orbitals, which also gives the order of the "blocks" in the periodic table:


title: Atomic orbital

text: The "periodic" nature of the filling of orbitals, as well as emergence of the s, p, d, and f "blocks", is more obvious if this order of filling is given in matrix form, with increasing principal quantum numbers starting the new rows ("periods") in the matrix. Then, each subshell (composed of the first two quantum numbers) is repeated as many times as required for each pair of electrons it may contain. The result is a compressed periodic table, with each entry representing two successive elements:


title: Atomic orbital

text: Although this is the general order of orbital filling according to the Madelung rule, there are exceptions, and the actual electronic energies of each element are also dependent upon additional details of the atoms (see ).


title: Atomic orbital

text: The number of electrons in an electrically neutral atom increases with the atomic number. The electrons in the outermost shell, or "valence electrons", tend to be responsible for an element's chemical behavior. Elements that contain the same number of valence electrons can be grouped together and display similar chemical properties.


title: Atomic orbital

text: For elements with high atomic number , the effects of relativity become more pronounced, and especially so for s electrons, which move at relativistic velocities as they penetrate the screening electrons near the core of high- atoms. This relativistic increase in momentum for high speed electrons causes a corresponding decrease in wavelength and contraction of 6s orbitals relative to 5d orbitals (by comparison to corresponding s and d electrons in lighter elements in the same column of the periodic table); this results in 6s valence electrons becoming lowered in energy.


title: Atomic orbital

text: Examples of significant physical outcomes of this effect include the lowered melting temperature of mercury (which results from 6s electrons not being available for metal bonding) and the golden color of gold and caesium.