Nomadic empire

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Nomadic_empire 

 

A horserider of probable Xiongnu origin: the rider wears a hairbun characteristic of the oriental steppes, and his horse has characteristically Xiongnu horse trappings. 2nd-1st century BC. Excavated in Saksanokhur (near Farkhor), Tajikistan. National Museum of Antiquities of Tajikistan.

Nomadic empires, sometimes also called steppe empires, Central or Inner Asian empires, were the empires erected by the bow-wielding, horse-riding, nomadic people in the Eurasian Steppe, from classical antiquity (Scythia) to the early modern era (Dzungars). They are the most prominent example of non-sedentary polities.

Some nomadic empires consolidated by establishing a capital city inside a conquered sedentary state and then exploiting the existing bureaucrats and commercial resources of that non-nomadic society. In such a scenario, the originally nomadic dynasty may become culturally assimilated to the culture of the occupied nation before it is ultimately overthrown. Ibn Khaldun (1332–1406) described a similar cycle on a smaller scale in 1377 in his Asabiyyah theory.

Historians of the early medieval period may refer to these polities as "khanates" (after khan, the title of their rulers). After the Mongol conquests of the 13th century the term orda ("horde") also came into use — as in "Golden Horde".

Background

In the history of China, Central Plain polities relied on horses to resist nomadic incursions into their territories, but was only able to purchase the needed horses from the nomads. Trading in horses actually gave these nomadic groups the means to acquire goods by commercial means and reduced the number of attacks and raids into the territories of Central Plain regimes.

Nomads were generally unable to hold onto conquered territories for long without reducing the size of their cavalry forces because of the limitations of pasture in a settled lifestyle. Therefore, settled civilizations usually became reliant on nomadic ones to provide the supply of horses as needed—because they did not have resources to maintain these numbers of horses themselves.

Camel-oriented Bedouin societies in Arabia have functioned as desert-based analogues of Central-Asian horse-oriented nomadic empires.

History

Ancient history

Cimmeria

Distribution of "Thraco-Cimmerian" finds.

 

Main article: Cimmerians

The Cimmerians were an ancient Indo-European people living north of the Caucasus and the Sea of Azov as early as 1300 BCE until they were driven southward by the Scythians into Anatolia during the 8th century BCE. Linguistically they are usually regarded as Iranian, or possibly Thracian with an Iranian ruling class.

• The Pontic–Caspian steppe: southern Russia and Ukraine until 7th century BCE.
• The northern Caucasus area, including Georgia and modern day Azerbaijan
• Central, East and North Anatolia 714–626 BCE.

Scythia

Main article: Scythia

 

Scythia

Scythia (/ˈsɪθiə/; Ancient Greek: Σκυθική) was a region of Central Eurasia in classical antiquity, occupied by the Eastern Iranian Scythians, encompassing parts of Eastern Europe east of the Vistula River and Central Asia, with the eastern edges of the region vaguely defined by the Greeks. The Ancient Greeks gave the name Scythia (or Great Scythia) to all the lands north-east of Europe and the northern coast of the Black Sea. The Scythians—the Greeks' name for this initially nomadic people—inhabited Scythia from at least the 11th century BCE to the 2nd century CE.

Sarmatia

Main article: Sarmatians

The Sarmatians (Latin: Sarmatæ or Sauromatæ; Ancient Greek: Σαρμάται, Σαυρομάται) were a large confederation of Iranian people during classical antiquity, flourishing from about the 6th century BCE to the 4th century CE. They spoke Scythian, an Indo-European language from the Eastern Iranian family. According to authors Arrowsmith, Fellowes and Graves Hansard in their book A Grammar of Ancient Geography published in 1832, Sarmatia had two parts, Sarmatia Europea and Sarmatia Asiatica  covering a combined area of 503,000 sq mi or 1,302,764 km². Sarmatians were basically Scythian veterans (Saka, Iazyges, Skolotoi, Parthians...) returning to the Pontic–Caspian steppe after the siege of Nineveh. Many noble families of Polish Szlachta claimed a direct descent from Sarmatians as a part of Sarmatism.

Xiongnu

Xiongnu Empire

 

Main article: Xiongnu

The Xiongnu were a confederation of nomadic tribes from northern China and Inner Asia with a ruling class of unknown origin and other subjugated tribes. They lived on the Mongolian Plateau between the 3rd century BCE and the 460s CE, their territories including the modern-day northern China, Mongolia, southern Siberia. The Xiongnu was the first unified empire of nomadic peoples. Relations between early Central Plain dynasties and the Xiongnu were complicated and included military conflict, exchanges of tribute and trade, and marriage alliances. When Qin Shi Huang drove them away from the south of the Yellow River, he built the Great Wall to prevent the Xiongnu from returning.

Kushan Empire

Kushan Empire

 

Main article: Kushan Empire

The Kushan Empire was a syncretic empire, formed by the Yuezhi who originally hailed from the modern-day Chinese province of Gansu under the pressure of the Xiongnu, in the Bactrian territories in the early 1st century. It spread to encompass much of modern-day Afghanistan, and then the northern parts of the Indian subcontinent at least as far as Saketa and Sarnath near Varanasi (Benares), where inscriptions have been found dating to the era of the Kushan emperor Kanishka the Great.

Xianbei

Xianbei Empire

 

Main article: Xianbei state

The Xianbei state or Xianbei confederation was a nomadic empire which existed in modern-day Inner Mongolia, northern Xinjiang, Northeast China, Gansu, Mongolia, Buryatia, Zabaykalsky Krai, Irkutsk Oblast, Tuva, Altai Republic and eastern Kazakhstan from 156 to 234 CE. Like most ancient peoples known through Chinese historiography, the ethnic makeup of the Xianbei is unclear. The Xianbei were a northern branch of the earlier Donghu and it is likely at least some were proto-Mongols. After it collapsed, the tribe immigrated into the Central Plain and founded the Northern Wei dynasty.

Hephthalite Empire

Hephthalite Empire

 

Main article: Hephthalite Empire

The Hephthalites, Ephthalites, Ye-tai, White Huns, or, in Sanskrit, the Sveta Huna, were a confederation of nomadic and settled people in Central Asia who expanded their domain westward in the 5th century. At the height of its power in the first half of the 6th century, the Hephthalite Empire controlled territory in present-day Afghanistan, Turkmenistan, Uzbekistan, Tajikistan, Kyrgyzstan, Kazakhstan, Pakistan, India and China.

Hunnic Empire

The Hunnic Empire, at its height under Attila.

 

Main article: Huns

The Huns were a confederation of Eurasian tribes from the Steppes of Central Asia. Appearing from beyond the Volga River some years after the middle of the 4th century, they conquered all of eastern Europe, ending up at the border of the Roman Empire in the south, and advancing far into modern day Germany in the north. Their appearance in Europe brought with it great ethnic and political upheaval and may have stimulated the Great Migration. The empire reached its largest size under Attila between 447 and 453.

Post-classical history

Mongolic people and Turkic expansion

Further information: Turkic expansion, Turkic tribal confederations, Bulgars, Khazars, and Pannonian Avars

Bulgars

Bulgars led by Khan Krum pursue the Byzantines at the Battle of Versinikia (813)

 

Main articles: Bulgars and Old Great Bulgaria

 

The migration of the Bulgars after the fall of Old Great Bulgaria in the 7th century.

The Bulgars (also Bulghars, Bulgari, Bolgars, Bolghars, Bolgari, Proto-Bulgarians) were Turkic semi-nomadic warrior tribes that flourished in the Pontic–Caspian steppe and the Volga region during the 7th century. Emerging as nomadic equestrians in the Volga-Ural region, according to some researchers their roots can be traced to Central Asia. During their westward migration across the Eurasian steppe the Bulgars absorbed other ethnic groups and cultural influences, including Hunnic and Indo-European peoples. Modern genetic research on Central Asian Turkic people and ethnic groups related to the Bulgars points to an affiliation with Western Eurasian populations. The Bulgars spoke a Turkic language, i.e. Bulgar language of Oghuric branch. They preserved the military titles, organization and customs of Eurasian steppes, as well as pagan shamanism and belief in the sky deity Tangra.

After Dengizich's death, the Huns seem to have been absorbed by other ethnic groups such as the Bulgars. Kim, however, argues that the Huns continued under Ernak, becoming the Kutrigur and Utigur Hunno-Bulgars. This conclusion is still subject to some controversy. Some scholars also argue that another group identified in ancient sources as Huns, the North Caucasian Huns, were genuine Huns. The rulers of various post-Hunnic steppe peoples are known to have claimed descent from Attila in order to legitimize their right to the power, and various steppe peoples were also called "Huns" by Western and Byzantine sources from the fourth century onward.

The first clear mention and evidence of the Bulgars was in 480, when they served as the allies of the Byzantine Emperor Zeno (474–491) against the Ostrogoths. Anachronistic references about them can also be found in the 7th-century geography work Ashkharatsuyts by Anania Shirakatsi, where the Kup'i Bulgar, Duč'i Bulkar, Olxontor Błkar and immigrant Č'dar Bulkar tribes are mentioned as being in the North Caucasian-Kuban steppes. An obscure reference to Ziezi ex quo Vulgares, with Ziezi being an offspring of Biblical Shem, is in the Chronography of 354.

The Bulgars became semi-sedentary during the 7th century in the Pontic-Caspian steppe, establishing the polity of Old Great Bulgaria c. 635, which was absorbed by the Khazar Empire in 668 CE.

In c. 679, Khan Asparukh conquered Scythia Minor, opening access to Moesia, and established the First Bulgarian Empire, where the Bulgars became a political and military elite. They merged subsequently with established Byzantine populations, as well as with previously settled Slavic tribes, and were eventually Slavicized, thus forming the ancestors of modern Bulgarians.

Rouran

The Rouran Khaganate, c. 500 CE

 

Main article: Rouran Khaganate

The Rouran (柔然), Juan Juan (蠕蠕), or Ruru (茹茹) were a confederation of Mongolic-speaking nomadic tribes in northern China from the late 4th century until the late 6th century. They controlled an area corresponding to modern-day northern China, Mongolia, and southern Siberia.

Göktürks

Gökturk khaganates at their height, c. 600 CE :

  Western Göktürk: Lighter area is direct rule; darker areas show sphere of influence.

  Eastern Göktürk: Lighter area is direct rule; darker areas show sphere of influence.

 

Main article: Göktürks

The Göktürks or Kök-Türks were a Turkic people of inhabiting much of northern China and Inner Asia. Under the leadership of Bumin Khan and his sons they established the First Turkic Khaganate around 546, taking the place of the earlier Xiongnu as the main power in the region. They were the first Turkic tribe to use the name Türk as a political name. The empire was split into a western and an eastern part around 600, and both divisions were eventually conquered by the Tang dynasty. In 680, the Göktürks established the Second Turkic Khaganate which later declined after 734 following the establishment of the Uyghur Khaganate.

Kyrgyz

Main article: Yenisei Kyrgyz Khaganate

The Yenisei Kyrgyz Khaganate was a Turkic-led empire occupying the territories of modern-day northern China, Mongolia, and southern Siberia around the Yenisei River. The khaganate was founded in 693 by Bars Bek, and in 695, after a confrontation with the Second Turkic Khaganate, was recognised by Qapagan. In 710–711, as a result of the war with the Göktürks, the Kyrgyz Khaganate fell, and the descendants of Bars Bek remained vassals of the Second Turkic Khaganate until its fall in 744. After that, the Kyrgyz tribes became part of the ascendant Uyghur Khaganate. In 820, war broke out between the Kyrgyz and the Uyghur Khaganate, which continued with varying success for 20 years. In 840, the Uyghur Khaganate fell, and the Kyrgyz Khaganate was restored on its territory. It reached its peak of power at the end of the 9th century, but had little geopolitical influence thereafter. Eventually, the Kyrgyz Khaganate was finally dissolved in 1207 after becoming part of the Mongol Empire.

The Kyrgyz Khagnate at its peak

Uyghurs

Asia in 800 CE, showing the Uyghur Khanate and its neighbors.

 

Main article: Uyghur Khaganate

The Uyghur Khaganate was an empire that existed in present-day northern China, Mongolia, southern Siberia, and surrounding areas for about a century between the mid 8th and 9th centuries. It was a tribal confederation under the Orkhon Uyghur nobility. It was established by Kutlug I Bilge Kagan in 744, taking advantage of the power vacuum in the region after the fall of the Gökturk Empire. It collapsed after a Kyrgyz invasion in 840.

Khitans

Main articles: Khitan people and Liao dynasty

 

"Khitan State"

The Liao dynasty was ruled by the Yelü clan of the Khitan people in northern China. It was founded by Yelü Abaoji (Emperor Taizu of Liao) around the time of the collapse of the Tang dynasty and was the first state to control all of Manchuria. After the Liao dynasty fell to the Jin dynasty in the 12th century, remnants of the Liao imperial clan led by Yelü Dashi (Emperor Dezong of Western Liao) fled west and established the Western Liao dynasty.

Seljuk Empire

Map of the Seljuk Empire (1090)

 

Main article: Seljuk Empire

The founder of the Seljuk dynasty was an Oghuz Turkic chieftain Seljuk that had served under Khazar army. Ancestors of Seljuk remained unclarified except for his father, Dukak. Dukak was a competent man in Oghuz Yabgu State, and like him Seljuk also gained a seat the court of the Oghuz Yabgu. Afterwards Seljuk fell into disfavor in the court, and he decided to move into Jend with his clan in 961. Rumor has it that he converted to İslam in order to gain the power from İslamic countries. The Oghuz Turks sought a proper homeland that includes vast pastures for their herdes, and consistently fought against Kara-Khanid Khanate, Ghaznavids and Eastern Roman Empire. They followed changeable policies among contiguous states due to tending to keep the balance of power. The grandsons of Seljuk, Tughril and Chagri Begs decisively defeated Ghaznavids in the Battle of Dandanaqan, gained the power in the Khorasan. Tughril Beg sent Chagri Beg into Eastern Anatolia to seek proper pastures, so the conflicts between Oghuz Turks and Byzantine Empire began. During Tughril's reign, the life styles of nomadic Oghuz tribes changed as they conquered lands of Persia.

Mongol Empire

Expansion of the Mongol Empire

 

Main articles: Mongol Empire, Tartary, and Mongol invasion of Kievan Rus'

The Mongol Empire was the largest contiguous land empire in history at its peak, with an estimated population of over 100 million people. The Mongol Empire was founded by Genghis Khan in 1206, and at its height, it encompassed the majority of the territories from East Asia to Eastern Europe.

After unifying the Turco-Mongol tribes, the Empire expanded through conquests throughout continental Eurasia. During its existence, the Pax Mongolica facilitated cultural exchange and trade on the Silk Route between the East, West, and the Middle East in the period of the 13th and 14th centuries. It had significantly eased communication and commerce across Asia during its height.

After the death of Möngke Khan in 1259, the empire split into four parts (Yuan dynasty, Ilkhanate, Chagatai Khanate and Golden Horde), each of which was ruled by its own monarch, although the emperors of the Yuan dynasty had nominal title of Khagan. After the disintegration of the western khanates and the fall of the Yuan dynasty in 1368, the empire finally broke up.

Timurid Empire

Timurid continental map

 

Main article: Timurid Empire

The Timurids, self-designated Gurkānī, were a Turko-Mongol dynasty, established by the warlord Timur in 1370 and lasting until 1506. At its zenith, the Timurid Empire included the whole of Central Asia, Iran and modern Afghanistan, as well as large parts of Mesopotamia and the Caucasus.

Modern history

Mongol residual states and domains by the 15th century

Later Mongol-ruled khanates

Main articles: Northern Yuan dynasty, Kalmyk Khanate, and Dzungar Khanate

 

Map showing Dzungar–Qing Wars between Manchu Dynasty and Dzungar Khanate

Later Mongol-led khanates such as the Northern Yuan dynasty and the Dzungar Khanate were also nomadic empires. After the fall of the Yuan dynasty in 1368, the Ming dynasty rebuilt the Great Wall, which had been begun many hundreds of years earlier to keep the northern nomads out of the Central Plain. During the subsequent centuries, the Northern Yuan dynasty tended to continue their nomadic way of life. On the other hand, the Dzungars were a confederation of several Oirat tribes who formed and maintained the last horse archer empire from the early 17th century to the middle 18th century. They emerged in the early 17th century to fight the Altan Khan of the Khalkha, the Jasaghtu Khan and their Manchu patrons for dominion and control over the Mongol tribes. In 1756, this last nomadic power was dissolved due to the Oirat princes' succession struggle and costly war with the Qing dynasty.

Popular misconceptions

Khitans, originally a nomadic steppe people who ruled northern China as the Liao dynasty

The Qing dynasty is mistakenly confused as a nomadic empire by people who wrongly think that the Manchus were a nomadic people, when in fact they were not nomads, but instead were a sedentary agricultural people who lived in fixed villages, farmed crops, and practiced hunting and mounted archery.

The Sushen used flint-headed wooden arrows, farmed, hunted, and fished and lived in caves and trees. The cognates Sushen or Jichen (稷真) again appear in the Shan Hai Jing and Book of Wei during the dynastic era referring to Tungusic Mohe tribes of the far northeast. The Mohe enjoyed eating pork, practiced pig farming extensively, and were mainly sedentary, and also used both pig and dog skins for coats. They were predominantly farmers and grew soybean, wheat, millet, and rice, in addition to engaging in hunting.

The Jurchens were sedentary, settled farmers with advanced agriculture. They farmed grain and millet as their cereal crops, grew flax, and raised oxen, pigs, sheep, and horses. Their farming way of life was very different from the pastoral nomadism of the Mongols and the Khitan on the steppes. "At the most", the Jurchen could only be described as "semi-nomadic" while the majority of them were sedentary.

The Manchu way of life (economy) was described as agricultural, with farming crops and raising animals on farms. Manchus practiced slash-and-burn agriculture in the areas north of Shenyang. The Haixi Jurchens were "semi-agricultural, the Jianzhou Jurchens and Maolian (毛怜) Jurchens were sedentary, and hunting and fishing was the way of life of the "Wild Jurchens". Han Chinese society resembled that of the sedentary Jianzhou and Maolian, who were farmers. Hunting, archery on horseback, horsemanship, livestock raising, and sedentary agriculture were all practiced by the Jianzhou Jurchens as part of their culture. In spite of the fact that the Manchus practiced archery on horseback and equestrianism, the Manchu's immediate progenitors practiced sedentary agriculture. Although the Manchus also partook in hunting, they were sedentary. Their primary mode of production was farming, and they lived in villages, forts, and towns surrounded by walls. Farming was practiced by their Jurchen Jin predecessors.

“建州毛怜则渤海大氏遗孽，乐住种，善缉纺，饮食服用，皆如华人，自长白山迤南，可拊而治也。" "The (people of) Chien-chou and Mao-lin [YLSL always reads Mao-lien] are the descendants of the family Ta of Po-hai. They love to be sedentary and sow, and they are skilled in spinning and weaving. As for food, clothing and utensils, they are the same as (those used by) the Chinese. (Those living) south of the Ch'ang-pai mountain are apt to be soothed and governed."

— 据魏焕《皇明九边考》卷二《辽东镇边夷考》Translation from Sino-J̌ürčed relations during the Yung-Lo period, 1403–1424 by Henry Serruys

For political reasons, the Jurchen leader Nurhaci chose variously to emphasize either differences or similarities in lifestyles with other peoples like the Mongols. Nurhaci said to the Mongols, "The languages of the Chinese and Koreans are different, but their clothing and way of life is the same. It is the same with us Manchus (Jušen) and Mongols. Our languages are different, but our clothing and way of life is the same." Later, Nurhaci indicated that the bond with the Mongols was not based in any real shared culture. It was for pragmatic reasons of "mutual opportunism" since Nurhaci said to the Mongols, "You Mongols raise livestock, eat meat and wear pelts. My people till the fields and live on grain. We two are not one country and we have different languages."

Only the Mongols and the northern "wild" Jurchen were semi-nomadic, unlike the mainstream Jiahnzhou Jurchens descended from the Jin dynasty who were farmers that foraged, hunted, herded and harvested crops in the Liao and Yalu river basins. They gathered ginseng root, pine nuts, hunted for came pels in the uplands and forests, raised horses in their stables, and farmed millet and wheat in their fallow fields. They engaged in dances, wrestling and drinking strong liquor as noted during midwinter by the Korean Sin Chung-il when it was very cold. These Jurchens who lived in the north-east's harsh cold climate sometimes half sunk their houses in the ground which they constructed of brick or timber and surrounded their fortified villages with stone foundations on which they built wattle and mud walls to defend against attack. Village clusters were ruled by beile, hereditary leaders. They fought each other and dispensed weapons, wives, slaves, and lands to their followers in them. The Jurchens who founded the Qing lived and their ancestors lived in such a way before the Jin. Alongside Mongols and Jurchen clans there were migrants from Liaodong provinces of the Ming dynasty and Joseon living among those Jurchens in a cosmopolitan manner. Nurhaci who was hosting Sin Chung-il was uniting all of them into his own army, having them adopt the Jurchen hairstyle of a long queue and a shaved fore=crown and wearing leather tunics. His armies had black, blue, red, white, and yellow flags. They became the Eight Banners, which was initially capped to 4 and then grew to 8 with three different types of ethnic banners as Han, Mongol and Jurchen were recruited into Nurhaci's forces. Jurchens like Nurhaci spoke both their native Tungusic language and Chinese and adopted the Mongol script for their own language unlike the Jin Jurchen's script, which was derived from Khitan. They adopted Confucian values and practiced their shamanist traditions.

The Qing stationed "New Manchu" Warka foragers in Ningguta and attempted to turn them into normal agricultural farmers like normal Old Manchus, but the Warka just reverted to hunter gathering and requested money to buy cattle for beef broth. The Qing wanted the Warka to become soldier-farmers and imposed that on them, but the Warka simply left their garrison at Ningguta and went back to the Sungari River to their homes to herd, fish, and hunt. The Qing accused them of desertion.

Similarly, the Indo-European dominions, like the Cimmerian, Scythian, Sarmatian or Kushan ones, were not strictly nomadic or strictly empires. They were organized in small Kšatrapies/Voivodeships that sometimes united into a bigger Mandala to repel surrounding despotic empires trying to annex their homelands. Only the pastoral part of the population and military troops migrated frequently, but most of the population lived in organized agricultural and industrial small scale townships, which are called in Europe gords. Examples are the oases of Sogdia and Sparia along the Silk Road (Śaka, Tokarians/Tokharians etc.) and around the Tarim Basin (Tarim mummies, Kingdom of Khotan) or the rural areas of Europe (Sarmatia, Pannonia, Vysperia, Spyrgowa/Spirgovia, Boioaria/Boghoaria...) and Indian subcontinent (Kaśperia, Pandžab etc.). Since the 2nd century BCE), the growing number of Turkic nomads and invaders among them, who adopted their horse-riding, metallurgy, technologies, clothing, and customs caused them to be also often confused with the latter, which mostly occurred in the case of the Scythians (Śaka, Sarmatians, Skolotoi, Iazyges, etc.). In India, the Śaka, although known earlier as Śakya or Kambojas, formed now the Kushan Empire but were confused with the Xionites invading them and were called Mleccha. The Turkic invaders exploited the subdued sedentary Indo-Europeans in agriculture, industry, and warfare (Mamluk, Janissaries). In some rare cases, the enslaved Indo-Europeans may rise to power like Aleksandra (Iškandara) Lisowska or Roxelana.

Aufbau principle

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Aufbau_principle

The aufbau principle (/ˈaʊfbaʊ/, from the German Aufbauprinzip, which means "building-up principle"), also called the aufbau rule, states that in the ground state of an atom or ion, electrons fill subshells of the lowest available energy, then they fill subshells of higher energy. For example, the 1s subshell is filled before the 2s subshell is occupied. In this way, the electrons of an atom or ion form the most stable electron configuration possible. An example is the configuration 1s² 2s² 2p⁶ 3s² 3p³ for the phosphorus atom, meaning that the 1s subshell has 2 electrons, and so on.

Electron behavior is elaborated by other principles of atomic physics, such as Hund's rule and the Pauli exclusion principle. Hund's rule asserts that if multiple orbitals of the same energy are available, electrons will occupy different orbitals singly and with the same spin before any are occupied doubly. If double occupation does occur, the Pauli exclusion principle requires that electrons that occupy the same orbital must have different spins (+1⁄2 and −1⁄2).

Passing from one element to another of the next higher atomic number, one proton and one electron are added each time to the neutral atom. The maximum number of electrons in any shell is 2n², where n is the principal quantum number. The maximum number of electrons in a subshell is equal to 2(2l + 1), where the azimuthal quantum number l is equal to 0, 1, 2, and 3 for s, p, d, and f subshells, so that the maximum numbers of electrons are 2, 6, 10, and 14 respectively. In the ground state, the electronic configuration can be built up by placing electrons in the lowest available subshell until the total number of electrons added is equal to the atomic number. Thus subshells are filled in the order of increasing energy, using two general rules to help predict electronic configurations:

1. Electrons are assigned to subshells in order of increasing value of n + l.
2. For subshells with the same value of n + l, electrons are assigned first to the subshell with lower n.

A version of the aufbau principle known as the nuclear shell model is used to predict the configuration of protons and neutrons in an atomic nucleus.^[1]

Madelung energy ordering rule

The states crossed by same red arrow have same n + l value. The direction of the red arrow indicates the order of state filling.

 

For multielectron atoms the energy spectra of shells interleave resulting in the n + l rule

In neutral atoms, the approximate order in which subshells are filled is given by the n + l rule, also known as the:

• Madelung rule (after Erwin Madelung)
• Janet rule (after Charles Janet)
• Klechkowsky rule (after Vsevolod Klechkovsky)
• Wiswesser's rule (after William Wiswesser)
• aufbau approximation or
• diagonal rule

Here n represents the principal quantum number and l the azimuthal quantum number; the values l = 0, 1, 2, 3 correspond to the s, p, d, and f subshells, respectively. The subshell ordering by this rule is 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p, 8s, 5g, ... For example titanium (Z = 22) has the ground-state configuration 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d².

Other authors write the subshell always in order of increasing n, such as Ti (Z = 22) 1s² 2s² 2p⁶ 3s² 3p⁶ 3d² 4s². This can be called "leaving order", since if this atom is ionized, electrons leave approximately in the order 4s, 3d, 3p, 3s, etc. For a given neutral atom, the two notations are equivalent since only the subshell occupancies have physical significance.

Subshells with a lower n + l value are filled before those with higher n + l values. In the case of equal n + l values, the subshell with a lower n value is filled first. In general, subshells with the same n + l value have similar energies, but the s-orbitals (with l = 0) are exceptional: their energy levels are appreciably far from those of their n + l group and are closer to those of the next n + l group. This is why the periodic table is usually drawn to begin with the s-block elements.

The Madelung energy ordering rule applies only to neutral atoms in their ground state. There are twenty elements (eleven in the d-block and nine in the f-block) for which the Madelung rule predicts an electron configuration that differs from that determined experimentally, although the Madelung-predicted electron configurations are at least close to the ground state even in those cases.

One inorganic chemistry textbook describes the Madelung rule as essentially an approximate empirical rule although with some theoretical justification, based on the Thomas–Fermi model of the atom as a many-electron quantum-mechanical system.

Exceptions in the d-block

The valence d-subshell "borrows" one electron (in the case of palladium two electrons) from the valence s-subshell.

A special exception is lawrencium ₁₀₃Lr, where the 6d electron predicted by the Madelung rule is replaced by a 7p electron: the rule predicts [Rn] 5f¹⁴ 6d¹ 7s², but the measured configuration is [Rn] 5f¹⁴ 7s² 7p¹.

Atom	24Cr	29Cu	41Nb	42Mo	44Ru	45Rh	46Pd	47Ag	78Pt	79Au	103Lr
Core electrons	[Ar]	[Ar]	[Kr]	[Kr]	[Kr]	[Kr]	[Kr]	[Kr]	[Xe] 4f14	[Xe] 4f14	[Rn] 5f14
Madelung rule	3d4 4s2	3d9 4s2	4d3 5s2	4d4 5s2	4d6 5s2	4d7 5s2	4d8 5s2	4d9 5s2	5d8 6s2	5d9 6s2	6d1 7s2
Experimental	3d5 4s1	3d10 4s1	4d4 5s1	4d5 5s1	4d7 5s1	4d8 5s1	4d10	4d10 5s1	5d9 6s1	5d10 6s1	7s2 7p1

For example, in copper ₂₉Cu, according to the Madelung rule, the 4s subshell (n + l = 4 + 0 = 4) is occupied before the 3d subshell (n + l = 3 + 2 = 5). The rule then predicts the electron configuration 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁹ 4s², abbreviated [Ar] 3d⁹ 4s² where [Ar] denotes the configuration of argon, the preceding noble gas. However, the measured electron configuration of the copper atom is [Ar] 3d¹⁰ 4s¹. By filling the 3d subshell, copper can be in a lower energy state.

Exceptions in the f-block

The valence d-subshell often "borrows" one electron (in the case of thorium two electrons) from the valence f-subshell. For example, in uranium ₉₂U, according to the Madelung rule, the 5f subshell (n + l = 5 + 3 = 8) is occupied before the 6d subshell (n + l = 6 + 2 = 8). The rule then predicts the electron configuration [Rn] 5f⁴ 7s² where [Rn] denotes the configuration of radon, the preceding noble gas. However, the measured electron configuration of the uranium atom is [Rn] 5f³ 6d¹ 7s².

Atom	57La	58Ce	64Gd	89Ac	90Th	91Pa	92U	93Np	96Cm
Core electrons	[Xe]	[Xe]	[Xe]	[Rn]	[Rn]	[Rn]	[Rn]	[Rn]	[Rn]
Madelung rule	4f1 6s2	4f2 6s2	4f8 6s2	5f1 7s2	5f2 7s2	5f3 7s2	5f4 7s2	5f5 7s2	5f8 7s2
Experimental	5d1 6s2	4f1 5d1 6s2	4f7 5d1 6s2	6d1 7s2	6d2 7s2	5f2 6d1 7s2	5f3 6d1 7s2	5f4 6d1 7s2	5f7 6d1 7s2

All these exceptions are not very relevant for chemistry, as the energy differences are quite small and the presence of a nearby atom can change the preferred configuration. The periodic table ignores them and follows idealised configurations. They occur as the result of interelectronic repulsion effects; when atoms are positively ionised, most of the anomalies vanish.

The above exceptions are predicted to be the only ones until element 120, where the 8s shell is completed. Element 121, starting the g-block, should be an exception in which the expected 5g electron is transferred to 8p (similarly to lawrencium). After this, sources do not agree on the predicted configurations, but due to very strong relativistic effects there are not expected to be many more elements that show the expected configuration from Madelung's rule beyond 120. The general idea that after the two 8s elements, there come regions of chemical activity of 5g, followed by 6f, followed by 7d, and then 8p, does however mostly seem to hold true, except that relativity "splits" the 8p shell into a stabilized part (8p_1/2, which acts like an extra covering shell together with 8s and is slowly drowned into the core across the 5g and 6f series) and a destabilized part (8p_3/2, which has nearly the same energy as 9p_1/2), and that the 8s shell gets replaced by the 9s shell as the covering s-shell for the 7d elements.

History

The aufbau principle in the new quantum theory

In the old quantum theory, orbits with low angular momentum (s- and p-subshell) get closer to the nucleus.

The principle takes its name from German, Aufbauprinzip, "building-up principle", rather than being named for a scientist. It was formulated by Niels Bohr and Wolfgang Pauli in the early 1920s. This was an early application of quantum mechanics to the properties of electrons and explained chemical properties in physical terms. Each added electron is subject to the electric field created by the positive charge of the atomic nucleus and the negative charge of other electrons that are bound to the nucleus. Although in hydrogen there is no energy difference between subshells with the same principal quantum number n, this is not true for the outer electrons of other atoms.

In the old quantum theory prior to quantum mechanics, electrons were supposed to occupy classical elliptical orbits. The orbits with the highest angular momentum are 'circular orbits' outside the inner electrons, but orbits with low angular momentum (s- and p-subshell) have high subshell eccentricity, so that they get closer to the nucleus and feel on average a less strongly screened nuclear charge.

The n + l energy ordering rule

A periodic table in which each row corresponds to one value of n + l (where the values of n and l correspond to the principal and azimuthal quantum numbers respectively) was suggested by Charles Janet in 1928, and in 1930 he made explicit the quantum basis of this pattern, based on knowledge of atomic ground states determined by the analysis of atomic spectra. This table came to be referred to as the left-step table. Janet "adjusted" some of the actual n + l values of the elements, since they did not accord with his energy ordering rule, and he considered that the discrepancies involved must have arisen from measurement errors. As it happens, the actual values were correct and the n + l energy ordering rule turned out to be an approximation rather than a perfect fit, although for all elements that are exceptions the regularised configuration is a low-energy excited state, well within reach of chemical bond energies.

In 1936, the German physicist Erwin Madelung proposed this as an empirical rule for the order of filling atomic subshells, and most English-language sources therefore refer to the Madelung rule. Madelung may have been aware of this pattern as early as 1926. The Russian-American engineer Vladimir Karapetoff was the first to publish the rule in 1930, though Janet also published an illustration of it the same year.

In 1945, American chemist William Wiswesser proposed that the subshells are filled in order of increasing values of the function

${\displaystyle W(n,l)=n+l-\frac{l}{l+1}.}$

This formula correctly predicts both the first and second parts of the Madelung rule (the second part being that for two subshells with the same value of n + l, the one with the smaller value of n fills first). Wiswesser argued for this formula based on both the pattern of nodal and radial nodes, the concept now known as orbital penetration, and the influence of the core electrons on the valence orbitals.

In 1961 the Russian agricultural chemist V.M. Klechkowski proposed a theoretical explanation for the importance of the sum n + l, based on the Thomas–Fermi model of the atom. Many French- and Russian-language sources therefore refer to the Klechkowski rule. The full Madelung rule was derived from a similar potential in 1971 by Yury N. Demkov and Valentin N. Ostrovsky. They consider the potential ${\displaystyle U_{1/2}(r)=-\frac{2v}{rR(r+R{)}^2}}$ where ${\displaystyle R}$ and ${\displaystyle v}$ are constant parameters; this approaches a Coulomb potential for small ${\displaystyle r}$. When ${\displaystyle v}$ satisfies the condition ${\displaystyle v=v_N=\frac{1}{4}{R}^{2}N(N+1)}$, where ${\displaystyle N=n+l}$, the zero-energy solutions to the Schrödinger equation for this potential can be described analytically with Gegenbauer polynomials. As ${\displaystyle v}$ passes through each of these values, a manifold containing all states with that value of ${\displaystyle N}$ arises at zero energy and then becomes bound, recovering the Madelung order. Perturbation-theory considerations show that states with smaller ${\displaystyle n}$ have lower energy, and that the s-orbitals (with ${\displaystyle l=0}$) have their energies approaching the next ${\displaystyle n+l}$ group.

In recent years it has been noted that the order of filling subshells in neutral atoms does not always correspond to the order of adding or removing electrons for a given atom. For example, in the fourth row of the periodic table, the Madelung rule indicates that the 4s subshell is occupied before the 3d. Therefore, the neutral atom ground state configuration for K is [Ar] 4s¹, Ca is [Ar] 4s², Sc is [Ar] 4s² 3d¹ and so on. However, if a scandium atom is ionized by removing electrons (only), the configurations differ: Sc is [Ar] 4s² 3d¹, Sc⁺ is [Ar] 4s¹ 3d¹, and Sc²⁺ is [Ar] 3d¹. The subshell energies and their order depend on the nuclear charge; 4s is lower than 3d as per the Madelung rule in K with 19 protons, but 3d is lower in Sc²⁺ with 21 protons. In addition to there being ample experimental evidence to support this view, it makes the explanation of the order of ionization of electrons in this and other transition metals more intelligible, given that 4s electrons are invariably preferentially ionized. Generally the Madelung rule should only be used for neutral atoms; however, even for neutral atoms there are exceptions in the d-block and f-block (as shown above).