Введение
Обозначение в квантовой физике
In atomic physics, a term symbol is an abbreviated description of the total spin and orbital angular momentum quantum numbers of the electrons in a multi electron atom. So while the word symbol suggests otherwise, it represents an actual value of a physical quantity. For a given electron configuration of an atom, its state depends also on its total angular momentum, including spin and orbital components, which are specified by the term symbol. The usual atomic term symbols assume LS coupling (also known as Russell–Saunders coupling) in which the all electron total quantum numbers for orbital (L), spin (S) and total (J) angular momenta are good quantum numbers. In the terminology of atomic spectroscopy, L and S together specify a term; L, S, and J specify a level; and L, S, J and the magnetic quantum number MJ specify a state. The conventional term symbol has the form 2S+1LJ, where J is written optionally in order to specify a level. L is written using spectroscopic notation: for example, it is written "S", "P", "D", or "F" to represent L = 0, 1, 2, or 3 respectively. For coupling schemes other that LS coupling, such as the jj coupling that applies to some heavy elements, other notations are used to specify the term. Term symbols apply to both neutral and charged atoms, and to their ground and excited states. Term symbols usually specify the total for all electrons in an atom, but are sometimes used to describe electrons in a given subshell or set of subshells, for example to describe each open subshell in an atom having more than one. The ground state term symbol for neutral atoms is described, in most cases, by Hund's rules. Neutral atoms of the chemical elements have the same term symbol for each column in the s block and p block elements, but differ in d block and f block elements where the ground state electron configuration changes within a column, where exceptions to Hund's rules occur. Ground state term symbols for the chemical elements are given below. Term symbols are also used to describe angular momentum quantum numbers for atomic nuclei and for molecules. For molecular term symbols, Greek letters are used to designate the component of orbital angular momenta along the molecular axis. The use of the word term for an atom's electronic state is based on the Rydberg–Ritz combination principle, an empirical observation that the wavenumbers of spectral lines can be expressed as the difference of two terms. This was later summarized by the Bohr model, which identified the terms with quantized energy levels, and the spectral wavenumbers of these levels with photon energies. Tables of atomic energy levels identified by their term symbols are available for atoms and ions in ground and excited states from the National Institute of Standards and Technology (NIST).). The spin orbit interaction then couples the total spin and orbital moments to give the total electronic angular momentum quantum number J. Atomic states are then well described by term symbols of the form:
where
S is the total spin quantum number for the atom's electrons. The value 2S + 1 written in the term symbol is the spin multiplicity, which is the number of possible values of the spin magnetic quantum number MS for a given spin S.
J is the total angular momentum quantum number for the atom's electrons. J has a value in the range from |L − S| to L + S.
L is the total orbital quantum number in spectroscopic notation, in which the symbols for L are:
L = 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 (continued alphabetically)
The orbital symbols S, P, D and F are derived from the characteristics of the spectroscopic lines corresponding to s, p, d, and f orbitals: sharp, principal, diffuse, and fundamental; the rest are named in alphabetical order from G onwards (omitting J, S and P). When used to describe electronic states of an atom, the term symbol is often written following the electron configuration. For example, 1s22s22p2 3P0 represents the ground state of a neutral carbon atom. The superscript 3 indicates that the spin multiplicity 2S + 1 is 3 (it is a triplet state), so S = 1; the letter "P" is spectroscopic notation for L = 1; and the subscript 0 is the value of J (in this case J = L − S). Small letters refer to individual orbitals or one electron quantum numbers, whereas capital letters refer to many electron states or their quantum numbers.
В атомной физике термический символ – это сокращенное описание полного спина и орбитального углового момента квантовых чисел электронов в многоэлектронном атоме. Таким образом, хотя слово «символ» предполагает обратное, он представляет собой фактическое значение физической величины. Для заданной электронной конфигурации атома его состояние зависит также от его полного углового момента, включая спиновые и орбитальные компоненты, которые определяются термическим символом. Обычные атомные термические символы предполагают LS-связывание (также известное как связывание Рассела — Сандерса), при котором все суммарные квантовые числа для орбитального (L), спинового (S) и полного (J) угловых моментов являются хорошими квантовыми числами. В терминологии атомной спектроскопии L и S вместе определяют термин; L, S и J определяют уровень; а L, S, J и магнитное квантовое число MJ определяют состояние. Стандартный термический символ имеет вид 2S+1LJ, где J записывается необязательно для указания уровня. L записывается с использованием спектроскопической нотации: например, для представления L = 0, 1, 2 или 3 используются обозначения "S", "P", "D" или "F" соответственно. Для схем связывания, отличных от LS-связывания, таких как jj-связывание, применимое к некоторым тяжелым элементам, используются другие обозначения для указания термина. Термические символы применимы как к нейтральным, так и к заряженным атомам, а также к их основным и возбужденным состояниям. Термические символы обычно указывают сумму для всех электронов в атоме, но иногда используются для описания электронов в заданной подуровне или наборе подуровней, например, для описания каждой открытой подуровни в атоме, имеющем более одного электрона. Термический символ основного состояния для нейтральных атомов в большинстве случаев описывается правилами Хунда. Нейтральные атомы химических элементов имеют один и тот же термический символ для каждого столбца в s-блоке и p-блоке элементов, но отличаются в d-блоке и f-блоке, где электронная конфигурация основного состояния меняется в пределах столбца, и возникают исключения из правил Хунда. Термические символы основного состояния для химических элементов приведены ниже. Термические символы также используются для описания квантовых чисел углового момента для атомных ядер и молекул. Для молекулярных термических символов греческие буквы используются для обозначения компоненты орбитального углового момента вдоль молекулярной оси. Использование термина для электронного состояния атома основано на принципе комбинации Ридберга — Рица, эмпирическом наблюдении, что волновые числа спектральных линий могут быть выражены как разность двух терминов. Это было позже обобщено моделью Бора, которая отождествила термины с квантованными энергетическими уровнями, а спектральные волновые числа этих уровней — с энергиями фотонов. Таблицы атомных энергетических уровней, идентифицируемые их термическими символами, доступны для атомов и ионов в основном и возбужденном состояниях в Национальном институте стандартов и технологий (NIST). Взаимодействие спин-орбиты затем связывает полный спин и орбитальный моменты, чтобы получить полное электронное квантовое число углового момента J. Атомные состояния хорошо описываются термическими символами формы:
In atomic physics, a term symbol is an abbreviated description of the total spin and orbital angular momentum quantum numbers of the electrons in a multi electron atom. So while the word symbol suggests otherwise, it represents an actual value of a physical quantity. For a given electron configuration of an atom, its state depends also on its total angular momentum, including spin and orbital components, which are specified by the term symbol. The usual atomic term symbols assume LS coupling (also known as Russell–Saunders coupling) in which the all electron total quantum numbers for orbital (L), spin (S) and total (J) angular momenta are good quantum numbers. In the terminology of atomic spectroscopy, L and S together specify a term; L, S, and J specify a level; and L, S, J and the magnetic quantum number MJ specify a state. The conventional term symbol has the form 2S+1LJ, where J is written optionally in order to specify a level. L is written using spectroscopic notation: for example, it is written "S", "P", "D", or "F" to represent L = 0, 1, 2, or 3 respectively. For coupling schemes other that LS coupling, such as the jj coupling that applies to some heavy elements, other notations are used to specify the term. Term symbols apply to both neutral and charged atoms, and to their ground and excited states. Term symbols usually specify the total for all electrons in an atom, but are sometimes used to describe electrons in a given subshell or set of subshells, for example to describe each open subshell in an atom having more than one. The ground state term symbol for neutral atoms is described, in most cases, by Hund's rules. Neutral atoms of the chemical elements have the same term symbol for each column in the s block and p block elements, but differ in d block and f block elements where the ground state electron configuration changes within a column, where exceptions to Hund's rules occur. Ground state term symbols for the chemical elements are given below. Term symbols are also used to describe angular momentum quantum numbers for atomic nuclei and for molecules. For molecular term symbols, Greek letters are used to designate the component of orbital angular momenta along the molecular axis. The use of the word term for an atom's electronic state is based on the Rydberg–Ritz combination principle, an empirical observation that the wavenumbers of spectral lines can be expressed as the difference of two terms. This was later summarized by the Bohr model, which identified the terms with quantized energy levels, and the spectral wavenumbers of these levels with photon energies. Tables of atomic energy levels identified by their term symbols are available for atoms and ions in ground and excited states from the National Institute of Standards and Technology (NIST).). The spin orbit interaction then couples the total spin and orbital moments to give the total electronic angular momentum quantum number J. Atomic states are then well described by term symbols of the form:
where
S is the total spin quantum number for the atom's electrons. The value 2S + 1 written in the term symbol is the spin multiplicity, which is the number of possible values of the spin magnetic quantum number MS for a given spin S.
J is the total angular momentum quantum number for the atom's electrons. J has a value in the range from |L − S| to L + S.
L is the total orbital quantum number in spectroscopic notation, in which the symbols for L are:
L = 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 (continued alphabetically)
The orbital symbols S, P, D and F are derived from the characteristics of the spectroscopic lines corresponding to s, p, d, and f orbitals: sharp, principal, diffuse, and fundamental; the rest are named in alphabetical order from G onwards (omitting J, S and P). When used to describe electronic states of an atom, the term symbol is often written following the electron configuration. For example, 1s22s22p2 3P0 represents the ground state of a neutral carbon atom. The superscript 3 indicates that the spin multiplicity 2S + 1 is 3 (it is a triplet state), so S = 1; the letter "P" is spectroscopic notation for L = 1; and the subscript 0 is the value of J (in this case J = L − S). Small letters refer to individual orbitals or one electron quantum numbers, whereas capital letters refer to many electron states or their quantum numbers.
где
S — полное спиновое квантовое число для электронов атома. Значение 2S + 1, записанное в термическом символе, — это спиновая мультиплетность, которая представляет собой число возможных значений спинового магнитного квантового числа MS для заданного спина S.
J — полное квантовое число углового момента для электронов атома. J имеет значение в диапазоне от |L − S| до L + S.
L — полное орбитальное квантовое число в спектроскопической нотации, в которой символы для L:
L = 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 (продолжается в алфавитном порядке)
In atomic physics, a term symbol is an abbreviated description of the total spin and orbital angular momentum quantum numbers of the electrons in a multi electron atom. So while the word symbol suggests otherwise, it represents an actual value of a physical quantity. For a given electron configuration of an atom, its state depends also on its total angular momentum, including spin and orbital components, which are specified by the term symbol. The usual atomic term symbols assume LS coupling (also known as Russell–Saunders coupling) in which the all electron total quantum numbers for orbital (L), spin (S) and total (J) angular momenta are good quantum numbers. In the terminology of atomic spectroscopy, L and S together specify a term; L, S, and J specify a level; and L, S, J and the magnetic quantum number MJ specify a state. The conventional term symbol has the form 2S+1LJ, where J is written optionally in order to specify a level. L is written using spectroscopic notation: for example, it is written "S", "P", "D", or "F" to represent L = 0, 1, 2, or 3 respectively. For coupling schemes other that LS coupling, such as the jj coupling that applies to some heavy elements, other notations are used to specify the term. Term symbols apply to both neutral and charged atoms, and to their ground and excited states. Term symbols usually specify the total for all electrons in an atom, but are sometimes used to describe electrons in a given subshell or set of subshells, for example to describe each open subshell in an atom having more than one. The ground state term symbol for neutral atoms is described, in most cases, by Hund's rules. Neutral atoms of the chemical elements have the same term symbol for each column in the s block and p block elements, but differ in d block and f block elements where the ground state electron configuration changes within a column, where exceptions to Hund's rules occur. Ground state term symbols for the chemical elements are given below. Term symbols are also used to describe angular momentum quantum numbers for atomic nuclei and for molecules. For molecular term symbols, Greek letters are used to designate the component of orbital angular momenta along the molecular axis. The use of the word term for an atom's electronic state is based on the Rydberg–Ritz combination principle, an empirical observation that the wavenumbers of spectral lines can be expressed as the difference of two terms. This was later summarized by the Bohr model, which identified the terms with quantized energy levels, and the spectral wavenumbers of these levels with photon energies. Tables of atomic energy levels identified by their term symbols are available for atoms and ions in ground and excited states from the National Institute of Standards and Technology (NIST).). The spin orbit interaction then couples the total spin and orbital moments to give the total electronic angular momentum quantum number J. Atomic states are then well described by term symbols of the form:
where
S is the total spin quantum number for the atom's electrons. The value 2S + 1 written in the term symbol is the spin multiplicity, which is the number of possible values of the spin magnetic quantum number MS for a given spin S.
J is the total angular momentum quantum number for the atom's electrons. J has a value in the range from |L − S| to L + S.
L is the total orbital quantum number in spectroscopic notation, in which the symbols for L are:
L = 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 (continued alphabetically)
The orbital symbols S, P, D and F are derived from the characteristics of the spectroscopic lines corresponding to s, p, d, and f orbitals: sharp, principal, diffuse, and fundamental; the rest are named in alphabetical order from G onwards (omitting J, S and P). When used to describe electronic states of an atom, the term symbol is often written following the electron configuration. For example, 1s22s22p2 3P0 represents the ground state of a neutral carbon atom. The superscript 3 indicates that the spin multiplicity 2S + 1 is 3 (it is a triplet state), so S = 1; the letter "P" is spectroscopic notation for L = 1; and the subscript 0 is the value of J (in this case J = L − S). Small letters refer to individual orbitals or one electron quantum numbers, whereas capital letters refer to many electron states or their quantum numbers.
Орбитальные символы S, P, D и F происходят из характеристик спектроскопических линий, соответствующих s-, p-, d- и f-орбиталям: острые, главные, диффузные и фундаментальные; остальные названы в алфавитном порядке, начиная с G (пропуская J, S и P). При описании электронных состояний атома термический символ часто записывается после электронной конфигурации. Например, 1s²2s²2p² ³P₀ представляет собой основное состояние нейтрального атома углерода. Надстрочный индекс 3 указывает, что спиновая мультиплетность 2S + 1 равна 3 (это триплетное состояние), следовательно, S = 1; буква "P" — спектроскопическое обозначение для L = 1; а индекс 0 — значение J (в данном случае J = L − S). Строчные буквы относятся к отдельным орбиталям или квантовым числам одного электрона, в то время как заглавные буквы относятся к состояниям многих электронов или их квантовым числам.
In atomic physics, a term symbol is an abbreviated description of the total spin and orbital angular momentum quantum numbers of the electrons in a multi electron atom. So while the word symbol suggests otherwise, it represents an actual value of a physical quantity. For a given electron configuration of an atom, its state depends also on its total angular momentum, including spin and orbital components, which are specified by the term symbol. The usual atomic term symbols assume LS coupling (also known as Russell–Saunders coupling) in which the all electron total quantum numbers for orbital (L), spin (S) and total (J) angular momenta are good quantum numbers. In the terminology of atomic spectroscopy, L and S together specify a term; L, S, and J specify a level; and L, S, J and the magnetic quantum number MJ specify a state. The conventional term symbol has the form 2S+1LJ, where J is written optionally in order to specify a level. L is written using spectroscopic notation: for example, it is written "S", "P", "D", or "F" to represent L = 0, 1, 2, or 3 respectively. For coupling schemes other that LS coupling, such as the jj coupling that applies to some heavy elements, other notations are used to specify the term. Term symbols apply to both neutral and charged atoms, and to their ground and excited states. Term symbols usually specify the total for all electrons in an atom, but are sometimes used to describe electrons in a given subshell or set of subshells, for example to describe each open subshell in an atom having more than one. The ground state term symbol for neutral atoms is described, in most cases, by Hund's rules. Neutral atoms of the chemical elements have the same term symbol for each column in the s block and p block elements, but differ in d block and f block elements where the ground state electron configuration changes within a column, where exceptions to Hund's rules occur. Ground state term symbols for the chemical elements are given below. Term symbols are also used to describe angular momentum quantum numbers for atomic nuclei and for molecules. For molecular term symbols, Greek letters are used to designate the component of orbital angular momenta along the molecular axis. The use of the word term for an atom's electronic state is based on the Rydberg–Ritz combination principle, an empirical observation that the wavenumbers of spectral lines can be expressed as the difference of two terms. This was later summarized by the Bohr model, which identified the terms with quantized energy levels, and the spectral wavenumbers of these levels with photon energies. Tables of atomic energy levels identified by their term symbols are available for atoms and ions in ground and excited states from the National Institute of Standards and Technology (NIST).). The spin orbit interaction then couples the total spin and orbital moments to give the total electronic angular momentum quantum number J. Atomic states are then well described by term symbols of the form:
where
S is the total spin quantum number for the atom's electrons. The value 2S + 1 written in the term symbol is the spin multiplicity, which is the number of possible values of the spin magnetic quantum number MS for a given spin S.
J is the total angular momentum quantum number for the atom's electrons. J has a value in the range from |L − S| to L + S.
L is the total orbital quantum number in spectroscopic notation, in which the symbols for L are:
L = 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 (continued alphabetically)
The orbital symbols S, P, D and F are derived from the characteristics of the spectroscopic lines corresponding to s, p, d, and f orbitals: sharp, principal, diffuse, and fundamental; the rest are named in alphabetical order from G onwards (omitting J, S and P). When used to describe electronic states of an atom, the term symbol is often written following the electron configuration. For example, 1s22s22p2 3P0 represents the ground state of a neutral carbon atom. The superscript 3 indicates that the spin multiplicity 2S + 1 is 3 (it is a triplet state), so S = 1; the letter "P" is spectroscopic notation for L = 1; and the subscript 0 is the value of J (in this case J = L − S). Small letters refer to individual orbitals or one electron quantum numbers, whereas capital letters refer to many electron states or their quantum numbers.
Символы атомных терминов химических элементов
В периодической таблице, поскольку атомы элементов в столбце обычно имеют одинаковую внешнюю электронную структуру, и всегда имеют одинаковую электронную структуру в элементах "s-блока" и "p-блока" (см. блок (периодическая таблица)), все элементы в столбце могут иметь один и тот же символ терма основного состояния. Таким образом, водород и щелочные металлы имеют 2S1/2, щелочноземельные металлы – 1S0, элементы бора – 2P1/2, элементы углерода – 3P0, пниктогены – 4S3/2, халькогены – 3P2, галогены – 2P3/2, а инертные газы – 1S0, в соответствии с правилом для заполненных оболочек и подуровней, указанным выше. Символы термов для основных состояний большинства химических элементов приведены в сводной таблице ниже. В d-блоке и f-блоке символы термов не всегда одинаковы для элементов в одном столбце периодической таблицы, поскольку незаполненные оболочки, содержащие несколько d- или f-электронов, имеют несколько близких по энергии термов, порядок которых часто нарушается при добавлении дополнительной заполненной оболочки для формирования следующего элемента в столбце. Например, в таблице показано, что первая пара вертикально соседних атомов с различными символами терма основного состояния – V и Nb. Основное состояние 6D1/2 Nb соответствует возбужденному состоянию V, находящемуся на 2112 см−1 выше основного состояния 4F3/2 V, которое, в свою очередь, соответствует возбужденному состоянию Nb, находящемуся на 1143 см−1 выше основного состояния Nb. Для общей электронной конфигурации , а именно k эквивалентных электронов, занимающих одну подуровень, общее рассмотрение и компьютерный код также можно найти в этой статье.