NIST: Atomic Spectra Database - Energy Levels Help File

The ASD database provides energy level data for atoms and ions. For more information consult Introduction to and Contents of the ASD.

Energy Levels Search Form

The ASD Levels Search Form, referred to as the Levels Form, provides access to the energy level data. Submitting the Levels with information specified by the user generates a level list for a specified spectrum.

At a minimum, the user must enter a spectrum of interest (e.g., Fe I) and then click "Retrieve Data".

The Levels Form prompts the user for the following information:

Spectrum of interest (e.g., Fe I).
Energy level units (selected from the pulldown menu).
Energy levels may be displayed in one of the following units:
- cm⁻¹ (reciprocal centimeter or wavenumber), the default unit
- eV (electron Volt)
- Rydberg
- Hartree (=2×Rydberg)
- GHz
Choice of viewing the output as an HTML table, ASCII table, a CSV or tab-delimited data file (selected from the pulldown menu).
Choice of viewing (scrollable) data all at once, or one page at a time (selected from the pulldown menu).
Page size.
Choice of energy ordering of the output, i.e., term ordered or energy ordered.
Choice of the output information for levels.
Choice of the output of the relevant available bibliographic references.
For most ions, bibliographic references are available and can be retrieved by selecting the "Bibliographic references" checkbox.
Choice of the output of the level splitting, i.e., the difference between two adjacent energy levels (different levels may be "adjacent" with different ordering of output).
Electron temperature T_e for calculation of partition function.

For levels output, the default is to display the following data:

Principal Configuration
Principal Term
Level
Uncertainty
J
Landé g-factor
Leading Percentages
Bibliographic References

To suppress display of any of the information listed above, the corresponding checkbox can be unclicked.

Additional search criteria are available for all ions and can be reached by pressing the "Set Additional Criteria" button.

Selecting a Spectrum for Levels Searches

To specify an element on the Levels Form, simply enter the chemical symbol for the element (e.g., Fe or fe). To indicate a particular spectrum (ionization stage), enter (after a space) either a Roman numeral or an Arabic numeral after the element symbol (NOTE: Fe I = Fe0+, Fe II = Fe1+, etc.). Alternatively, a spectrum may be specified by the name of its isoelectronic sequence (e.g., Si Li-like = Si XII, Si Na-like = Si IV). The user can also specify a particular isotope by including an atomic mass number before the element symbol, e.g., 198Hg I. Isotopes of hydrogen can also be specified by using their alternate element symbols, D I or T I. The symbol H I will produce the same results as 1H I. For levels searches, output can only be generated for one spectrum at a time.

Examples of Spectrum Notation

To specify	Enter
Neutral sodium	Na I
Neutral sodium	Na 0
Neutral iron	fe i
Lithium-like magnesium	Mg x
Lithium-like magnesium	mg Li-like
Singly-ionized ¹¹B	11B II

Setting Additional Criteria (from the Levels Form)

Clicking the "Set Additional Criteria" button on the Levels Form causes a list of additional search criteria to be displayed. These options are set to default values. Therefore, it is not mandatory that the options be set before using the database.

Before selecting the button "Set Additional Criteria," the user must specify a spectrum on the Levels Form.

The following search criteria may be specified:

Upper bound of energy (in the energy units selected on the Levels Form).
Parity. The default is to retrieve levels of both parities. The user may specify either odd or even parity.
Configuration. The search criteria are used to create a list of possible configurations for the chosen. The default is that no configuration bound is specified. The pulldown menu can be used to select a configuration bound of interest. Alternatively, the text box can be used to type in the initial or ending portion of a configuration of interest.
term. The search criteria are used to create a list of possible configurations for the chosen ion. The default is that no term bound is specified. The pulldown menu can be used to select a term bound of interest. Alternatively, the text box can be used to type the initial or ending portion of a term of interest.
J value

If the spectrum on the Levels Form is changed, then clicking on the "Update Criteria" button on the Levels Form will update the list of additional search criteria.

Output for Levels
(by table column heading)

Configuration
Term
- Naming of Levels
J: Total Electronic Angular-Momentum Quantum Number
Level
Uncertainty
Landé g: Experimental Magnetic Landé g Factor
Leading Percentages
Bibliographic References
Partition Function

Configuration

For most of the headings, we discuss separately the cases of levels tabulated with and without leading percentages.

Levels Tabulated With Leading Percentages

The electronic configuration for the largest component in the calculated eigenvector for the level is normally given in this column. (The configuration is for the largest component to within the estimated uncertainty of the calculation; see "Term.") Any ancestor terms or J values appropriate to this component are normally included with the configuration, as in the examples in the Introduction to Atomic Spectroscopy.

A question mark "?" after the configuration indicates that the assignment of the observed level to the calculated eigenvector is uncertain. This particular notation for an uncertain assignment usually implies that at least one other plausible assignment of the level would give a different configuration or set of parent terms for the leading component.

The configuration is listed only once for a set of levels grouped into a term. All notations given with the configuration, including any question marks, apply to each level of such a term.

In cases of strong configuration interaction, more than half the percentage composition of a level may be due to components from a configuration different from that for the leading component; such an example makes it clear that the configuration given in the first column does not necessarily represent a configuration assignment of the level. A particular configuration may appear in the first column for more levels than the pure configuration is allowed. In such cases of strong configuration interaction, the label used in the Configuration column may correspond not to the largest, but to a minor component of the eigenvector composition. For such heavily mixed levels, the configuration label has little or no physical meaning and is used in the database for bookkeeping purposes only. The configuration labels of such mixed levels are usually assigned so as to satisfy the requirement of uniqueness of the combination of the combination of the configuration, term, and J values for each level.

Levels Tabulated Without Leading Percentages

The reliability and indeed the meaning of configuration assignments made without supporting calculations vary greatly. Even in the most complex spectra, there may be some levels or groups of levels belonging largely to a single configuration. The observed structure, magnetic g values, intensities, isotope shifts, and other data can in such cases lead to unambiguous assignments representing high purity. (Examples are the lower levels of most 4f ^N6s², 4f ^N6s, and 4f ^N configurations in the rare earths.) Quite often, however, the levels to be interpreted comprise a dense structure to which several configurations are known or expected to contribute. Some preliminary configuration assignments may be possible and useful in such cases, but such assignments for the bulk of the levels are often best regarded as tentative until confirmed by calculations. In many cases, meaningful single-configuration assignments do not exist.

We have tried to indicate doubtful features of the interpretations in the discussions of particular spectra in our compilations and, to some extent, in the tables. A question mark following the configuration indicates explicitly that the assignment is doubtful. A doubtful ancestor term is indicated by a question mark after the term symbol within parentheses.

In some cases, the configuration for a level may be known, although the appropriate ancestor terms (or even the preferred order of coupling of the electrons) cannot be determined without calculations. Such a configuration assignment (together with the final term and J value) without full ancestry does not in general serve as a unique name for the level.

Limits

The wavenumber corresponding to the principal ionization energy is entered in proper sequence under "Level." The corresponding entry in the first column is the symbol for the next higher spectrum of the element, followed by the configuration and term designations and the J value for the ground level of this next ion. The word "Limit" appears in the "Term" column (the levels of the higher ion being limits for series in the lower spectrum). If the known levels of the lower ion (or atom) extend above the principal limit, one or more of the higher limits are also given at appropriate positions.

Term

Naming of Levels, Grouping of Levels into Terms, Other Conventions

A term symbol in the second column belongs to the eigenvector component whose configuration and ancestry appear in the first column. The assignment of a set of levels to a term is indicated by grouping the levels and by listing the configuration and term symbol for only the first (lowest) level of the group. The presence of both a configuration with all necessary ancestor terms in the first column and a term symbol in the second column guarantees that each of the levels grouped with the term is uniquely designated by the symbols in the first two columns, together with the J value; i.e., such levels have names. This naming convention also applies to isolated levels not grouped into terms. The use of the (J_l, J₂) term symbols in this connection should be noticed; a J₁,J₂ configuration notation in the first column is indicated as a name for the associated level(s) only if a (J₁, J₂) symbol appears in the second column.

In our various NIST compilations we have not followed a single set of guidelines in retaining or forming terms (by grouping levels). Probably the strictest criteria were applied to the rare-earth spectra, where we usually retained or formed a term if half or more of the candidate levels for the term were known and had leading components approximately 45 % or larger. The 45 % requirement was sometimes lowered significantly for levels having leading components sufficiently larger than the corresponding second components. Additional levels of lower purity (~30 % to 45 %) were retained (or assigned) to help complete a multilevel term provided certain conditions were met. Thus the component for an assigned term name is normally the leading component in the eigenvector, and is also as large a percentage of the particular name as occurs in the eigenvector of any other level (known or not) with the same J value. We also tried to avoid a name for which the configuration contributes less to the total composition of the level than some other configuration. These are minimal requirements for avoiding completely inappropriate names.

One can assure more generally satisfactory names by disallowing any name representing significantly less than 50 % eigenvector purity; and in the case of a leading percentage near 50 %, by requiring that the second percentage be significantly smaller (alternate designation clearly less appropriate), and that no other eigenvector should have a comparable leading percentage (~50 %) for the same designation. The weaker criteria for the grouping and naming of levels outlined above were adopted to allow practically any significant term structure within a single configuration to be exhibited in the tables.

In cases of strong configuration interaction, it sometimes happens that assignment to a particular term type remains appropriate for a level or level group for which no meaningful configuration assignment is possible. Such term names may usually be deduced by examination of the two leading eigenvector percentages. In some cases of this type, we have entered the appropriate term name under "Term," along with a letter indicating the situation (see, for example, the "y ²D" term of Al I).

Most of the calculated leading percentages for levels in question as to naming are probably uncertain by several percent. In order to facilitate term assignments, we have allowed a relatively few small deviations (by up to ~4 %) from the above requirements on naming. These deviations are probably within the uncertainties of the calculations.

Many of the resulting terms are incomplete, in the sense that no observed level is listed for one or more of the possible J values of the term. A level "missing" from such a term may not have been found in the analysis; alternatively, it may be that no theoretical eigenvector is appropriate for the corresponding designation, even under the relaxed criteria described above. The first case is distinguished in the tables by printing the J value of the level, and leaving a blank space in the "Level" column. The leading percentages for such a missing level are given if available. In the second case, the best candidate levels for the missing designation are usually known and lie in the same region as the levels assigned to the term.

Levels belonging to a term most of whose levels have not been found may nevertheless be grouped if the term appears to be an important one or lies in a region where most terms are more complete. The printed J values of the missing levels explicitly indicate possible extensions of the analysis. No predicted term is shown. However, unless at least one level is known, and we emphasize that missing predicted levels are generally not indicated in these tables: no term symbols or J values are listed for missing levels having low eigenvector purities or belonging to terms the levels of which are not grouped (for whatever reason). The user is urged to consult the references to published calculations for additional predicted levels.

A level with the leading percentage >45 % from a single-level term (singlet, S term, etc.) is usually so named (shown as a term) if the second percentage is significantly smaller, and if the other conditions outlined above are met. Isolated levels (those remaining after the formation of all terms) are named according to similar conditions.

Some levels of f ^N and d^N configurations have large eigenvector components from two or more terms of the same LS type. Since the resultant lowering of the purities has no physical significance, we have retained the names of such levels having adequate total purity of a particular LS type and labeled them with the Nielson-Koster index number for the term of the leading component. (Of course, the corresponding group-theoretical numbers have little meaning for such a low-purity term.) Similar considerations have been applied in designating parent (or grandparent) terms arising from f ^N configurations.

A question mark (?) after a term designation indicates that the assignment of the observed level(s) to the calculated eigenvector(s) is uncertain.

J: Total Electronic Angular-Momentum Quantum Number

The total angular momentum, J, is known for the vast preponderance of energy levels. An uncertain J value for a level is usually known to within two or three possible values; in such cases all the possible J values, separated by 'or', are listed. Two or more comma-separated J values may be listed at a single energy position to denote unresolved levels.

Level

The levels are normally given as they are stored in the database, in units of cm⁻¹, with respect to the ground level at zero cm⁻¹. In HTML output, odd-parity levels are shown in italics. The odd parity is also indicated in the HTML output by a small circle symbol (°), or in the ASCII output by an asterisk (*) at the end of the term label.

Levels within terms are listed in order of position. Terms are listed in order of lowest (known) levels, with ungrouped levels being treated as separate terms. The J value and blank space indicating a missing level of a term are given in the order of the corresponding calculated level if such a value is available.

A question mark (?) following a level always indicates that the level may not be real.

For levels having a configuration label, the question mark after the energy also implies that the correlation of the calculated eigenvector to the experimental level is questionable. Sometimes, instead of the question mark, we use the dagger symbol '†' after the level value. This notation is used mainly for questionably assigned levels included in terms. An uncertain assignment of an isolated level may be indicated by '†', but only if the configuration in the first column would be unchanged by any possible reassignment of the level (no question mark in the first column).

The values of certain levels in some spectra are followed by "+x," and such notations may be extended to "+y," "+z," etc., for additional sets of levels of a particular spectrum. The relative positions of the levels within such a system are accurate within experimental uncertainties, but no experimental connection between this system and the other levels of the spectrum has been made; the error of the assumed connection (estimated or calculated) is represented by "+x."

The letter "a" following a level value indicates substantial autoionization broadening. The decision whether to add this notation after a particular level was more qualitative than quantitative, and no consistent criteria were used for different spectra. Levels given with an "a" for a particular spectrum may have autoionization rates varying by several orders of magnitude. No indication of observed autoionization broadening was given for many spectra. In no case should a level lying above the principal ionization energy but given without an "a" be assumed to have a small autoionization rate.

Some level energies are in square brackets "[ ]" and some are in parentheses "( )". Square brackets indicate the energies determined by interpolation, extrapolation, or other semi-empirical procedure relying on some known experimental values. Parentheses indicate the energies determined from ab-initio calculation or by other means not involving evaluated experimental data. In ASD, they mostly occur for level data taken from transition probability tables, for which experimental values could not be found in NIST energy level compilations. Theoretical data may also be given for hydrogen-like and helium-like spectra where the accuracy of quantum-electrodynamic calculations often exceeds that of experimental observations.

Uncertainty

Uncertainty of the level value is given a column next to level values, if it is available in ASD, provided that the corresponding checkbox is checked in the input form. If no explicit information about the uncertainty is available, it will be blank in the output. In such cases, the number of significant figures in the level value gives an approximate estimate of the uncertainty. The uncertainty of the level positions in units of the last decimal place is not constant; it may vary by an order of magnitude even within a single analysis. If no uncertainty value is available in ASD, it is usually safe to assume that the probable error is between 2.5 and ~25 units in the last place. About 90 % of data in ASD satisfies this assumption. A better estimate of the uncertainty in a particular case may sometimes be obtained by consulting the original paper(s) or the line list.

The most accurate representation of the energy levels is in the default units of cm⁻¹, as they are stored in ASD. Conversion to other units (eV or Rydberg) involves an additional uncertainty of the conversion factor. These factors, as well as their uncertainties, are taken from the latest CODATA recommended conversion factors. Before ASD version 5.5 of October 2017, uncertainties of these conversion factors were not taken into account in the displayed data. Starting with v.5.5, these uncertainties are combined in quadrature with the uncertainties of the stored data, and the output quantities are rounded off according to the combined uncertainties. Thus, the accuracy of the output energies is somewhat degraded when the units of eV or Rydberg are used.

All uncertainties given in ASD are meant to be on the level of one standard deviation.

Landé g: Experimental Magnetic Landé g Factor

These (dimensionless) magnetic splitting factors are usually obtained from measurements of weak-field Zeeman patterns. The relation between the uncertainty and the number of decimal places given differs according to the observer and the particular value; the range covered by this relation is similar to that for the level values (see above). More specific comments are made on the g values for some spectra.

A colon following a g value indicates that it may be significantly less accurate than values given to the same number of decimal places but not so marked. Values followed by a question mark are tentative, usually being based on assumptions made to allow reduction of the Zeeman patterns.

Leading Percentages

This column normally gives one or two percentages from the calculated eigenvector of the level. The space for the second percentage (on the right) is used in either of two ways, as explained below. All percentages are rounded off to the nearest percent, and the "%" symbol is omitted.

Any use of this column in a manner not outlined below is explained in the tables for particular spectra as given in our compilations.

First Percentages

If the level has an assigned name, the first percentage is for this "name" component. A first percentage followed by a term symbol represents the largest component in the eigenvector of a level having no assigned term name or named differently for bookkeeping purposes. The configuration and ancestry for this component are shown under "Configuration."

Second Percentage from Same Eigenvector as First Percentage

If two percentages are listed without the word "or " between them, the second percentage is the largest of the remaining percentages from the same eigenvector as the first percentage. If the second component belongs to the same configuration as the first, we have in some cases omitted the configuration after the second percentage and given only the parent terms (or parent levels where appropriate) and final term for the second component. For some spectra, a second component having both configuration and all parent terms unchanged from the first component is given with only the final term. Electron subshells common to different configurations for the first and second percentages may be omitted from the second configuration. Term notations common to all second percentages listed for the levels of a term may be given only once.

The coupling scheme for a second eigenvector component belonging to a different configuration may be different from the scheme for the first component; this should not be confused with case (see below), where the second listed percentage is the leading percentage in a different coupling scheme.

Since many authors list only the largest percentage for at least some levels, the absence of a second percentage in this compilation does not necessarily mean that it is less than the smallest percentage used here (0.5 %, given as 1 %).

The relative signs of the two eigenvector components are not given. These are often not given in the original publications. Furthermore, these signs depend on certain conventions, no one set of which has been accepted by all authors. The original articles can be consulted for (possibly) more complete eigenvectors with signs.

Second Percentage for Leading Component of Eigenvector in Alternate Coupling Scheme

Where the eigenvectors from a calculation are available in more than one coupling scheme, we often give in the second percentage space the leading percentage from the eigenvector calculated in an alternate scheme. This use of the second percentage space is indicated by the word "or" between the two percentages, since each is a leading percentage. Competitively high coupling purities for a configuration in different coupling schemes were, of course, regarded as an argument for giving leading percentages in alternate schemes, as was the case in which a second scheme for the configuration in question is the preferred scheme for a related configuration (two configurations connected by a strong transition array, etc.). We have favored LS coupling as a second scheme in cases where another scheme was used for naming the levels.

It should be noted that the leading component in a second scheme is not necessarily a name for the level in that scheme; in cases of low purity, the eigenvectors of two (or more) levels of the same J value may have the same leading component.

For some configurations, the alternate coupling schemes are both LS coupling, but with the electrons coupled differently in the two cases. In this case it is usually possible to set up terms in either scheme (see Eu I 4f ⁷5d6p, for example).

Bibliographic References

For information on viewing references, see the Locating references in the ASD Bibliography section of the "Help" file.

Partition Function

If the electron temperature T_e is entered in the entry page, a partition function Z defined as:

Z = Σ_i(g_i·exp(-E_i/T_e))

is printed at the bottom of the output page. Here i is the level number, g_i is the statistical weight of the atomic level, and E_i is the energy.

Creating an output for importing into a spreadsheet

Two options are available from the Format Output pull-down menu for creating an output in a format suitable for importing into a spreadsheet: CSV (comma-separated ASCII file) or tab-delimited ASCII file. Both options produce output in the user's browser window, which needs to be saved on the local computer by using the browser's interface options and opened with a spreadsheet software. For importing data into Excel, the most convenient format is CSV. If the output is saved in a file with a .csv extension, some browsers (e.g., Chrome) even allow the user to open it directly from the browser. Users of the OpenOffice software may prefer the tab-delimited format, as it conveniently allows setting the format of all columns enclosed in double quotes as "text." This is required, for example, for the J-values, which can be half-integers stored as strings, e.g., "1/2." If such columns are not set as text, the spreadsheet software will most likely automatically convert them to dates. Even for columns containing only numbers, text format is needed to preserve the number of decimal places, which indicates an implicit uncertainty of value. For this reason, the CSV-format output contains formulas instead of plain values. After importing such a file into a spreadsheet, the user should "select all cells" (in Excel, this can be done by clicking on the small triangle in the upper left corner of the spreadsheet), copy the selection, and paste it back as values.