Atomic term symbols by group representation methods

In multielectron atoms or molecules, quantized electronic energy states known as term states provide a framework for interpreting absorption and emission spectra. Enumerating the term states associated with any particular electron configuration is possible using time-honored procedures, but the underpinnings of the methods do not always receive the attention they deserve. Rounding out the discussion with another approach to term states would provide added perspective. In particular, for systems involving two electrons distributing among two orbitals one can begin by identifying plausible wave functions. The states generated are few in number but noteworthy in that analogous states occur in a host of systems, including helium, titanocene, and molecular hydrogen. Parallels among the systems become evident from the forms of the wave functions.

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confidence: 99%

Coming to Terms with Term States

McMillin

2020

“…The R−S terms for the configurations of multiequivalent electrons can also be generalized by the new method using eqs and , which can also be found in refs , , and . For example, using eqs and along with Table , the R−S terms for p 3 and d 3 configurations can be obtained and they are shown in Table χ( g 3 ) for representations p and d are given in Table .…”

Section: The R−s Terms For Atomic Configurations Of Equivalent Electronsmentioning

confidence: 99%

A New Method for Obtaining Russell−Saunders Terms

Liu

2010

Many familiar concepts deserve reconsideration (1). We report a novel method to solve the fundamental problem of determining atomic spectral terms. Atomic spectral terms are of fundamental importance in the investigation of atomic structure. The usual methods are categorized as (a) the determinant-wave function method that involves establishing the eigenfunctions of the Russell-Saunders (R-S) terms, (b) the electronic-arrangement method (2) that involves explicitly writing down all possible microstates of a configuration, (c) the spin-factor method (3-5) in which the spin multiplets are classified by the number of unpaired electrons, and (d) the partial-term method in which the R-S partial terms of R and β spins are used to derive the R-S terms of a given configuration for atoms or molecules (6, 7). Other methods that are less well-known include that of Tuttle (8), which involves establishing a set of rules to guarantee that each adopted quantum number set is allowed by the Pauli principle and occurs only once, and that of Curl and Kilpatrick (9) who employ a method for generating functions to obtain the proper term symbols from a given configuration. Readers who are interested in those methods are directed to the original literature.We report a novel but simple method that shares some common features with those methods that determine molecular electronic terms, especially those that determine the splitting of S, P, D terms in weak ligand fields and of s, p, d orbitals in strong ligand. The innovative feature of this new method is the decomposition of an atomic configuration to R-S terms. But its application in identifying R-S terms has not been reported previously to our knowledge. The new method for determining atomic terms also adopts the same principles used in molecular systems for ruling out impossible microstates for equivalent electron configurations. It is significantly different but complementary to previously published methods for obtaining atomic terms. It shows students that creative thought is worthwhile even in well-developed traditional fields and that applying methods that have already been used in one field can be particularly useful.

“…Due to the restriction of the Pauli principle, it is a much more arduous work to derive the terms of equivalent electrons than that of nonequivalent electrons. To this end, several different methods have been proposed. − Among them, many methods use group theory. − Dated back to the 1960s, Curl and Kilpatrick proposed the generating function method. Meanwhile, Ford systematically exploited the symmetric group method, in which a spin function is characterized by a standard Young diagram, whereas the corresponding spatial function is characterized by the irreducible representation of S n conjugated to the spin one.…”

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confidence: 99%

“…Meanwhile, Ford systematically exploited the symmetric group method, in which a spin function is characterized by a standard Young diagram, whereas the corresponding spatial function is characterized by the irreducible representation of S n conjugated to the spin one. Based on the group representation theory, Ford’s method was lately adopted and extended by Chen . More powerfully, combining the group theory with the spin factor idea originally developed by Shudeman in 1937, McDaniel proposed the spin factor method .…”

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confidence: 99%

“…Based on the group representation theory, Ford's method was lately adopted and extended by Chen. 8 More powerfully, combining the group theory with the spin factor idea originally developed by Shudeman in 1937, 9 McDaniel proposed the spin factor method. 3 A refinement of the spin factor method, called the "short-cut calculation method", 10 was lately developed by Liu and Ellzey.…”

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confidence: 99%

See 1 more Smart Citation

String-Based Method for Deriving Russell–Saunders Terms

Zhang

Chen

2023

In this paper, we propose a novel method for deriving Russell–Saunders terms of complex atomic systems with an arbitrary number of equivalent electrons in orbitals with a higher azimuthal number. The method can be regarded as an extension of the classic works of Douglas, McDaniel, and Hyde but with several notable improvements, including the introduction of symmetry and spin string, that simplify the enumeration process. Moreover, the method is simple for undergraduate students’ apprehension, requiring only basic knowledge of combinatorial mathematics at the high-school level. Last but not least, it reduces the computational cost for complex systems, which is illustrated not only by the paradigmatic example of the nd 4 configuration in the text but also by two other much more complicated examples of nf m and ng m . Considering both the simplicity and efficiency of the new method, we expect that it would be generally applicable to the teaching practice of the derivation of Russell–Saunders terms in advanced physical chemistry courses.