a visual representation of the elements grouped by similar properties

Periodic Table of Element Groups

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One reason the periodic table of the elements is so useful is that it is a means of arranging elements according to their similar properties. This is what is meant by periodicity or periodic table trends .

There are multiple ways of grouping the elements, but they are commonly divided into metals, semimetals (metalloids), and nonmetals. You'll find more specific groups, like transition metals, rare earths , alkali metals, alkaline earth, halogens, and noble gasses.

Groups in the Periodic Table of Elements

Click on an element to read about the chemical and physical properties of the group to which that element belongs.

Alkali Metals

• Less dense than other metals
• One loosely bound valence electron
• Highly reactive, with reactivity increasing moving down the group
• The largest atomic radius of elements in their period
• Low ionization energy
• Low electronegativity

Alkaline Earth Metals

• Two electrons in the valence shell
• Readily form divalent cations
• Low electron affinity

Transition Metals

The lanthanides (rare earth) and actinides are also transition metals. The basic metals are similar to transition metals but tend to be softer and to hint at nonmetallic properties. In their pure state, all of these elements tend to have a shiny, metallic appearance. While there are radioisotopes of other elements, all of the actinides are radioactive.

• Very hard, usually shiny, ductile, and malleable
• High melting and boiling points
• High thermal and electrical conductivity
• Form cations (positive oxidation states)
• Tend to exhibit more than one oxidation state

Metalloids or Semimetals

• Electronegativity and ionization energy intermediate between that of metals and nonmetals
• May possess a metallic luster
• Variable density, hardness, conductivity, and other properties
• Often make good semiconductors
• Reactivity depends on the nature of other elements in the reaction

The halogens and noble gases are nonmetals, although they have their own groups, too.

• High ionization energy
• High electronegativity
• Poor electrical and thermal conductors
• Form brittle solids
• Little if any metallic luster
• Readily gain electrons

The halogens exhibit different physical properties from each other but do share chemical properties.

• Extremely high electronegativity
• Very reactive
• Seven valence electrons, so elements from this group typically exhibit a -1 oxidation state

Noble Gases

The noble gasses have complete valence electron shells, so they act differently. Unlike other groups, noble gasses are unreactive and have very low electronegativity or electron affinity.

Click on the element symbol in the table for further information.

• Alkali Metal
• Alkaline Earth
• Transition Metal
• Basic Metal
• List of Periodic Table Groups
• Introduction to the Periodic Table
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Periodic Table Groups and Periods

Groups and periods organize elements on the periodic table of the elements . A group is a vertical column down the periodic table, while a period is a horizontal row across the table. Both groups and periods reflect the organization of electrons in atoms. Element atomic number increases as you move down a group from top to bottom or across a period from left to right.

• An element group is a vertical column on the periodic table. Atoms in a group share the same number of valence electrons. There are 18 element groups.
• An element period is a horizontal row on the periodic table. Atoms in a period have the same number of electron shells. There are 7 element periods.

Element Groups

Elements within the same group share the same number of valence electrons . The number of valence electrons depends on the octet rule. For example, elements in group 1 have 1 valence electron, elements in groups 3-12 have a variable number of valence electrons, and elements in group 17 have 7 valence electrons. The lanthanides and actinides, located below the main table, all fit within group 3.

There are 18 element groups. Elements in the same group share common chemical and physical properties. For example, the group 1 elements are all soft, reactive metals. The group 17 elements are highly reactive, colorful nonmetals.

Alternate Group Classification System

Sometimes chemists classify element groups according to shared properties, which do not strictly adhere to individual columns. These groups go by the names alkali metals, alkaline earth metals, transition metals, basic metals, nonmetals, halogens, noble gases , lanthanides, and actinides. Under this system, hydrogen is a nonmetal . The nonmetals, halogens, and noble gases are all types of nonmetals. The metalloids have properties intermediate between metals and nonmetals. The alkali metals, alkaline earths, lanthanides, actinides, transition metals, and basic metals are all groups of metals.

Element Periods

Elements within a period share the same number of electron shells and the same highest unexcited electron energy level. Elements within a period display periodic table trends , moving from left to right, involving atomic and ionic radius, electronegativity, There are seven element periods. Some periods contain more elements than others because the number of included elements depends on the number of electrons allowed in an energy sublevel. Note that the lanthanides are within period 6 and the actinides are in period 7.

• Period 1: H, He (does not follow the octet rule)
• Period 2: Li, Be, B, C, N, O, F, Ne (involves s and p orbitals)
• Period 3: Na, Mg, Al, Si, P, S, Cl, Ar (all have at least 1 stable isotope)
• Period 4: K, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Ga, Ge, As, Se, Br, Kr (first period with d-block elements)
• Period 5: Rb, Sr, Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd, In, Sn, Sn, Te, I, Xe (same number of elements as period 4, same general structure, and includes the first exclusively radioactive element , Tc)
• Period 6: Cs, Ba, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, Hf, Ta, W, Re, Os, Ir, Pt, Au, Hg, Tl, Pb, Bi, Po, At, Rn (first period with f-block elements)
• Period 7: Fr, Ra, Ac, Th, Pa, U, Np, Pu, Am, Cm, Bk, Cf, Es, Fm, Md, No, Lr, Rd, Db, Sg, Bh, Hs, Mt, Ds, Rg, Cn, Nh, Fl, Mc, Lv, Ts, Og (all elements are radioactive; contains heaviest natural elements and many synthesized elements)
• Fluck, E. (1988).  “ New Notations in the Periodic Table” .  Pure Appl. Chem.  IUPAC.  60  (3): 431–436. doi: 10.1351/pac198860030431
• Greenwood, Norman N.; Earnshaw, Alan (1997). Chemistry of the Elements (2nd ed.). Butterworth-Heinemann. ISBN 978-0-08-037941-8.
• Scerri, E. R. (2007). The periodic table, its story and its significance . Oxford University Press. ISBN 978-0-19-530573-9.

Related Posts

Module 2: Atoms, Molecules, and Ions

The periodic table, learning outcomes.

• State the periodic law and explain the organization of elements in the periodic table
• Predict the general properties of elements based on their location within the periodic table
• Identify metals, nonmetals, and metalloids by their properties and/or location on the periodic table

As early chemists worked to purify ores and discovered more elements, they realized that various elements could be grouped together by their similar chemical behaviors. One such grouping includes lithium (Li), sodium (Na), and potassium (K): These elements all are shiny, conduct heat and electricity well, and have similar chemical properties. A second grouping includes calcium (Ca), strontium (Sr), and barium (Ba), which also are shiny, good conductors of heat and electricity, and have chemical properties in common. However, the specific properties of these two groupings are notably different from each other. For example: Li, Na, and K are much more reactive than are Ca, Sr, and Ba; Li, Na, and K form compounds with oxygen in a ratio of two of their atoms to one oxygen atom, whereas Ca, Sr, and Ba form compounds with one of their atoms to one oxygen atom. Fluorine (F), chlorine (Cl), bromine (Br), and iodine (I) also exhibit similar properties to each other, but these properties are drastically different from those of any of the elements above.

Dimitri Mendeleev in Russia (1869) and Lothar Meyer in Germany (1870) independently recognized that there was a periodic relationship among the properties of the elements known at that time. Both published tables with the elements arranged according to increasing atomic mass. But Mendeleev went one step further than Meyer: He used his table to predict the existence of elements that would have the properties similar to aluminum and silicon, but were yet unknown. The discoveries of gallium (1875) and germanium (1886) provided great support for Mendeleev’s work. Although Mendeleev and Meyer had a long dispute over priority, Mendeleev’s contributions to the development of the periodic table are now more widely recognized (Figure 1).

Figure 1. (a) Dimitri Mendeleev is widely credited with creating (b) the first periodic table of the elements. (credit a: modification of work by Serge Lachinov; credit b: modification of work by “Den fjättrade ankan”/Wikimedia Commons)

You can view the transcript for “The Periodic Table: Crash Course Chemistry #4” here (opens in new window) .

By the twentieth century, it became apparent that the periodic relationship involved atomic numbers rather than atomic masses. The modern statement of this relationship, the periodic law , is as follows: the properties of the elements are periodic functions of their atomic numbers . A modern periodic table arranges the elements in increasing order of their atomic numbers and groups atoms with similar properties in the same vertical column (Figure 2). Each box represents an element and contains its atomic number, symbol, average atomic mass, and (sometimes) name. The elements are arranged in seven horizontal rows, called periods or series , and 18 vertical columns, called groups . Groups are labeled at the top of each column. In the United States, the labels traditionally were Roman numerals with capital letters. However, IUPAC recommends that the numbers 1 through 18 be used, and these labels are more common. For the table to fit on a single page, parts of two of the rows, a total of 14 columns, are usually written below the main body of the table.

Figure 2. Elements in the periodic table are organized according to their properties.

Many elements differ dramatically in their chemical and physical properties, but some elements are similar in their behaviors. For example, many elements appear shiny, are malleable (able to be deformed without breaking) and ductile (can be drawn into wires), and conduct heat and electricity well. Other elements are not shiny, malleable, or ductile, and are poor conductors of heat and electricity. We can sort the elements into large classes with common properties: metals (elements that are shiny, malleable, good conductors of heat and electricity—shaded yellow); nonmetals (elements that appear dull, poor conductors of heat and electricity—shaded green); and metalloids (elements that conduct heat and electricity moderately well, and possess some properties of metals and some properties of nonmetals—shaded purple).

The elements can also be classified into the main-group elements (or representative elements ) in the columns labeled 1, 2, and 13–18; the transition metals in the columns labeled 3–12; and inner transition metals in the two rows at the bottom of the table (the top-row elements are called lanthanides and the bottom-row elements are actinides ; Figure 3). The elements can be subdivided further by more specific properties, such as the composition of the compounds they form. For example, the elements in group 1 (the first column) form compounds that consist of one atom of the element and one atom of hydrogen. These elements (except hydrogen) are known as alkali metals , and they all have similar chemical properties. The elements in group 2 (the second column) form compounds consisting of one atom of the element and two atoms of hydrogen: These are called alkaline earth metals , with similar properties among members of that group. Other groups with specific names are the pnictogens (group 15), chalcogens (group 16), halogens (group 17), and the noble gases (group 18, also known as inert gases ). The groups can also be referred to by the first element of the group: For example, the chalcogens can be called the oxygen group or oxygen family. Hydrogen is a unique, nonmetallic element with properties similar to both group 1 and group 17 elements. For that reason, hydrogen may be shown at the top of both groups, or by itself.

Figure 3. The periodic table organizes elements with similar properties into groups.

Example 1:  Naming Groups of Elements

Atoms of each of the following elements are essential for life. Give the group name for the following elements:

• alkaline earth metal
• alkali metal

Check Your Learning

Give the group name for each of the following elements:

In studying the periodic table, you might have noticed something about the atomic masses of some of the elements. Element 43 (technetium), element 61 (promethium), and most of the elements with atomic number 84 (polonium) and higher have their atomic mass given in square brackets. This is done for elements that consist entirely of unstable, radioactive isotopes (you will learn more about radioactivity in the nuclear chemistry module ). An average atomic weight cannot be determined for these elements because their radioisotopes may vary significantly in relative abundance, depending on the source, or may not even exist in nature. The number in square brackets is the atomic mass number (and approximate atomic mass) of the most stable isotope of that element.

Key Concepts and Summary

The discovery of the periodic recurrence of similar properties among the elements led to the formulation of the periodic table, in which the elements are arranged in order of increasing atomic number in rows known as periods and columns known as groups. Elements in the same group of the periodic table have similar chemical properties. Elements can be classified as metals, metalloids, and nonmetals, or as a main-group elements, transition metals, and inner transition metals. Groups are numbered 1–18 from left to right. The elements in group 1 are known as the alkali metals; those in group 2 are the alkaline earth metals; those in 15 are the pnictogens; those in 16 are the chalcogens; those in 17 are the halogens; and those in 18 are the noble gases.

Metal or Nonmetal?

1. (a) metal, inner transition metal; (b) nonmetal, representative element; (c) metal, representative element; (d) nonmetal, representative element; (e) metal, transition metal; (f) metal, inner transition metal; (g) metal, transition metal; (h) nonmetal, representative element; (i) nonmetal, representative element; (j) metal, representative element

Identifying Elements

• noble gases
• alkaline earth metals
• alkali metals
• the noble gas in the same period as germanium
• the alkaline earth metal in the same period as selenium
• the halogen in the same period as lithium
• the chalcogen in the same period as cadmium
• the halogen in the same period as the alkali metal with 11 protons
• the alkaline earth metal in the same period with the neutral noble gas with 18 electrons
• the noble gas in the same row as an isotope with 30 neutrons and 25 protons
• the noble gas in the same period as gold
• the alkali metal with 11 protons and a mass number of 23
• the noble gas element with and 75 neutrons in its nucleus and 54 electrons in the neutral atom
• the isotope with 33 protons and 40 neutrons in its nucleus
• the alkaline earth metal with 88 electrons and 138 neutrons
• the chalcogen with a mass number of 125
• the halogen whose longest-lived isotope is radioactive
• the noble gas, used in lighting, with 10 electrons and 10 neutrons
• the lightest alkali metal with three neutrons

1. (a) He; (b) Be; (c) Li; (d) O

3. (a) krypton, Kr; (b) calcium, Ca; (c) fluorine, F; (d) tellurium, Te

5. (a) [latex]{}_{11}^{23}\text{Na}[/latex] ; (b) [latex]{}_{54}^{129}\text{Xe}[/latex] ; (c) [latex]{}_{33}^{73}\text{As}[/latex] ; (d) [latex]{}_{88}^{226}\text{Ra}[/latex]

actinide:  inner transition metal in the bottom of the bottom two rows of the periodic table

alkali metal:  element in group 1

alkaline earth metal:  element in group 2

chalcogen:  element in group 16

group:  vertical column of the periodic table

halogen:  element in group 17

inert gas:  (also, noble gas) element in group 18

inner transition metal:  (also, lanthanide or actinide) element in the bottom two rows; if in the first row, also called lanthanide, of if in the second row, also called actinide

lanthanide:  inner transition metal in the top of the bottom two rows of the periodic table

main-group element:  (also, representative element) element in columns 1, 2, and 12–18

metal:  element that is shiny, malleable, good conductor of heat and electricity

metalloid:  element that conducts heat and electricity moderately well, and possesses some properties of metals and some properties of nonmetals

noble gas:  (also, inert gas) element in group 18

nonmetal:  element that appears dull, poor conductor of heat and electricity

period:  (also, series) horizontal row of the period table

periodic law:  properties of the elements are periodic function of their atomic numbers.

periodic table:  table of the elements that places elements with similar chemical properties close together

pnictogen:  element in group 15

representative element:  (also, main-group element) element in columns 1, 2, and 12–18

series:  (also, period) horizontal row of the period table

transition metal:  element in columns 3–11

• Chemistry 2e. Provided by : OpenStax. Located at : https://openstax.org/ . License : CC BY: Attribution . License Terms : Access for free at https://openstax.org/books/chemistry-2e/pages/1-introduction
• The Periodic Table: Crash Course Chemistry #4. Authored by : CrashCourse. Located at : https://youtu.be/0RRVV4Diomg . License : Other . License Terms : Standard YouTube License

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Primary details, user comments (1), more than meets the eye.

Author: Mary Salit Posted: September 16, 2012 at 1:27PM Source: The Physics Front collection

There is some unique content beneath the shiny interface and pretty graphics here.  Almost every element has a link to a podcast (and a transcript) describing its history and uses in an approachable narrative form, and links to videos and "resources." The resources in particular seem like material that could be incorporated into a lesson plan rather than simply used as reference material. In many cases they outline activities which could be done in a laboratory session or as a demonstration. In other cases, such as the reaction of rubidium with water (a little dangerous for an in class demo) they feature videos of the experiment instead. It is the resources section which differentiates this site from similar ones, and makes it useful for teachers, not just students preparing reports.

• Standards (4)

AAAS Benchmark Alignments (1993 Version)

4. the physical setting.

• 4D (6-8) #1.   All matter is made up of atoms, which are far too small to see directly through a microscope. The atoms of any element are alike but are different from atoms of other elements. Atoms may stick together in well-defined molecules or may be packed together in large arrays. Different arrangements of atoms into groups compose all substances.
• 4D (6-8) #5.   Scientific ideas about elements were borrowed from some Greek philosophers of 2,000 years earlier, who believed that everything was made from four basic substances: air, earth, fire, and water. It was the combinations of these "elements" in different proportions that gave other substances their observable properties. The Greeks were wrong about those four, but now over 100 different elements have been identified, some rare and some plentiful, out of which everything is made. Because most elements tend to combine with others, few elements are found in their pure form.
• 4D (6-8) #6.   There are groups of elements that have similar properties, including highly reactive metals, less-reactive metals, highly reactive nonmetals (such as chlorine, fluorine, and oxygen), and some almost completely nonreactive gases (such as helium and neon). An especially important kind of reaction between substances involves combination of oxygen with something elseÑas in burning or rusting. Some elements don't fit into any of the categories; among them are carbon and hydrogen, essential elements of living matter.
• 4D (9-12) #1.   Atoms are made of a positive nucleus surrounded by negative electrons. An atom's electron configuration, particularly the outermost electrons, determines how the atom can interact with other atoms. Atoms form bonds to other atoms by transferring or sharing electrons.

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Additional resources:

Scientists had a rudimentary understanding of the periodic table of the elements centuries ago. But in the late 19th century, Russian chemist Dmitri Mendeleev published his first attempt at grouping chemical elements according to their atomic weights. There were only about 60 elements known at the time, but Mendeleev realized that when the elements were organized by weight, certain types of elements occurred in regular intervals, or periods.

Today, 150 years later, chemists officially recognize 118 elements (after the addition of four newcomers in 2016) and still use Mendeleev's periodic table of elements to organize them. The table starts with the simplest atom, hydrogen, and then organizes the rest of the elements by atomic number, which is the number of protons each contains. With a handful of exceptions, the order of the elements corresponds with the increasing mass of each atom.

The table has seven rows and 18 columns. Each row represents one period; the period number of an element indicates how many of its energy levels house electrons. Sodium, for instance, sits in the third period, which means a sodium atom typically has electrons in the first three energy levels. Moving down the table, periods are longer because it takes more electrons to fill the larger and more complex outer levels.

The columns of the table represent groups, or families, of elements. The elements in a group often look and behave similarly, because they have the same number of electrons in their outermost shell — the face they show to the world. Group 18 elements, on the far right side of the table, for example, have completely full outer shells and rarely participate in chemical reactions .

Elements are typically classified as either a metal or nonmetal, but the dividing line between the two is fuzzy. Metal elements are usually good conductors of electricity and heat. The subgroups within the metals are based on the similar characteristics and chemical properties of these collections. Our description of the periodic table uses commonly accepted groupings of elements, according to the Los Alamos National Laboratory .

Groups of the Periodic table

Alkali metals: The alkali metals make up most of Group 1, the table's first column. Shiny and soft enough to cut with a knife, these metals start with  lithium (Li) and end with  francium (Fr). They are also extremely reactive and will  burst into flame or even explode on contact with water, so chemists store them in oils or inert gases . Hydrogen, with its single electron, also lives in Group 1, but the gas is considered a nonmetal.

Alkaline-earth metals: The alkaline-earth metals make up Group 2 of the periodic table, from  beryllium (Be) through  radium (Ra). Each of these elements has two electrons in its outermost energy level, which makes the alkaline earths reactive enough that they're rarely found alone in nature. But they're not as reactive as the alkali metals. Their chemical reactions typically occur more slowly and produce less heat compared to the alkali metals.

Lanthanides: The third group is much too long to fit into the third column, so it is broken out and flipped sideways to become the top row of the island that floats at the bottom of the table. This is the lanthanides, elements 57 through 71 —  lanthanum (La) to  lutetium (Lu). The elements in this group have a silvery white color and tarnish on contact with air.

Actinides: The actinides line the bottom row of the island and comprise elements 89,  actinium (Ac), through 103,  lawrencium (Lr). Of these elements, only  thorium (Th) and  uranium (U) occur naturally on Earth in substantial amounts. All are radioactive. The actinides and the lanthanides together form a group called the inner transition metals.

Transition metals: Returning to the main body of the table, the remainder of Groups 3 through 12 represent the rest of the transition metals. Hard but malleable, shiny, and possessing good conductivity, these elements are what you typically think of when you hear the word metal. Many of the greatest hits of the metal world — including gold , silver , iron and platinum — live here.

Post-transition metals: Ahead of the jump into the nonmetal world, shared characteristics aren't neatly divided along vertical group lines. The post-transition metals are  aluminum (Al),  gallium (Ga),  indium (In),  thallium (Tl),  tin (Sn),  lead (Pb) and  bismuth (Bi), and they span Group 13 to Group 17. These elements have some of the classic characteristics of the transition metals, but they tend to be softer and conduct more poorly than other transition metals. Many periodic tables will feature a bolded "staircase" line below the diagonal connecting boron with astatine. The post-transition metals cluster to the lower left of this line.

Metalloids: The metalloids are  boron (B),  silicon (Si),  germanium (Ge),  arsenic (As),  antimony (Sb),  tellurium (Te) and  polonium (Po). They form the staircase that represents the gradual transition from metals to nonmetals. These elements sometimes behave as semiconductors (B, Si, Ge) rather than as conductors. Metalloids are also called "semimetals" or "poor metals."

Nonmetals: Everything else to the upper right of the staircase — plus  hydrogen (H), stranded way back in Group 1 — is a nonmetal. These include  carbon (C),  nitrogen (N),  phosphorus (P),  oxygen (O),  sulfur (S) and  selenium (Se).

Halogens: The top four elements of Group 17, from  fluorine (F) through  astatine (At), represent one of two subsets of the nonmetals. The halogens are  quite chemically reactive and tend to pair up with alkali metals to produce various types of salt. The table salt in your kitchen, for example, is a marriage between the alkali metal sodium and the halogen chlorine.

Noble gases: Colorless, odorless and almost completely nonreactive, the inert, or noble gases round out the table in Group 18. Many chemists expect oganesson (previously designated " ununoctium "), one of the four newly named elements, to share these characteristics; however, because this element has a half-life measuring in the milliseconds, no one has been able to test it directly. Oganesson completes the seventh period of the periodic table, so if anyone manages to synthesize element 119 (and  the race to do so is already underway ), it will loop around to start row eight in the alkali metal column.

Because of the cyclical nature created by the periodicity that gives the table its name, some chemists prefer to visualize  Mendeleev's table as a circle .

• Watch this brief video about the periodic table and element groups, from Crash Course .
• Flip through this interactive periodic table of elements at ptable.com .
• Check out this free, online educational resource for understanding elemental groups from CK-12 .

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Visual elements: a visual interpretation of the table of elements, web-based resource, grade levels, course, subject.

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CONSTANCY AND CHANGE

Identify characteristic properties of matter that can be used to separate one substance from the other.

Differentiate between elements, compounds, and mixtures.  

Identify groups of elements that have similar properties.

Explain how materials are characterized by having a specific amount of mass in each unit of volume ( density ).

Identify atoms as the basic building blocks of matter and that elements are composed of one type of atom.

Identify characteristics of elements derived from the periodic table.

Predict properties of elements using trends of the periodic table.

Identify properties of matter that depend on sample size.

Explain the unique properties of water ( polarity , high boiling point, forms hydrogen bonds , high specific heat ) that support life on Earth.

Differentiate between physical properties and chemical properties.

Differentiate between pure substances and mixtures; differentiate between heterogeneous and homogeneous mixtures.

Explain the relationship of an element’s position on the periodic table to its atomic number, ionization energy, electro-negativity, atomic size, and classification of elements.

Use electro-negativity to explain the difference between polar and non-polar covalent bonds

Description

Elements text - Dr. John Emsley, Science Writer in Residence at Cambridge University, editor of Chem@Cam , and acclaimed author of the following two books : The Elements and Molecules at an Exhibition (both Oxford University Press 1998).

Periodic Landscapes text - Dr Ann Prescott, Lecturer in Chemistry, Abertay University, Dundee, whose previous experience in the initiation of science/art exhibitions has been invaluable.

Animation - Alastair Wells, video maker & animator, Genetix, Glasgow.

Soundtracks - M.P.Lancaster, Memory Bank Studio, Glasgow.

Printed matter - David Wells, Portfolio Graphics, Glasgow.

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Encyclopedia of Database Systems pp 3405–3410 Cite as

Visual Representation

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Graphical representation

The concept of “representation” captures the signs that stand in for and take the place of something else [ 5 ]. Visual representation, in particular, refers to the special case when these signs are visual (as opposed to textual, mathematical, etc.). On the other hand, there is no limit on what may be (visually) represented, which may range from abstract concepts to concrete objects in the real world or data items.

In addition to the above, however, the term “representation” is often overloaded and used to imply the actual process of connecting the two worlds of the original items and of their representatives. Typically, the context determines quite clearly which of the two meanings is intended in each case, hence, the term is used for both without further explanation.

Underneath any visual representation lies a mapping between the set of items that are being represented and the set of visual elements that are used to represent them, i.e., to...

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Recommended Reading

Card S.K., Mackinlay J.D., and Shneiderman B. Information visualization. In Readings in Information Visualization: Using Vision to Think, 1999, pp. 1–34.

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Foley J.D., van Dam A., Feiner S.K., and Hughes J.F. Computer Graphics: Principles and Practice. Addison-Wesley, Reading, MA, 1990.

Haber E.M., Ioannidis Y., and Livny M. Foundations of visual metaphors for schema display. J. Intell. Inf. Syst., 3(3/4):263–298, 1994.

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Tufte E.R. Envisioning Information. Graphics Press, Cheshire, CO, 1990.

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Ioannidis, Y. (2009). Visual Representation. In: LIU, L., ÖZSU, M.T. (eds) Encyclopedia of Database Systems. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-39940-9_449

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Visual Representation

What is visual representation.

Visual Representation refers to the principles by which markings on a surface are made and interpreted. Designers use representations like typography and illustrations to communicate information, emotions and concepts. Color, imagery, typography and layout are crucial in this communication.

Alan Blackwell, cognition scientist and professor, gives a brief introduction to visual representation:

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We can see visual representation throughout human history, from cave drawings to data visualization :

Art uses visual representation to express emotions and abstract ideas.

Financial forecasting graphs condense data and research into a more straightforward format.

Icons on user interfaces (UI) represent different actions users can take.

The color of a notification indicates its nature and meaning.

Van Gogh's "The Starry Night" uses visuals to evoke deep emotions, representing an abstract, dreamy night sky. It exemplifies how art can communicate complex feelings and ideas.

© Public domain

Importance of Visual Representation in Design

Designers use visual representation for internal and external use throughout the design process . For example:

Storyboards are illustrations that outline users’ actions and where they perform them.

Sitemaps are diagrams that show the hierarchy and navigation structure of a website.

Wireframes are sketches that bring together elements of a user interface's structure.

Usability reports use graphs and charts to communicate data gathered from usability testing.

User interfaces visually represent information contained in applications and computerized devices.

This usability report is straightforward to understand. Yet, the data behind the visualizations could come from thousands of answered surveys.

© Interaction Design Foundation, CC BY-SA 4.0

Visual representation simplifies complex ideas and data and makes them easy to understand. Without these visual aids, designers would struggle to communicate their ideas, findings and products . For example, it would be easier to create a mockup of an e-commerce website interface than to describe it with words.

Visual representation simplifies the communication of designs. Without mockups, it would be difficult for developers to reproduce designs using words alone.

Types of Visual Representation

Below are some of the most common forms of visual representation designers use.

Text and Typography

Text represents language and ideas through written characters and symbols. Readers visually perceive and interpret these characters. Typography turns text into a visual form, influencing its perception and interpretation.

We have developed the conventions of typography over centuries , for example, in documents, newspapers and magazines. These conventions include:

Text arranged on a grid brings clarity and structure. Gridded text makes complex information easier to navigate and understand. Tables, columns and other formats help organize content logically and enhance readability.

Contrasting text sizes create a visual hierarchy and draw attention to critical areas. For example, headings use larger text while body copy uses smaller text. This contrast helps readers distinguish between primary and secondary information.

Adequate spacing and paragraphing improve the readability and appearance of the text. These conventions prevent the content from appearing cluttered. Spacing and paragraphing make it easier for the eye to follow and for the brain to process the information.

Balanced image-to-text ratios create engaging layouts. Images break the monotony of text, provide visual relief and illustrate or emphasize points made in the text. A well-planned ratio ensures neither text nor images overwhelm each other. Effective ratios make designs more effective and appealing.

Designers use these conventions because people are familiar with them and better understand text presented in this manner.

This table of funerals from the plague in London in 1665 uses typographic conventions still used today. For example, the author arranged the information in a table and used contrasting text styling to highlight information in the header.

Illustrations and Drawings

Designers use illustrations and drawings independently or alongside text. An example of illustration used to communicate information is the assembly instructions created by furniture retailer IKEA. If IKEA used text instead of illustrations in their instructions, people would find it harder to assemble the furniture.

IKEA assembly instructions use illustrations to inform customers how to build their furniture. The only text used is numeric to denote step and part numbers. IKEA communicates this information visually to: 1. Enable simple communication, 2. Ensure their instructions are easy to follow, regardless of the customer’s language.

© IKEA, Fair use

Illustrations and drawings can often convey the core message of a visual representation more effectively than a photograph. They focus on the core message , while a photograph might distract a viewer with additional details (such as who this person is, where they are from, etc.)

For example, in IKEA’s case, photographing a person building a piece of furniture might be complicated. Further, photographs may not be easy to understand in a black-and-white print, leading to higher printing costs. To be useful, the pictures would also need to be larger and would occupy more space on a printed manual, further adding to the costs.

But imagine a girl winking—this is something we can easily photograph. 

Ivan Sutherland, creator of the first graphical user interface, used his computer program Sketchpad to draw a winking girl. While not realistic, Sutherland's representation effectively portrays a winking girl. The drawing's abstract, generic elements contrast with the distinct winking eye. The graphical conventions of lines and shapes represent the eyes and mouth. The simplicity of the drawing does not draw attention away from the winking.

A photo might distract from the focused message compared to Sutherland's representation. In the photo, the other aspects of the image (i.e., the particular person) distract the viewer from this message.

© Ivan Sutherland, CC BY-SA 3.0 and Amina Filkins, Pexels License

Information and Data Visualization

Designers and other stakeholders use data and information visualization across many industries.

Data visualization uses charts and graphs to show raw data in a graphic form. Information visualization goes further, including more context and complex data sets. Information visualization often uses interactive elements to share a deeper understanding.

For example, most computerized devices have a battery level indicator. This is a type of data visualization. IV takes this further by allowing you to click on the battery indicator for further insights. These insights may include the apps that use the most battery and the last time you charged your device.

macOS displays a battery icon in the menu bar that visualizes your device’s battery level. This is an example of data visualization. Meanwhile, macOS’s settings tell you battery level over time, screen-on-usage and when you last charged your device. These insights are actionable; users may notice their battery drains at a specific time. This is an example of information visualization.

© Low Battery by Jemis Mali, CC BY-NC-ND 4.0, and Apple, Fair use

Information visualization is not exclusive to numeric data. It encompasses representations like diagrams and maps. For example, Google Maps collates various types of data and information into one interface:

Data Representation: Google Maps transforms complex geographical data into an easily understandable and navigable visual map.

Interactivity: Users can interactively customize views that show traffic, satellite imagery and more in real-time.

Layered Information: Google Maps layers multiple data types (e.g., traffic, weather) over geographical maps for comprehensive visualization.

User-Centered Design : The interface is intuitive and user-friendly, with symbols and colors for straightforward data interpretation.

The volume of data contained in one screenshot of Google Maps is massive. However, this information is presented clearly to the user. Google Maps highlights different terrains with colors and local places and businesses with icons and colors. The panel on the left lists the selected location’s profile, which includes an image, rating and contact information.

© Google, Fair use

Symbolic Correspondence

Symbolic correspondence uses universally recognized symbols and signs to convey specific meanings . This method employs widely recognized visual cues for immediate understanding. Symbolic correspondence removes the need for textual explanation.

For instance, a magnifying glass icon in UI design signifies the search function. Similarly, in environmental design, symbols for restrooms, parking and amenities guide visitors effectively.

The Interaction Design Foundation (IxDF) website uses the universal magnifying glass symbol to signify the search function. Similarly, the play icon draws attention to a link to watch a video.

How Designers Create Visual Representations

Visual language.

Designers use elements like color , shape and texture to create a communicative visual experience. Designers use these 8 principles:

Size – Larger elements tend to capture users' attention readily.

Color – Users are typically drawn to bright colors over muted shades.

Contrast – Colors with stark contrasts catch the eye more effectively.

Alignment – Unaligned elements are more noticeable than those aligned ones.

Repetition – Similar styles repeated imply a relationship in content.

Proximity – Elements placed near each other appear to be connected.

Whitespace – Elements surrounded by ample space attract the eye.

Texture and Style – Users often notice richer textures before flat designs.

The 8 visual design principles.

In web design , visual hierarchy uses color and repetition to direct the user's attention. Color choice is crucial as it creates contrast between different elements. Repetition helps to organize the design—it uses recurring elements to establish consistency and familiarity.

In this video, Alan Dix, Professor and Expert in Human-Computer Interaction, explains how visual alignment affects how we read and absorb information:

Correspondence Techniques

Designers use correspondence techniques to align visual elements with their conceptual meanings. These techniques include color coding, spatial arrangement and specific imagery. In information visualization, different colors can represent various data sets. This correspondence aids users in quickly identifying trends and relationships .

Color coding enables the stakeholder to see the relationship and trend between the two pie charts easily.

In user interface design, correspondence techniques link elements with meaning. An example is color-coding notifications to state their nature. For instance, red for warnings and green for confirmation. These techniques are informative and intuitive and enhance the user experience.

The IxDF website uses blue for call-to-actions (CTAs) and red for warnings. These colors inform the user of the nature of the action of buttons and other interactive elements.

Perception and Interpretation

If visual language is how designers create representations, then visual perception and interpretation are how users receive those representations. Consider a painting—the viewer’s eyes take in colors, shapes and lines, and the brain perceives these visual elements as a painting.

In this video, Alan Dix explains how the interplay of sensation, perception and culture is crucial to understanding visual experiences in design:

Copyright holder: Michael Murphy _ Appearance time: 07:19 - 07:37 _ Link: https://www.youtube.com/watch?v=C67JuZnBBDc

Visual perception principles are essential for creating compelling, engaging visual representations. For example, Gestalt principles explain how we perceive visual information. These rules describe how we group similar items, spot patterns and simplify complex images. Designers apply Gestalt principles to arrange content on websites and other interfaces. This application creates visually appealing and easily understood designs.

In this video, design expert and teacher Mia Cinelli discusses the significance of Gestalt principles in visual design . She introduces fundamental principles, like figure/ground relationships, similarity and proximity.

Interpretation

Everyone's experiences, culture and physical abilities dictate how they interpret visual representations. For this reason, designers carefully consider how users interpret their visual representations. They employ user research and testing to ensure their designs are attractive and functional.

Leonardo da Vinci's "Mona Lisa", is one of the most famous paintings in the world. The piece is renowned for its subject's enigmatic expression. Some interpret her smile as content and serene, while others see it as sad or mischievous. Not everyone interprets this visual representation in the same way.

Color is an excellent example of how one person, compared to another, may interpret a visual element. Take the color red:

In Chinese culture, red symbolizes luck, while in some parts of Africa, it can mean death or illness.

A personal experience may mean a user has a negative or positive connotation with red.

People with protanopia and deuteranopia color blindness cannot distinguish between red and green.

In this video, Joann and Arielle Eckstut, leading color consultants and authors, explain how many factors influence how we perceive and interpret color:

Learn More about Visual Representation

Read Alan Blackwell’s chapter on visual representation from The Encyclopedia of Human-Computer Interaction.

Learn about the F-Shaped Pattern For Reading Web Content from Jakob Nielsen.

Read Smashing Magazine’s article, Visual Design Language: The Building Blocks Of Design .

Take the IxDF’s course, Perception and Memory in HCI and UX .

Questions related to Visual Representation

Some highly cited research on visual representation and related topics includes:

Roland, P. E., & Gulyás, B. (1994). Visual imagery and visual representation. Trends in Neurosciences, 17(7), 281-287. Roland and Gulyás' study explores how the brain creates visual imagination. They look at whether imagining things like objects and scenes uses the same parts of the brain as seeing them does. Their research shows the brain uses certain areas specifically for imagination. These areas are different from the areas used for seeing. This research is essential for understanding how our brain works with vision.

Lurie, N. H., & Mason, C. H. (2007). Visual Representation: Implications for Decision Making. Journal of Marketing, 71(1), 160-177.

This article looks at how visualization tools help in understanding complicated marketing data. It discusses how these tools affect decision-making in marketing. The article gives a detailed method to assess the impact of visuals on the study and combination of vast quantities of marketing data. It explores the benefits and possible biases visuals can bring to marketing choices. These factors make the article an essential resource for researchers and marketing experts. The article suggests using visual tools and detailed analysis together for the best results.

Lohse, G. L., Biolsi, K., Walker, N., & Rueter, H. H. (1994, December). A classification of visual representations. Communications of the ACM, 37(12), 36+.

This publication looks at how visuals help communicate and make information easier to understand. It divides these visuals into six types: graphs, tables, maps, diagrams, networks and icons. The article also looks at different ways these visuals share information effectively.

​​If you’d like to cite content from the IxDF website , click the ‘cite this article’ button near the top of your screen.

Some recommended books on visual representation and related topics include:

Chaplin, E. (1994). Sociology and Visual Representation (1st ed.) . Routledge.

Chaplin's book describes how visual art analysis has changed from ancient times to today. It shows how photography, post-modernism and feminism have changed how we see art. The book combines words and images in its analysis and looks into real-life social sciences studies.

Mitchell, W. J. T. (1994). Picture Theory. The University of Chicago Press.

Mitchell's book explores the important role and meaning of pictures in the late twentieth century. It discusses the change from focusing on language to focusing on images in cultural studies. The book deeply examines the interaction between images and text in different cultural forms like literature, art and media. This detailed study of how we see and read visual representations has become an essential reference for scholars and professionals.

Koffka, K. (1935). Principles of Gestalt Psychology. Harcourt, Brace & World.

"Principles of Gestalt Psychology" by Koffka, released in 1935, is a critical book in its field. It's known as a foundational work in Gestalt psychology, laying out the basic ideas of the theory and how they apply to how we see and think. Koffka's thorough study of Gestalt psychology's principles has profoundly influenced how we understand human perception. This book has been a significant reference in later research and writings.

A visual representation, like an infographic or chart, uses visual elements to show information or data. These types of visuals make complicated information easier to understand and more user-friendly.

Designers harness visual representations in design and communication. Infographics and charts, for instance, distill data for easier audience comprehension and retention.

For an introduction to designing basic information visualizations, take our course, Information Visualization .

Text is a crucial design and communication element, transforming language visually. Designers use font style, size, color and layout to convey emotions and messages effectively.

Designers utilize text for both literal communication and aesthetic enhancement. Their typography choices significantly impact design aesthetics, user experience and readability.

Designers should always consider text's visual impact in their designs. This consideration includes font choice, placement, color and interaction with other design elements.

In this video, design expert and teacher Mia Cinelli teaches how Gestalt principles apply to typography:

Designers use visual elements in projects to convey information, ideas, and messages. Designers use images, colors, shapes and typography for impactful designs.

In UI/UX design, visual representation is vital. Icons, buttons and colors provide contrast for intuitive, user-friendly website and app interfaces.

Graphic design leverages visual representation to create attention-grabbing marketing materials. Careful color, imagery and layout choices create an emotional connection.

Product design relies on visual representation for prototyping and idea presentation. Designers and stakeholders use visual representations to envision functional, aesthetically pleasing products.

Our brains process visuals 60,000 times faster than text. This fact highlights the crucial role of visual representation in design.

Our course, Visual Design: The Ultimate Guide , teaches you how to use visual design elements and principles in your work effectively.

Visual representation, crucial in UX, facilitates interaction, comprehension and emotion. It combines elements like images and typography for better interfaces.

Effective visuals guide users, highlight features and improve navigation. Icons and color schemes communicate functions and set interaction tones.

UX design research shows visual elements significantly impact emotions. 90% of brain-transmitted information is visual.

To create functional, accessible visuals, designers use color contrast and consistent iconography. These elements improve readability and inclusivity.

An excellent example of visual representation in UX is Apple's iOS interface. iOS combines a clean, minimalist design with intuitive navigation. As a result, the operating system is both visually appealing and user-friendly.

Michal Malewicz, Creative Director and CEO at Hype4, explains why visual skills are important in design:

Learn more about UI design from Michal in our Master Class, Beyond Interfaces: The UI Design Skills You Need to Know .

The fundamental principles of effective visual representation are:

Clarity : Designers convey messages clearly, avoiding clutter.

Simplicity : Embrace simple designs for ease and recall.

Emphasis : Designers highlight key elements distinctively.

Balance : Balance ensures design stability and structure.

Alignment : Designers enhance coherence through alignment.

Contrast : Use contrast for dynamic, distinct designs.

Repetition : Repeating elements unify and guide designs.

Designers practice these principles in their projects. They also analyze successful designs and seek feedback to improve their skills.

Read our topic description of Gestalt principles to learn more about creating effective visual designs. The Gestalt principles explain how humans group elements, recognize patterns and simplify object perception.

Color theory is vital in design, helping designers craft visually appealing and compelling works. Designers understand color interactions, psychological impacts and symbolism. These elements help designers enhance communication and guide attention.

Designers use complementary , analogous and triadic colors for contrast, harmony and balance. Understanding color temperature also plays a crucial role in design perception.

Color symbolism is crucial, as different colors can represent specific emotions and messages. For instance, blue can symbolize trust and calmness, while red can indicate energy and urgency.

Cultural variations significantly influence color perception and symbolism. Designers consider these differences to ensure their designs resonate with diverse audiences.

For actionable insights, designers should:

Experiment with color schemes for effective messaging. 

Assess colors' psychological impact on the audience. 

Use color contrast to highlight critical elements. 

Ensure color choices are accessible to all.

In this video, Joann and Arielle Eckstut, leading color consultants and authors, give their six tips for choosing color:

Learn more about color from Joann and Arielle in our Master Class, How To Use Color Theory To Enhance Your Designs .

Typography and font choice are crucial in design, impacting readability and mood. Designers utilize them for effective communication and expression.

Designers' perception of information varies with font type. Serif fonts can imply formality, while sans-serifs can give a more modern look.

Typography choices by designers influence readability and user experience. Well-spaced, distinct fonts enhance readability, whereas decorative fonts may hinder it.

Designers use typography to evoke emotions and set a design's tone. Choices in font size, style and color affect the emotional impact and message clarity.

Designers use typography to direct attention, create hierarchy and establish rhythm. These benefits help with brand recognition and consistency across mediums.

Read our article to learn how web fonts are critical to the online user experience .

Designers create a balance between simplicity and complexity in their work. They focus on the main messages and highlight important parts. Designers use the principles of visual hierarchy, like size, color and spacing. They also use empty space to make their designs clear and understandable.

The Gestalt law of Prägnanz suggests people naturally simplify complex images. This principle aids in making even intricate information accessible and engaging.

Through iteration and feedback, designers refine visuals. They remove extraneous elements and highlight vital information. Testing with the target audience ensures the design resonates and is comprehensible.

Michal Malewicz explains how to master hierarchy in UI design using the Gestalt rule of proximity:

Literature on Visual Representation

Here’s the entire UX literature on Visual Representation by the Interaction Design Foundation, collated in one place:

Learn more about Visual Representation

Take a deep dive into Visual Representation with our course Perception and Memory in HCI and UX .

How does all of this fit with interaction design and user experience? The simple answer is that most of our understanding of human experience comes from our own experiences and just being ourselves. That might extend to people like us, but it gives us no real grasp of the whole range of human experience and abilities. By considering more closely how humans perceive and interact with our world, we can gain real insights into what designs will work for a broader audience: those younger or older than us, more or less capable, more or less skilled and so on.

“You can design for all the people some of the time, and some of the people all the time, but you cannot design for all the people all the time.“ – William Hudson (with apologies to Abraham Lincoln)

While “design for all of the people all of the time” is an impossible goal, understanding how the human machine operates is essential to getting ever closer. And of course, building solutions for people with a wide range of abilities, including those with accessibility issues, involves knowing how and why some human faculties fail. As our course tutor, Professor Alan Dix, points out, this is not only a moral duty but, in most countries, also a legal obligation.

Portfolio Project

In the “ Build Your Portfolio: Perception and Memory Project ”, you’ll find a series of practical exercises that will give you first-hand experience in applying what we’ll cover. If you want to complete these optional exercises, you’ll create a series of case studies for your portfolio which you can show your future employer or freelance customers.

This in-depth, video-based course is created with the amazing Alan Dix , the co-author of the internationally best-selling textbook  Human-Computer Interaction and a superstar in the field of Human-Computer Interaction . Alan is currently a professor and Director of the Computational Foundry at Swansea University.

Gain an Industry-Recognized UX Course Certificate

Use your industry-recognized Course Certificate on your resume , CV , LinkedIn profile or your website.

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4.3: Properties and Representations of Groups

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Group Multiplication

Now we will investigate what happens when we apply two symmetry operations in sequence. As an example, consider the \(NH_3\) molecule, which belongs to the \(C_{3v}\) point group. Consider what happens if we apply a \(C_3\)rotation (120˚ counter-clockwise) followed by a \(\sigma_v\) reflection (reflection over the \(\sigma_v\) axis) . We write this combined operation \(\sigma_v\)\(C_3\) (when written, symmetry operations operate on the thing directly to their right, just as operators do in quantum mechanics – we therefore have to work backwards from right to left from the notation to get the correct order in which the operators are applied). As we shall soon see, the order in which the operations are applied is important.

The combined operation \(\sigma_v\)\(C_3\) is equivalent to \(\sigma_v''\) (note the double prime on \(\sigma_v''\)!) , which is also a symmetry operation of the \(C_{3v}\) point group. Now let’s see what happens if we apply the operators in the reverse order, i.e., \(C_3\)\(\sigma_v\) is ( \(\sigma_v\) followed by \(C_3\) ).

Again, the combined operation \(C_3\)\(\sigma_v\) is equivalent to another operation of the point group, this time \(\sigma_v'\) (note the single prime on \(\sigma_v'\)!) .

There are two important points that are illustrated by this example:

• The order in which two operations are applied is important. For two symmetry operations \(A\) and \(B\), \(AB\) is not necessarily the same as \(BA\), i.e. symmetry operations do not in general commute . In some groups the symmetry elements do commute; such groups are said to be Abelian .
• If two operations from the same point group are applied in sequence, the result will be equivalent to another operation from the point group. Symmetry operations that are related to each other by other symmetry operations of the group are said to belong to the same class . In \(NH_3\), the three mirror planes \(\sigma_v\) , \(\sigma_v'\) and \(\sigma_v''\) belong to the same class (related to each other through a \(C_3\) rotation), as do the rotations \(C_3^+\) and \(C_3^-\) (anticlockwise and clockwise rotations about the principal axis, related to each other by a vertical mirror plane).

Four Properties of Mathematical Groups

Now that we have explored some of the properties of symmetry operations and elements and their behavior within point groups, we are ready to introduce the formal mathematical definition of a group. The definitions below will be put into the context of molecular symmetry.

A mathematical group is defined as a set of elements (\(A_1\), \(A_2\), \(A_3\)...) together with a rule for forming combinations \(A_i\),\(A_j\)... For our purposes, \(A_1\), \(A_2\), \(A_3\), etc. are symmetry elements and \(A_i\), \(A_j\), etc. are symmetry operations described in a previous section . The elements of the group and the rule for combining them must satisfy the following four criteria.

• The group must include the identity \(E\) , which commutes with other members of the group. In other terms, \(E A_i= A_i \) for all the elements of the group. Application of the identity operation before or after another operation, \(A_i\), results in the same outcome as \(A_i\) alone.
• The elements must satisfy the group property that the combination of any pair of elements is also an element of the group. For example, in the \(C_{3v}\) point group, a C 3 rotation followed by a \(\sigma_v\) gives another operation that is already part of the group: a \(\sigma_v"\).
• Each symmetry operation \(A_i\) must have an inverse \(A_i^{-1}\), which is also an element of the group, such that \[A_i A_i^{-1} = A_i^{-1}A_i = E \nonumber \] The inverse \(g_i^{-1}\) effectively 'undoes’ the effect of the symmetry operation \(g_i\). For example, in the \(C_{3v}\) point group, the inverse of \(C_3^+\) is \(C_3^-\).
• The rule of combination must be associative \[(A_i A_j )(A_k) = A_i(A_jA_k) \nonumber \] Or \(A(BC)=(AB)C\). In other words, the order of operations should not matter.

Group theory is an important area in mathematics, and luckily for chemists the mathematicians have already done most of the work for us. Along with the formal definition of a group comes a comprehensive mathematical framework that allows us to carry out a rigorous treatment of symmetry in molecular systems and learn about its consequences.

Many problems involving operators or operations (such as those found in quantum mechanics or group theory) may be reformulated in terms of matrices. Any of you who have come across transformation matrices before will know that symmetry operations such as rotations and reflections may be represented by matrices. It turns out that the set of matrices representing the symmetry operations in a group obey all the conditions laid out above in the mathematical definition of a group, and using matrix representations of symmetry operations simplifies carrying out calculations in group theory. Before we learn how to use matrices in group theory, it will probably be helpful to review some basic definitions and properties of matrices.

*This page was adapted from here (click) .

Contributors and Attributions

Claire Vallance (University of Oxford)

Curated or created by Kathryn Haas