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Molecular model
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 | This article includes a list of general references, but it lacks sufficient corresponding inline citations. (February 2023) |
A molecular model is a physical model of an atomistic system that represents molecules and their processes. They play an important role in understanding chemistry and generating and testing hypotheses. The creation of mathematical models of molecular properties and behavior is referred to as molecular modeling, and their graphical depiction is referred to as molecular graphics.
The term, "molecular model" refer to systems that contain one or more explicit atoms (although solvent atoms may be represented implicitly) and where nuclear structure is neglected. The electronic structure is often also omitted unless it is necessary in illustrating the function of the molecule being modeled.
Molecular models may be created for several reasons – as pedagogic tools for students or those unfamiliar with atomistic structures; as objects to generate or test theories (e.g., the structure of DNA); as analogue computers (e.g., for measuring distances and angles in flexible systems); or as aesthetically pleasing objects on the boundary of art and science.
The construction of physical models is often a creative act, and many bespoke examples have been carefully created in the workshops of science departments. There is a very wide range of approaches to physical modeling, including ball-and-stick models available for purchase commercially, to molecular models created using 3D printers. The main strategy, initially in textbooks and research articles and more recently on computers. Molecular graphics has made the visualization of molecular models on computer hardware easier, more accessible, and inexpensive, although physical models are widely used to enhance the tactile and visual message being portrayed.
History
[edit]
In the 1600s, Johannes Kepler speculated on the symmetry of snowflakes and the close packing of spherical objects such as fruit.[1] The symmetrical arrangement of closely packed spheres informed theories of molecular structure in the late 1800s, and many theories of crystallography and solid state inorganic structure used collections of equal and unequal spheres to simulate packing and predict structure.
John Dalton represented compounds as aggregations of circular atoms, and although Johann Josef Loschmidt did not create physical models, his diagrams based on circles are two-dimensional analogues of later models.[2] August Wilhelm von Hofmann is credited with the first physical molecular model around 1860.[3] Note how the size of the carbon appears smaller than the hydrogen. The importance of stereochemistry was not then recognised and the model is essentially topological (it should be a 3-dimensional tetrahedron).
Jacobus Henricus van 't Hoff and Joseph Le Bel introduced the concept of chemistry in three dimensions of space, that is, stereochemistry. Van 't Hoff built tetrahedral molecules representing the three-dimensional properties of carbon.[citation needed]
Models based on spheres
[edit]
Repeating units will help to show how easy it is and clear it is to represent molecules through balls that represent atoms.
The binary compounds sodium chloride (NaCl) and caesium chloride (CsCl) have cubic structures but have different space groups. This can be rationalised in terms of close packing of spheres of different sizes. For example, NaCl can be described as close-packed chloride ions (in a face-centered cubic lattice) with sodium ions in the octahedral holes. After the development of X-ray crystallography as a tool for determining crystal structures, many laboratories built models based on spheres. With the development of plastic or polystyrene balls it is now easy to create such models.
Models based on ball-and-stick
[edit]The concept of the chemical bond as a direct link between atoms can be modelled by linking balls (atoms) with sticks/rods (bonds). This has been extremely popular and is still widely used today. Initially atoms were made of spherical wooden balls with specially drilled holes for rods. Thus carbon can be represented as a sphere with four holes at the tetrahedral angles cos−1(−1⁄3) ≈ 109.47°.
A problem with rigid bonds and holes is that systems with arbitrary angles could not be built. This can be overcome with flexible bonds, originally helical springs but now usually plastic. This also allows double and triple bonds to be approximated by multiple single bonds.
The model shown to the left represents a ball-and-stick model of proline. The balls have colours: black represents carbon (C); red, oxygen (O); blue, nitrogen (N); and white, hydrogen (H). Each ball is drilled with as many holes as its conventional valence (C: 4; N: 3; O: 2; H: 1) directed towards the vertices of a tetrahedron. Single bonds are represented by (fairly) rigid grey rods. Double and triple bonds use two longer flexible bonds which restrict rotation and support conventional cis/trans stereochemistry.
However, most molecules require holes at other angles and specialist companies manufacture kits and bespoke models. Besides tetrahedral, trigonal and octahedral holes, there were all-purpose balls with 24 holes. These models allowed rotation about the single rod bonds, which could be both an advantage (showing molecular flexibility) and a disadvantage (models are floppy). The approximate scale was 5 cm per ångström (0.5 m/nm or 500,000,000:1), but was not consistent over all elements.
Arnold Beevers in Edinburgh created small models using PMMA balls and stainless steel rods. By using individually drilled balls with precise bond angles and bond lengths in these models, large crystal structures to be accurately created, but with light and rigid form. Figure 4 shows a unit cell of ruby in this style.
Skeletal models
[edit]Crick and Watson's DNA model and the protein-building kits of Kendrew were among the first skeletal models. These were based on atomic components where the valences were represented by rods; the atoms were points at the intersections. Bonds were created by linking components with tubular connectors with locking screws.
André Dreiding introduced a molecular modelling kit in the late 1950s which dispensed with the connectors. A given atom would have solid and hollow valence spikes. The solid rods clicked into the tubes forming a bond, usually with free rotation. These were and are very widely used in organic chemistry departments and were made so accurately that interatomic measurements could be made by ruler.
More recently, inexpensive plastic models (such as Orbit) use a similar principle. A small plastic sphere has protuberances onto which plastic tubes can be fitted. The flexibility of the plastic means that distorted geometries can be made.
Polyhedral models
[edit]Many inorganic solids consist of atoms surrounded by a coordination sphere of electronegative atoms (e.g. PO4 tetrahedra, TiO6 octahedra). Structures can be modelled by gluing together polyhedra made of paper or plastic.
Composite models
[edit]
A good example of composite models is the Nicholson approach, widely used from the late 1970s for building models of biological macromolecules. The components are primarily amino acids and nucleic acids with preformed residues representing groups of atoms. Many of these atoms are directly moulded into the template, and fit together by pushing plastic stubs into small holes. The plastic grips well and makes bonds difficult to rotate, so that arbitrary torsion angles can be set and retain their value. The conformations of the backbone and side chains are determined by pre-computing the torsion angles and then adjusting the model with a protractor.
The plastic is white and can be painted to distinguish between O and N atoms. Hydrogen atoms are normally implicit and modelled by snipping off the spokes. A model of a typical protein with approximately 300 residues could take a month to build. It was common for laboratories to build a model for each protein solved. By 2005, so many protein structures were being determined that relatively few models were made.
Computer-based models
[edit]
With the development of computer-based physical modelling, it is now possible to create complete single-piece models by feeding the coordinates of a surface into the computer. Figure 6 shows models of anthrax toxin, left (at a scale of approximately 20 Å/cm or 1:5,000,000) and green fluorescent protein, right (5 cm high, at a scale of about 4 Å/cm or 1:25,000,000) from 3D Molecular Design. Models are made of plaster or starch, using a rapid prototyping process.
It has also recently become possible to create accurate molecular models inside glass blocks using a technique known as subsurface laser engraving. The image at right shows the 3D structure of an E. coli protein (DNA polymerase beta-subunit, PDB code 1MMI) etched inside a block of glass by British company Luminorum Ltd.
Computational Models
[edit]Computers can also model molecules mathematically. Programs such as Avogadro can run on typical desktops and can predict bond lengths and angles, molecular polarity and charge distribution, and even quantum mechanical properties such as absorption and emission spectra. However, these sorts of programs cannot model molecules as more atoms are added, because the number of calculations is quadratic in the number of atoms involved; if four times as many atoms are used in a molecule, the calculations with take 16 times as long. For most practical purposes, such as drug design or protein folding, the calculations of a model require supercomputing or cannot be done on classical computers at all in a reasonable amount of time. Quantum computers can model molecules with fewer calculations because the type of calculations performed in each cycle by a quantum computer are well-suited to molecular modelling.
Common colors
[edit]Some of the most common colors used in molecular models are as follows:[4][better source needed]
Hydrogen white Alkali metals violet Alkaline earth metals dark green Boron, most transition metals Pink Carbon black Nitrogen blue Oxygen red Fluorine green yellow Chlorine lime green Bromine dark red Iodine dark violet Noble gases cyan Phosphorus orange Sulfur yellow Titanium gray Copper apricot Mercury light grey
Chronology
[edit]This table is an incomplete chronology of events where physical molecular models provided major scientific insights.
| Developer(s) | Date | Technology | Comments |
|---|---|---|---|
| Johannes Kepler | c. 1600 | sphere packing, symmetry of snowflakes. | |
| Johann Josef Loschmidt | 1861 | 2-D graphics | representation of atoms and bonds by touching circles |
| August Wilhelm von Hofmann | 1860 | ball-and-stick | first recognisable physical molecular model |
| Jacobus Henricus van 't Hoff | 1874 | paper? | representation of atoms as tetrahedra supported the development of stereochemistry |
| John Desmond Bernal | c. 1930 | Plasticine and spokes | model of liquid water |
| Robert Corey, Linus Pauling, Walter Koltun (CPK coloring) | 1951 | Space-filling models of alpha-helix, etc. | Pauling's "Nature of the Chemical Bond" covered all aspects of molecular structure and influenced many aspects of models |
| Francis Crick and James D. Watson | 1953 | spikes, flat templates and connectors with screws | model of DNA |
| Molecular graphics | c. 1960 | display on computer screens | complements rather than replaces physical models |
| Zeinalipour-Yazdi, Peterson, Pullman, Catlow | c. 2005 | sphere-in-contact models of graphite | physical molecular models that show correctly the electron density of carbon materials[5][6] |
See also
[edit]References
[edit]- ^ Kepler, Johannes; Hardie, Colin (translated) (1611). Strena, seu de Nive sexangula. Clarendon Press. Retrieved 13 June 2022.
- ^ Dalton, John (1808). A New System of Chemical Philosophy. London, United Kingdom: Henderson & Spalding. Retrieved 14 June 2022.
- ^ McBride, M. "Models and Structural Diagrams in the 1860s". Yale University. Retrieved 14 June 2022.
- ^ "Atom Colours".
- ^ C.D. Zeinalipour-Yazdi, K. Peterson, D.P. Pullman, Origin of contrast in STM images of Graphite STM images of Graphite, March 2005, DOI: 10.13140/RG.2.2.32948.17282, Conference: 229th ACS Spring National Meeting
- ^ Zeinalipour-Yazdi, C.D., Pullman, D.P. & Catlow, C.R.A. The sphere-in-contact model of carbon materials. J Mol Model 22, 40 (2016). https://doi.org/10.1007/s00894-015-2895-7
Further reading
[edit]- Barlow, W. (1883). "Probable Nature of the Internal Symmetry of Crystals". Nature. 29 (738): 186–8. Bibcode:1883Natur..29..186B. doi:10.1038/029186a0.
- Barlow, W.; Pope, W.J. (1906). "A development of the atomic theory which correlates chemical and crystalline structure and leads to a demonstration of the nature of valency". J. Chem. Soc. 89: 1675–1744. doi:10.1039/ct9068901675.
- Whittaker, A.G. (2009). "Molecular Models - Tangible Representations of the Abstract". PDB Newsletter. 41: 4–5. [1]
- history of molecular models Paper presented at the EuroScience Open Forum (ESOF), Stockholm on August 25, 2004, W. Gerhard Pohl, Austrian Chemical Society. Photo of van't Hoff's tetrahedral models, and Loschmidt's organic formulae (only 2-dimensional).
- Wooster, W.A.; et al. (1945). "A Spherical Template for Drilling Balls for Crystal Structure Models". J. Sci. Instrum. 22 (7): 130. Bibcode:1945JScI...22..130W. doi:10.1088/0950-7671/22/7/405. Wooster's biographical notes including setting up of Crystal Structure Ltd.
External links
[edit]- History of Visualization of Biological Macromolecules by Eric Martz and Eric Francoeur. Contains a mixture of physical models and molecular graphics.
Molecular model
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Fundamentals
Definition and Purpose
A molecular model is a three-dimensional representation, either physical or digital, of a molecule's atomic arrangement, bonds, and overall geometry, designed to illustrate the spatial relationships between atoms without depicting the detailed distribution of electrons.[2] These models simplify complex molecular structures into tangible or visual forms that capture essential features like atom positions and bond orientations, aiding in the comprehension of molecular architecture.[8] The primary purposes of molecular models include facilitating the visualization of intricate three-dimensional molecular structures that are difficult to infer from two-dimensional diagrams, enabling predictions of molecular behavior, interactions, and physicochemical properties such as reactivity and solubility.[2] They also support educational efforts by allowing learners to manipulate representations for better spatial understanding, while in research and design, they assist in simulating interactions for applications in drug development and materials science.[9] Overall, these models bridge theoretical concepts with practical insights across chemistry and related disciplines.[8] At their core, molecular models represent atoms as spheres or nodes and bonds as connecting sticks or lines, with sizes scaled according to atomic properties like van der Waals radii for overall molecular volume or covalent bond lengths for connectivity.[10] This scaling ensures realistic proportions, such as using van der Waals radii in space-filling representations to approximate intermolecular contacts or covalent radii to reflect bond strengths.[8] For instance, a simple molecular model of water (H₂O) depicts the oxygen atom at the center with two hydrogen atoms attached via bonds, illustrating the bent molecular geometry derived from a tetrahedral electron arrangement, which helps explain its polarity and hydrogen bonding capabilities.[2]Historical Development
The development of molecular models began in the 19th century, rooted in the atomic theory proposed by John Dalton in 1808, which posited that matter consists of indivisible atoms combining in fixed ratios to form molecules.[11] This theory, refined by Amedeo Avogadro's 1811 hypothesis distinguishing atoms from molecules and establishing equal volumes of gases containing equal numbers of molecules, provided the conceptual foundation for visualizing molecular structures through physical representations.[12] These ideas shifted chemistry from qualitative descriptions to quantitative models, paving the way for the first tangible physical models by enabling chemists to depict atomic connections and valences. A pivotal advancement occurred in 1865 when August Wilhelm von Hofmann introduced the first physical molecular models using colored croquet balls to represent atoms (such as white for hydrogen, red for oxygen, green for chlorine, and blue for nitrogen) connected by sticks to illustrate bonds and valences.[13] These "glyptic formulae" were demonstrated at the Royal Institution in London, allowing visualization of organic molecules like methane and aiding in teaching structural chemistry.[14] In 1874, Jacobus Henricus van 't Hoff further revolutionized modeling by proposing tetrahedral geometry for the carbon atom to explain optical isomerism, using cardboard cutouts and later ball-and-stick constructions to represent asymmetric carbon centers.[15] This stereochemical insight, independently supported by Joseph Achille Le Bel, established three-dimensional representations as essential for understanding molecular chirality.[16] In the 20th century, Linus Pauling's resonance theory, developed in the 1930s, influenced molecular model designs by accounting for delocalized electrons and partial bond orders in molecules like benzene, prompting models to incorporate variable bond lengths and hybrid orbitals for more accurate depictions of electronic structure. This theoretical framework, detailed in Pauling's 1939 book The Nature of the Chemical Bond, integrated quantum mechanics with empirical data to refine physical models. A practical outcome was the 1952 development of space-filling models by Robert Corey and Linus Pauling at Caltech, later enhanced by Walter Koltun, which used interlocking plastic components to represent atomic van der Waals radii and steric interactions in biomolecules.[6] The mid-20th century saw a shift from rigid physical models to flexible and digital ones, accelerated by computing advances in the 1960s; Cyrus Levinthal at MIT pioneered interactive computer graphics for rotating and manipulating protein models on early systems like the Kluge, enabling dynamic visualization beyond static constructions.[17] Concurrently, advances in spectroscopy, particularly X-ray crystallography, validated and refined models; for instance, James Watson and Francis Crick's 1953 double-helix DNA model was constructed using data from Rosalind Franklin's crystallographic images, confirming base-pairing and helical parameters through physical wire models tested against diffraction patterns.[18] This integration of experimental techniques with modeling marked a transition toward evidence-based structural determination.Key Principles and Representations
Molecular models are grounded in core principles that dictate the spatial arrangement of atoms and bonds, ensuring accurate geometric representation. The Valence Shell Electron Pair Repulsion (VSEPR) theory, developed by Ronald J. Gillespie and Ronald S. Nyholm, posits that the geometry of a molecule arises from the repulsion between electron pairs in the valence shell of the central atom, leading to arrangements that minimize these interactions. For instance, in methane (CH₄), four bonding pairs arrange tetrahedrally to achieve this minimization. Complementing VSEPR, the concept of orbital hybridization, introduced by Linus Pauling, explains bond angles by mixing atomic orbitals to form hybrid orbitals of equal energy. In sp³ hybridization, typical of tetrahedral carbon, one s and three p orbitals combine to yield four equivalent orbitals at 109.5° angles; sp² hybridization, as in ethene, produces three orbitals at 120° for trigonal planar geometry; and sp hybridization, seen in acetylene, results in two orbitals at 180° for linear structures. Representations in molecular models distinguish atomic sizes and bond lengths to reflect chemical reality. Atomic radii are categorized into covalent radii, which approximate half the distance in a single bond, and van der Waals radii, which account for non-bonded interactions. For carbon, the covalent radius is 77 pm, used to depict bonding regions, while the van der Waals radius is 170 pm, illustrating the effective size in crowded molecular environments./08%3A_Periodic_Properties_of_the_Elements/8.06%3A_Periodic_Trends_in_the_Size_of_Atoms_and_Effective_Nuclear_Charge)[19] Bond lengths follow from these radii; a typical carbon-carbon single bond measures approximately 154 pm, as in ethane, providing a benchmark for model construction.[20] Stereochemistry is a critical aspect captured in molecular models to convey three-dimensional arrangement. Chirality is depicted through non-superimposable mirror-image configurations around tetrahedral centers, such as in amino acids where four different substituents create enantiomers. Cis-trans isomerism, or geometric isomerism, is shown by the relative positions of substituents around double bonds or in rings; for example, in 2-butene, the cis form has methyl groups on the same side, while trans places them opposite. Conformational analysis extends this by illustrating rotatable single bonds, like the staggered versus eclipsed ethane conformers, to highlight energy minima without altering connectivity./Chirality/Chirality_and_Stereoisomers) Scaling and proportions in molecular models prioritize relative interatomic distances over absolute atomic masses to facilitate visualization. Bonds and atoms are proportionally sized—often exaggerating bond lengths for clarity—while ignoring mass differences, as models focus on geometry rather than dynamics; for instance, CPK space-filling models scale van der Waals surfaces to show packing without overlap.[10] Despite their utility, molecular models have inherent limitations in representation, as they simplify complex behaviors. They depict static equilibrium structures, neglecting dynamic molecular vibrations that cause bond lengths to fluctuate around mean values, and overlook quantum effects such as electron delocalization or tunneling that influence true geometries.Physical Models
Space-Filling Models
Space-filling models represent atoms as full spheres scaled to their van der Waals radii, illustrating the volume each atom occupies in a molecule without depicting explicit chemical bonds. These models emphasize the interlocking nature of atoms, where spheres touch or slightly overlap to mimic non-bonded interactions, providing a realistic depiction of molecular contours and packing density.[4] The development of space-filling models began in the early 20th century, with the first designs attributed to German chemist H.A. Stuart in 1934, who created spherical atom representations to account for atomic volumes. These were further refined in the 1950s by Robert B. Corey and Linus Pauling at Caltech, who produced precision models for protein structure analysis, and later improved by Walter Koltun in 1965 through a patented system of molded plastic components with snap connectors, known as Corey-Pauling-Koltun (CPK) models.[21][6][22] A key advantage of space-filling models lies in their ability to visualize steric hindrance, where atomic bulk prevents certain molecular conformations, as well as the overall shape of molecules and their arrangement in crystalline lattices. By filling the space around atoms, these models highlight close-packing efficiencies and potential voids, aiding in the understanding of intermolecular forces like van der Waals interactions.[4][23] Representative examples include methane (CH₄), depicted as a central carbon sphere surrounded by four equivalent hydrogen spheres in a tetrahedral arrangement, demonstrating the compact, symmetric volume of the smallest hydrocarbon. Benzene (C₆H₆) appears as a planar hexagonal array of carbon spheres with hydrogen spheres protruding outward, forming a flat, prism-like structure that underscores the molecule's aromatic planarity and edge-to-face packing tendencies.[24][25] Traditionally, space-filling models were constructed from wood or early plastics for durability, but CPK versions shifted to lightweight, hollow molded plastics for ease of assembly and reduced weight. Modern kits often incorporate magnetic connections or snap-fit mechanisms to allow quick reconfiguration, enhancing their utility in educational and research settings.[6][26]Ball-and-Stick Models
Ball-and-stick models represent atoms as spheres whose sizes are proportional to their covalent radii, connected by rods or sticks that depict chemical bonds with lengths scaled to actual bond distances and directions indicating bond angles. This design allows for the explicit illustration of molecular connectivity and three-dimensional geometry, with the spheres often drilled with holes at standard bond angles (such as 109.5° for tetrahedral carbon) to facilitate accurate assembly./02:_Structural_Organic_Chemistry/2.02:_The_Sizes_and_Shapes_of_Organic_Molecules)[27] These models were popularized by Jacobus Henricus van 't Hoff in his 1874 publication La Chimie dans l'Espace, where he introduced tetrahedral arrangements for carbon atoms using early physical models to demonstrate stereochemistry and optical activity. By the 20th century, ball-and-stick designs became standard in educational and research settings through commercial kits, such as those from Prentice Hall introduced in the 1980s, which provided modular plastic components for constructing organic molecules.[28][29] A key advantage of ball-and-stick models is their ability to clearly visualize different bond types—represented by single sticks for sigma bonds, double sticks or springs for pi bonds, and triple for triple bonds—along with precise bond angles and the overall molecular framework, aiding in the understanding of conformational flexibility and steric effects. Unlike space-filling models that emphasize atomic volumes, these prioritize bonding topology, making them ideal for studying reaction mechanisms and isomerism./02:_Structural_Organic_Chemistry/2.02:_The_Sizes_and_Shapes_of_Organic_Molecules)[30] Representative examples include the ball-and-stick model of ethane (C₂H₆), which demonstrates free rotation around the central C-C single bond and the resulting staggered or eclipsed conformations. For larger biomolecules, such models are used to depict protein backbones, as in a subunit of hemoglobin, where sticks highlight the alpha-helical secondary structure and connectivity between amino acid residues.[31][32] Variations of ball-and-stick models incorporate flexible joints, such as hinged or rotatable connectors, to explore dynamic conformations and torsional strain in real-time during assembly. Some advanced kits include stubs or short rods extending from atomic spheres to represent lone electron pairs, particularly useful for illustrating VSEPR theory in molecules like water or ammonia.[33][34]Skeletal and Polyhedral Models
Skeletal models represent molecular bonds as lines or wires, with atoms implied at their intersections, particularly carbon atoms at vertices in organic molecules where hydrogens are omitted for simplicity. This abstraction emphasizes connectivity and geometry without explicit atomic spheres, making it a streamlined approach for depicting carbon-based frameworks. Introduced in the late 1950s by Swiss chemist André Dreiding through his stereomodel kit, these models featured atoms with solid and hollow valence sites that interlocked directly via rods, eliminating separate connectors for more rigid constructions.[35] By the 1960s, skeletal models became standard in organic chemistry for illustrating chain and ring structures, evolving from earlier wireframe designs to support stereochemical analysis.[4] The primary advantages of skeletal models lie in their open framework, which facilitates direct measurement of bond angles, lengths, and torsional relationships using calipers or protractors, unlike more opaque representations. This efficiency proves invaluable for large or complex molecules, such as proteins and nanomaterials, where focusing on backbone topology reveals folding patterns and connectivity without the clutter of full atomic details. For instance, the diamond lattice is commonly modeled as a skeletal graph of tetrahedral carbon vertices linked by edges, highlighting the infinite three-dimensional network of covalent bonds in crystalline carbon.[4][36] Such models prioritize structural hierarchy and scalability, enabling chemists to grasp macromolecular architectures at a glance.[37] Polyhedral models further simplify cluster compounds by approximating their frameworks as regular geometric solids, such as Platonic or Archimedean polyhedra, where vertices represent atomic centers and edges denote bonds. These are particularly suited to electron-deficient species like boranes, which form closed-cage deltahedra due to multicenter bonding. In the 1970s, British chemist Kenneth Wade formulated electron-counting rules—known as Wade's rules—to predict polyhedral geometries based on the number of skeletal electron pairs, transforming the understanding of borane structures from ad hoc descriptions to a systematic polyhedral paradigm.[38] Wade's seminal 1971 paper demonstrated that closo-boranes, for example, adopt structures with n+1 skeletal electron pairs for n vertices, yielding shapes like the icosahedron for B12H12^{2-}.[38][39] By abstracting to polyhedra, these models underscore symmetry and topological features over precise interatomic distances, aiding analysis of cluster stability and reactivity in nanomaterials and inorganic chemistry. This approach excels for compounds where delocalized bonding dominates, such as in borane anions that mimic deltahedral forms from trigonal bipyramids (n=5) to dodecahedra (n=12). A prominent example is the fullerene C60, modeled as a truncated icosahedron with 60 carbon vertices at the junctions of 12 pentagons and 20 hexagons, illustrating the soccer-ball-like cage topology that earned its 1996 Nobel recognition.[40] Polyhedral representations thus provide conceptual clarity for designing and interpreting advanced materials with polyhedral motifs.[41]Composite and Hybrid Models
Composite and hybrid models integrate elements from multiple representational styles, such as ball-and-stick and space-filling approaches, to provide a more versatile visualization of molecular structures. In these designs, atoms are often depicted with partial space-filling spheres connected by rods, allowing users to observe both bond connectivity and approximate atomic volumes without the full occlusion of a pure space-filling model. For instance, semi-space-filling configurations use shorter links to position atoms closer together, creating compact representations that mimic van der Waals interactions while maintaining openness for structural analysis.[42] These models emerged prominently in the 1980s within biochemistry, driven by the need to represent complex biomolecules like nucleic acids. Hybrid kits specifically for DNA-RNA modeling, such as those based on Corey-Pauling-Koltun (CPK) atomic models, enabled the construction of helical segments for DNA, RNA, and their hybrids, facilitating studies of base pairing and structural transitions.[43] Earlier foundations trace to mid-20th-century innovations, but the 1980s saw tailored adaptations for biochemical applications, including modular sets from manufacturers like Spiring Enterprises (Molymod), which supported biochemistry-focused assemblies.[44] The primary advantages of composite and hybrid models lie in their balance of detail and accessibility, offering clearer insights into molecular interactions than single-style representations. By combining skeletal frameworks for backbone clarity with ball-like elements for side chains or functional groups, these models simplify the depiction of enzyme-substrate binding or protein folding dynamics, enhancing educational and research utility without excessive complexity.[4] Representative examples include protein models featuring a skeletal backbone traced with rods to highlight secondary structures like alpha-helices and beta-sheets, augmented with colored balls for side-chain residues to emphasize steric effects. In drug design contexts, hybrid assemblies approximate nanoscale interactions, such as ligand docking, by integrating space-filling heads on key pharmacophore sites within an otherwise open framework. For nucleic acids, CPK-based kits construct DNA-RNA hybrid helices, illustrating conformational differences in A-form versus B-form geometries.[43][45] Contemporary implementations leverage advanced materials, including 3D-printed composites that fuse modular components for customizable hybrids. These allow multicolor printing of semi-space-filling atoms using consumer-grade filaments, enabling precise replication of biochemical structures like protein active sites with integrated skeletal and volumetric features. Modular kits, such as those from Molymod, further support disassembly and reconfiguration for iterative modeling in research settings.[46][47]Digital and Computational Models
Computer Visualization Models
Computer visualization models involve the digital rendering of three-dimensional molecular structures on computer displays, facilitating interactive exploration of atomic arrangements and molecular dynamics without physical constructs. These models typically employ vector-based or raster graphics to depict atoms as spheres or points and bonds as lines or cylinders, allowing users to manipulate views in real time. Early developments in the 1960s, led by Cyrus Levinthal at MIT, introduced interactive wireframe displays on cathode ray tube systems connected to mainframe computers, marking the transition from static drawings to dynamic visualizations.[17] By the early 1970s, mainframe-based systems like GRIP at the University of North Carolina enabled researchers such as Jane and David Richardson to visualize protein backbones without relying on physical models, using shaded representations for depth perception.[17] The 1990s saw a significant expansion with the advent of web-accessible tools, including Virtual Reality Modeling Language (VRML), which allowed browser-based rendering of interactive 3D molecular scenes, democratizing access to structural data.[48] Key techniques in computer visualization include wireframe rendering, which outlines atomic connectivity with lines for clear skeletal views; stick models, emphasizing bond lengths and angles through cylindrical connections; and surface rendering, which generates continuous envelopes around molecular volumes to highlight shape and solvent accessibility. Ray-tracing algorithms simulate light paths to produce realistic effects like shadows, reflections, and depth-of-field, enhancing perceptual accuracy in complex scenes such as protein-ligand interactions. These methods support multiple display modes, often toggled within software interfaces, to suit analytical needs—from rapid wireframe overviews to photorealistic surface images. Advantages of these visualizations encompass full rotatability and zooming for inspecting hidden features, animation of conformational changes to study flexibility, and direct integration with structural databases like the Protein Data Bank (PDB), where users can load entries for immediate rendering.[49] For example, the ubiquitin protein (PDB ID: 1UBQ) can be visualized in Jmol as an animated wireframe model to trace its beta-sheet folds or in PyMOL as a ray-traced surface to reveal ubiquitin-binding sites. Advancements in hardware have evolved from high-cost 1980s workstations like Evans & Sutherland systems, which supported real-time wireframe rotations at 30 frames per second, to affordable desktop applications in the 2000s and immersive platforms in the 2020s. Modern setups leverage graphics processing units (GPUs) for smooth rendering of large assemblies, while augmented reality (AR) and virtual reality (VR) headsets enable spatial interactions, such as gesture-based molecule manipulation in tools like Nanome. In VR environments, users can "walk around" a rendered macromolecule, scaling it to human size for intuitive assessment of steric clashes, as demonstrated in collaborative sessions for structural biology. These hardware integrations extend visualization beyond screens, fostering applications in education and remote teamwork while maintaining compatibility with PDB-derived data.[17][50][51]Quantum and Molecular Dynamics Simulations
Quantum methods in molecular modeling rely on solving the time-independent Schrödinger equation to determine the wavefunction and energy levels of molecular systems, providing a foundation for ab initio calculations that treat electrons explicitly.[52] The Hartree-Fock method approximates the many-electron wavefunction as a single Slater determinant, minimizing the energy through self-consistent field iterations to compute electron densities and molecular orbitals without empirical parameters.[53] This ab initio approach captures electron correlation at a mean-field level, enabling predictions of molecular geometries and vibrational frequencies for small to medium-sized systems.[54] Density functional theory (DFT) extends these quantum methods by mapping the many-body problem to a non-interacting electron system via the electron density, as established by the Hohenberg-Kohn theorems, which prove that the ground-state density uniquely determines all molecular properties.[55] The Kohn-Sham formulation introduces auxiliary orbitals to compute the density self-consistently, incorporating exchange-correlation effects through functionals like the local density approximation or generalized gradient approximation, making DFT computationally efficient for larger molecules while yielding accurate electron densities and energies.[56] These quantum simulations output electronic structures that inform molecular models, such as potential energy surfaces for reactivity. Molecular dynamics (MD) simulations model atomic trajectories using classical Newtonian mechanics, integrating equations of motion to evolve positions and velocities over time under interatomic forces derived from potential energy functions.[57] Force fields like AMBER and CHARMM parameterize these potentials empirically, expressing the total energy as a sum of bonded terms—such as harmonic bonds —and non-bonded interactions including van der Waals and electrostatics, calibrated against quantum calculations and experimental data for biomolecules.[58][59] This approach simulates dynamic processes at femtosecond timescales, revealing conformational changes inaccessible to static quantum methods. A pivotal advancement in combining quantum and MD simulations occurred with the Car-Parrinello method in 1985, which treats electronic degrees of freedom dynamically alongside nuclear motion using Lagrangian mechanics and DFT, enabling ab initio MD for complex systems like liquids and surfaces without separate geometry optimizations. In the 2000s, graphics processing unit (GPU) acceleration dramatically scaled MD simulations, with early implementations achieving up to 100-fold speedups for non-bonded force calculations in biomolecular systems, facilitating million-atom trajectories.[60] These simulations find applications in predicting chemical reaction paths by mapping minimum energy pathways on potential surfaces from quantum or force-field calculations, and in protein folding, where MD explores ensemble dynamics starting from AlphaFold-predicted structures to refine folding mechanisms and ligand binding post-2020.[57][61] Outputs include trajectory files recording atomic positions over time, which can be visualized to depict molecular vibrations through normal mode analysis or diffusion via mean-squared displacement metrics, providing insights into thermodynamic properties and transport phenomena.[62]Software Tools and Algorithms
Software tools for molecular modeling encompass a range of open-source, commercial, and web-based platforms that enable the construction, visualization, and analysis of molecular structures in computational chemistry.[63][64] Open-source options like Avogadro provide advanced editing and visualization capabilities for cross-platform use in molecular modeling and bioinformatics, supporting tasks such as building 3D structures from 2D sketches.[64] Similarly, RDKit, an open-source cheminformatics toolkit, facilitates molecule manipulation, descriptor calculation, and machine learning integration through its C++ and Python implementations.[65] Commercial suites, such as Schrödinger's platform, offer physics-based simulations for drug discovery and materials science, including tools for ligand docking and free energy calculations.[63] Web-based tools like MolView allow intuitive 2D-to-3D structure conversion and database searching directly in browsers, promoting accessibility for educational purposes.[66] Key algorithms underpin these tools for generating and optimizing molecular models. Distance geometry algorithms embed molecules in 3D space by satisfying interatomic distance constraints, commonly used for protein structure determination from NMR data.[67] SMILES parsing enables the generation of molecular structures from textual string representations, allowing efficient input and output of chemical data across software.[68] Monte Carlo methods, particularly Metropolis Monte Carlo, perform stochastic sampling for conformational optimization and energy minimization by exploring configuration space through random perturbations.[69] The development of molecular modeling software traces back to the 1980s with early systems like CAChe, which introduced graphical interfaces for molecular visualization and computation on personal computers.[70] In the 2010s, machine learning advanced model refinement, exemplified by neural network potentials that approximate quantum mechanical energies for faster simulations.[71] These tools support standard file formats such as PDB for atomic coordinates and connectivity in biomolecular structures, and MOL2 for detailed molecular representations including charges and atom types.[72] Scripting interfaces, like Python in RDKit, enable automation of workflows for batch processing and custom analyses. Recent integrations with AI, such as generative deep learning models, facilitate de novo molecular design by producing novel structures with targeted properties. As of 2025, advancements include large language models (LLMs) adapted for chemistry, such as those enabling molecular editing and prediction, alongside datasets like Open Molecules 2025 for accelerating molecular discovery.[73][74][75] Free open-source tools like Avogadro and MolView democratize access for educational settings, while commercial and high-performance computing resources in suites like Schrödinger support intensive research applications in academia and industry.[64][66][63]Applications and Conventions
Color Conventions
Color conventions in molecular models standardize the representation of atoms to facilitate rapid identification and ensure consistency across visualizations. The most widely adopted scheme is the CPK coloring system, named after chemists Robert Corey, [Linus Pauling](/page/Linus_Paul ing), and Walter Koltun, who developed it in 1952 at the California Institute of Technology for space-filling models.[6][76] In this system, common elements are assigned distinct colors: carbon is gray or black, oxygen is red, nitrogen is blue, hydrogen is white, sulfur is yellow, phosphorus is orange or purple, and chlorine is green. These choices draw from earlier 19th-century inspirations, such as August Wilhelm von Hofmann's 1865 models, but were refined for better visual distinction in three-dimensional representations.[77] The rationale for CPK colors emphasizes atomic properties and practical utility; for instance, red for oxygen evokes its role in combustion, while the palette prioritizes high contrast for quick element recognition under various lighting conditions. This standardization promotes compatibility between physical model kits and digital software, allowing seamless translation from tangible assemblies to computational renderings. The International Union of Pure and Applied Chemistry (IUPAC) reinforced these conventions in its 2008 Graphical Representation Standards for Chemical Structure Diagrams, recommending that two-dimensional depictions align with three-dimensional model colors to avoid confusion, such as depicting oxygen in yellow.[77][76]| Element | CPK Color | Hex Code (Approximate) |
|---|---|---|
| Hydrogen | White | #FFFFFF |
| Carbon | Gray | #909090 |
| Nitrogen | Blue | #3050F8 |
| Oxygen | Red | #FF0D0D |
| Sulfur | Yellow | #FFFF30 |
| Phosphorus | Orange | #FF8000 |
| Chlorine | Green | #00FF00 |
Educational and Research Uses
Molecular models play a crucial role in education by providing hands-on tools that enhance understanding of chemical structures at the K-12 level. Physical model kits, consisting of connectable atoms and bonds, allow students to construct and manipulate representations of molecules, fostering practical engagement with concepts like bonding and geometry.[78] These kits promote in-depth learning by enabling students to visualize abstract ideas, such as molecular shapes, in a tangible way, which is particularly effective for introductory chemistry curricula.[79] Popular brands of molecular model kits cater to various educational needs, with selections often based on factors such as age group, budget, and focus (basic versus advanced modeling). Molymod offers high-quality kits suitable for schools and universities, supporting both organic and inorganic structures.[80] Snatoms provides magnetic and intuitive models, developed by Derek Muller of Veritasium, ideal for hands-on exploration.[81] Duluth Labs produces affordable and durable sets focused on organic chemistry.[82] Old Nobby delivers budget-friendly options with extensive pieces for constructing complex molecules.[83] Happy Atoms features magnetic kits designed for younger learners, incorporating app integration for interactive learning.[84] Darling Models, under the Molecular Visions line, offers flexible kits for advanced organic, inorganic, and organometallic modeling.[85] Other notable options include Orbit sets from Cochranes of Oxford and comprehensive kits available from suppliers like Carolina Biological Supply or Flinn Scientific.[86][87] In response to the COVID-19 pandemic, virtual molecular labs emerged as essential tools for remote learning, simulating experimental environments without physical access to laboratories. These digital platforms allow students to build and interact with 3D molecular structures online, supporting chemistry education during school closures in 2020 and beyond.[88] Educators adapted virtual simulations to maintain hands-on-like experiences, emphasizing conceptual understanding through interactive visualizations that replicate real-world manipulations.[89] In research, molecular models are indispensable for drug discovery, particularly in modeling ligand binding to target proteins. Computational techniques like molecular docking predict how small molecules interact with receptors, guiding the design of potential therapeutics by evaluating binding affinities and orientations.[90] In materials science, multiscale molecular modeling aids nanostructure design by simulating atomic arrangements to predict properties like stability and conductivity in nanomaterials.[91] Additionally, these models are validated against experimental data from techniques such as NMR and X-ray crystallography to ensure accuracy, with restraint-based methods assessing structural consistency between predicted and observed conformations.[92] Case studies illustrate the impact of molecular models in scientific breakthroughs. During the 2020 COVID-19 response, molecular dynamics simulations of the SARS-CoV-2 spike protein revealed key conformational dynamics and binding interfaces with human ACE2 receptors, accelerating vaccine and inhibitor development.[93] Advancements in molecular modeling include haptic feedback in virtual reality (VR) systems, which provide tactile sensations for immersive learning of molecular interactions. These VR environments allow users to "feel" forces between atoms, enhancing multisensory comprehension in organic chemistry education.[94] In research, AI-assisted interpretation automates the analysis of complex model outputs, using machine learning to predict molecular behaviors and optimize designs in drug discovery pipelines.[95] The use of molecular models significantly improves spatial reasoning skills, as students and researchers better visualize 3D arrangements through physical and virtual manipulations, leading to higher accuracy in predicting molecular geometries.[96] Furthermore, these models accelerate hypothesis testing by enabling rapid iteration of structural predictions against experimental data, streamlining discovery processes in chemistry and biology.[97]Limitations and Advancements
Traditional molecular models, especially static physical and early digital representations, inherently overlook the dynamic aspects of molecular systems, such as vibrational motions, conformational flexibility, and time-dependent interactions that are essential for accurately depicting biomolecular functions.[98] These models struggle with scalability in large biomolecules like proteins and nucleic acids, where the sheer number of atoms—often exceeding thousands—poses significant computational and visualization challenges, limiting the ability to model entire cellular processes without excessive simplification.[99] Furthermore, inaccuracies in representing non-covalent interactions, including hydrogen bonding, π-π stacking, and dispersion forces, persist in many classical models, leading to unreliable predictions of molecular association and stability in complex environments.[100] Advancements in artificial intelligence have significantly addressed these shortcomings, with the 2021 AlphaFold model enabling unprecedented accuracy in predicting three-dimensional protein structures from amino acid sequences, revolutionizing the field by reducing reliance on experimental methods like X-ray crystallography for initial modeling.[101] Subsequent versions, such as AlphaFold 3 in 2024 and AlphaFold 4 in 2025, have further enhanced predictions to include biomolecular complexes and interactions.[102][103] Machine learning approaches, such as graph neural networks and deep learning frameworks, now generate precise molecular geometries and transition states, bypassing computationally intensive quantum mechanical calculations while achieving near-quantum accuracy for diverse chemical systems.[104] In physical modeling, 3D printing has enabled the production of customizable, tangible representations of complex molecules, allowing researchers to fabricate models tailored to specific structures for enhanced stereochemical visualization.[105] Hybrid quantum-classical simulations further bridge gaps by combining quantum mechanics for reactive cores with classical methods for surrounding environments, improving efficiency and fidelity in modeling enzyme reactions and solvent effects.[106] As of 2025, quantum computing advancements are being leveraged to simulate molecular behaviors at quantum scales, potentially resolving longstanding limitations in classical approaches for entangled electron systems in drug discovery.[107][108] Looking ahead, real-time augmented reality (AR) tools promise interactive, immersive modeling of molecular dynamics, enabling users to manipulate and explore structures in virtual space for intuitive analysis.[109] Ethical concerns accompany these AI-driven innovations, particularly biases in models trained on limited datasets that underrepresent diverse molecular contexts, potentially leading to skewed predictions in applications like protein-ligand binding and exacerbating inequities in research outcomes.[110]Chronology of Key Models
| Year | Development | Key Figure(s) | Description |
|---|---|---|---|
| 1865 | Ball-and-stick models | August Wilhelm von Hofmann | First physical 3D models using colored wooden spheres (e.g., white for hydrogen, black for carbon) connected by rods, introduced in a lecture to represent organic molecules like methane. Established early color-coding conventions.[3] |
| Late 1920s | Ball-and-peg kits | Charles D. Hurd | Affordable educational models inspired by Tinkertoy sets, featuring drilled wooden balls with holes indicating bond valences (e.g., four for carbon, two for oxygen). Developed at Northwestern University for classroom use.[5] |
| 1934 | Space-filling models | H.A. Stuart | Early designs using interlocking pieces based on van der Waals radii to depict atomic sizes and molecular packing, marking a shift toward realistic volume representations. Later commercialized.[111] |
| 1952 | Corey-Pauling models | Robert Corey, Linus Pauling | Precursor to CPK sets; precision space-filling models developed at Caltech using plastic calottes for accurate bond angles and atomic radii, aiding protein structure visualization.[6] |
| 1958 | CPK models | Robert Corey, Linus Pauling, Walter Koltun | Refined space-filling kits with standardized colors (e.g., black for carbon, red for oxygen) and sizes, widely adopted for research in biochemistry and crystallography.[6] |
| 1958 | Dreiding models | André Dreiding | Connector-less ball-and-stick kits with atoms at polyhedral intersections for flexible bond angles, emphasizing stereochemistry in organic synthesis.[112] |
| 1961 | Early computational modeling | James Hendrickson | First use of computers for force-field calculations on molecular conformations, transitioning from physical to digital simulations.[3] |
| 1965 | Molecular graphics | Various (e.g., Cyrus Levinthal) | Initial computer visualization of molecular structures on screens, enabling dynamic manipulation beyond physical constraints.[3] |