Visualization of 3D structures and spatial orientation has always been a major aspect of chemistry lectures (Oliver-Hoyo & Babilonia-Rosa, 2017). The typical representation in textbooks and on panels is a 2D projection of the 3D structure. For the understanding of complex geometries in the 3D space, molecular modelling kits with standardized sets of atoms and bonds are indispensable. Modern technologies allow for significantly improved representations of complex molecular structures. Recent examples are freely scalable and rotatable 3D models in software programs on tablets and smartphones (Chiu et al., 2018; Ping, Lok, Yeat, Cherynn, & Tan, 2018). Nevertheless, the combined haptic and visual feedback of a real 3D model is extremely helpful to discuss phenomena in the 3D world. Consequently, the technology of 3D-printing has been applied to generate true 3D models as scaled counterparts to the original molecular structure. These models can be handled as objects from molecular modelling kits, but have one significant advantage: They represent exactly scaled bond lengths and bond angles instead of standardized atom distances. Furthermore, unlimited amounts of 3D-models can be reproduced from the template file. First protocols for the printing of crystal structures have been published in 2013 (Scalfani, 2013), rapidly followed by various publications explaining the concept from molecular coordinates to 3D-printed structures in detail (Chen, Lee, Flood, & Miljanić, 2014; Kitson et al., 2014; Scalfani & Vaid, 2014). Subsequent publications concentrate on optimization and simplification of the process (Jones & Spencer, 2018; Rossi, Benaglia, Brenna, Porta, & Orlandi, 2015; van Wieren, Tailor, Scalfani, & Merbouh, 2017), optimization of the 3D-print for unit cells (Rodenbough, Vanti, & Chan, 2015), biomolecules (Jones & Spencer, 2018; Meyer, 2015; Rossi et al., 2015; van Wieren et al., 2017), larger structures by connection of independently printed fragments (Paukstelis, 2018), reversibly interacting structures based on 3D-printed parts and velcro (Babilonia-Rosa, Kuo, & Oliver-Hoyo, 2018; Cooper & Oliver-Hoyo, 2016), and the 3D-print of components for a large structure modelling kit (Penny et al., 2017). Further work presents the application of 3D-printed objects for the visualization of the structure of block-copolymers (Scalfani, Turner, Rupar, Jenkins, and Bara 2015), polyhedra for teaching of point groups (Casas & Estop, 2015), the Bohr atom model (Smiar & Mendez, 2016), VSEPR models generated with a 3D-printing pen (Dean, Ewan, & McIndoe, 2016), molecular orbitals (Carroll & Blauch, 2017; de Cataldo, Griffith, & Fogarty, 2018; Griffith, de Cataldo, & Fogarty, 2016; Robertson & Jorgensen, 2015) (with inserted magnets to realize reversible interactions (Carroll & Blauch, 2018)), and potential energy surfaces (Blauch & Carroll, 2014; Kaliakin, Zaari, & Varganov, 2015; Lolur & Dawes, 2014; Teplukhin & Babikov, 2015) as well as reaction progress data (Higman, Situ, Blacklin, & Hein, 2017) based on spectroscopic results and periodic tables which represent periodic trends by tactile information (LeSuer, 2019). 3D-printed structures have been established in larger courses with a focus on the transfer of 2D to 3D structures allowing each student to print one unique model (Fourches & Feducia, 2019). In general, the feedback of students on 3D-printed structures is very positive (Fourches & Feducia, 2019; Frohock, Winterrowd, & Gallardo-Williams, 2018).
As part of our work on 3D-printing in chemical laboratories (Lederle, Kaldun, Namyslo, & Hübner, 2016a; Lederle, Meyer, Brunotte, Kaldun, & Hübner, 2016b; Lederle, Meyer, Kaldun, Namyslo, & Hübner, 2017), we designed a set of 37 scaled structures for a lecture course and exercise (1 unit) in organic chemistry/stereochemistry for second/third year undergraduates. The course is intended for small groups of roughly to 20–30 students. The procedure for the generation of the scale models is based on the basic protocols given in literature (see Figure 1). In contrast to the protocols for the production of 3D models, which have been well established, the focus of our work was to fully integrate true scale models into the teaching concept. All structures discussed here have been 3D-printed on an affordable (€1000) fused deposition modeling printer and are attached as STL files ready for reproduction. Poly(lactic acid) (PLA) has been chosen as sustainable printing material.
Note: Various protocols are given in literature for the 3D-printing process of molecular models (Chen et al., 2014; Kitson et al., 2014; Scalfani, 2013; Scalfani & Vaid, 2014). The information given below is not a detailed description, but a summary of settings to allow for reproduction and extension towards further structures with the same appearance. All model numbers refer to the corresponding structure/STL file listed in the Supplementary material.
PDB files containing the atom coordinates have been taken from the Cambridge Structural Database (Groom, Bruno, Lightfoot, & Ward, 2016) (CSD) or from quantum chemical calculations (see below). File format inconsistencies have been corrected with Chem3D 126.96.36.199 (PerkinElmer Informatics). Ball and Stick models have been converted from the PDB files to 3D-printable STL files with Python Molecule Viewer (PMV) (Sanner, 1999) 1.5.6 with a stick radius of 0.12, a ball radius of 0 and a ball scale factor of 0.18. STL files have been scaled with a final factor of 1 : 1.8·108 with netfabb 5.2.1 (netfabb GmbH). Self-intersections have been removed with netfabb 5.2.1. 3D-Printing has been performed with BEEsoft 3.9.0 on a BEEthefirst 3D printer with black PLA from BeeVeryCreative, BEEVC – Electronic Systems Lda. All prints have been processed with a layer height of 50 μm and 40 % infill. In deviation from standard settings, a supportlinedistance of 1500 and supportXYdistance of 500 has been used for the implemented CURA slicer engine to realize prints of small spheres (hydrogen atoms). Supporting material has been removed by hand with knife and cutter. Atom coloring has been achieved with Revell email color (Revell GmbH).
All density-functional theory (DFT)-calculations to obtain geometry optimized structures were carried out by using the Jaguar 9.1.013 software (Schrodinger, Inc) (Bochevarov et al., 2013) running on Linux 2.6.18–238.el5 SMP (x86_64) on five AMD Phenom II X6 1090T processor workstations (Beowulf-cluster) parallelized with OpenMPI. MM2 optimized structures were used as starting geometries. Complete geometry optimizations were carried out on the implemented LACVP* (Hay-Wadt effective core potential (ECP) basis on heavy atoms, N31G6* for all other atoms) basis set and with the PBE0 density functional. PDB files have been exported with Maestro 10.5.013, the graphical interface of Jaguar.
3D-printing of structures
X-ray structures taken from the Cambridge Structural Database have been used as source for most 3D models intended for a discussion of bond length and angles and other spatial phenomena. The usage of X-ray structures provides a most realistic basis for the scaled molecular models. For the structures intended for the discussion of stereochemistry, X-ray structures and quantum chemically calculated structures have been used. The usage of calculated structures allows designing models which are reduced to the most important aspect for the stereochemical discussion. Still, structures derived from density functional calculations represent very exact geometries and a structural discussion is possible beyond the stereochemical aspect. The type of each structure (calculated vs. X-ray) and if appropriate, the corresponding PDB code is listed in the Supplementary material.
First, the optimal molecular representation was evaluated by some sample prints. Although space-filling CPK (Corey, Pauling, Koltun) models provide the most realistic structure (see models No. 36 and 37 of the Supplementary material), the measurement of bond distances and angles is hardly possible. Consequently, a ball and stick representation was chosen as optimal structure with well-defined atoms and bonds. Atom sizes have been scaled according to the standard sizes of the Python Molecule Viewer. All atoms have been colored by hand to allow direct identification of the chemical structure. The printing time for the structures differs from some hours to two days and all models have been printed during one semester parallel to the lecture. A scaling factor of 1 : 1.8·108 has been applied for all models. This leads to the apparent conversion rule “divide by 18” to transfer measured distances (mm) to the atomic unit Ångström (Å, 10−10 m). This factor is readily accepted and routinely applied by the students. Naturally, the scaling factor and the size of the printer limit the printable structures. Consequently, the set of structures presented here is based on rather small molecules <50 atoms which fitted our printer bed size of 19.0 × 13.5 cm at the given scaling factor (only the helicene model was slightly too large for our printer). The accuracy of the 3D-printing process is rather good and by using a standard divider caliper (or compass) which most of the students own from high-school courses, it is possible to measure the bond distance with an accuracy of 1 mm, i.e. 0.05 Å and angles with an accuracy of 1°. The fused deposition modeling process of the 3D-printer with its layered structure simplifies the determination of the atom center point. As an example, the carbon bond length of the cyclopropane derivatives (see Figure 2f) already differs visually from the shorter bond length of the three-membered rings in the cyclopropene and cyclopropabenzene derivatives (Figure 2c). The shorter bond length of the cyclopropene structure in comparison to the cyclopropabenzene structure (Figure 2c) is not readily recognized by eye, but is clearly determined after the measurement with a caliper. The slightly differing bond length (0.3 mm, 0.02 Å) of the cyclopropane structures (Figure 2f) is not resolved by the measurements any longer. Overall, this resolution is high enough for a detailed structural discussion.
Lecture and exercise
The lecture course is intended for second/third year undergraduate students, consequently all basic knowledge in periodic trends, electron configuration, orbitals and their geometry, hybridization, basic organic chemistry and aromaticity as well as point groups (taught in inorganic chemistry) are assumed to be present. The course presented here had been established in our department based on basically the same content before the introduction of scale models. Scope of the course (1 h per week) are spatial and stereochemical phenomena of organic molecules. The course is given accompanying to advanced courses in organic chemistry (synthesis, structure determination) and inorganic chemistry (including X-ray structure determination). The course presented here picks up the students at a basic level of knowledge from beginners’ courses, for example standard bond length or the stereochemistry of a fourfold substituted carbon atom. It rapidly moves over to more advanced problems such as border cases of organic structures and chirality of molecules in point groups beyond C1, including axial and planar chirality. The examples are always embedded in the context of the synthesis of the corresponding compounds and analytical methods.
To the beginning of the course, the standard values of bond angles and especially bond length of organic compounds have been handed to the students (Allen et al., 1987; Hauptmann & Mann, 1996). Starting with the first lecture, the true scale models have been passed to the students and they have been asked to measure the structural parameters of these models (see below for various examples concerning the measurement of bond angles and bond length). Measuring exact parameters from the scale molecular models takes time. Consequently, the concept is well-suited for combined lectures/exercises with time for a detailed discussion of the results. The values measured by the students have been compared to the standard parameters and reasons for the deviations have been discussed collaboratively. With a proceeding course, the students became familiar with the discussion of structural parameters and their influence on molecular properties and reactivity. Consequently, more general questions have been asked, which have been answered by the students with the help of structural parameters (see discussion of aromaticity given below).
Static stereochemistry – organic structures
As mentioned above, the standard bond length and angles in organic compounds are repeated to the beginning (Allen et al., 1987; Hauptmann & Mann, 1996). The tetrahedral bond angle of 109.5° is of course well known by all students. An interesting aspect are the deviations from the standard settings. The planarization of an sp3 carbon atom has been discussed as first example (Hoeve & Wynberg, 1980a,1980b). Azafenestrane has been chosen as prominent structure. The synthesis of azafenestrane is a nice organic synthesis which can be discussed in this context (Denmark, Kramps, & Montgomery, 2002). Looking at the scale model (Figure 2b) students are quite disappointed since the structure is far away from the planar (∠CCC = 180°) window-like 2D representation with an angle of 117° at the central carbon atom. Spiro compounds such as 2,6-dichlorospiro[3.3]heptane (Figure 2h) and comparable spiro[3.3]heptanes (Hulshof, Wynberg, van Dijk, & de Boer, 1976) can form a more linear geometry at the central carbon atom up to 126° (here, ∠CCC = 121°) but still the deviation from the standard angle is rather small.
In contrast, squeezing the CCsp3C bond angle is easier and well-known from cyclic compounds, i.e. three membered rings. An extremely small angle of 49° can be found in (cycloprop-1-en-3-yl)ethyne (Figure 2c) which is visually strongly more strained than standard cyclopropanes (Figure 2f). The ring strain is readily explained by the short CC bond length opposite to the CCC bond angle (see below). The bond angles at the sp2 carbon atom (ideally 120°) can be discussed similarly. Again, (cycloprop-1-en-3-yl)ethyne is a nice example for the ring strained situation with a CCsp2C angle of 65° (Baldridge et al., 1998). It should be noted, that the difference between the CCsp3C bond angle discussed above and the CCsp2C angle is nicely visible in the 3D-printed model by eye and easily confirmed by measuring with a protractor. The opposite situation, enlarging the CCsp2C bond angle, is demonstrated with 1,2-dihydrocyclobuta[a]cyclopropa[c]benzene (Figure 2c). The largest observed bond angle of 177° for an sp2 carbon atom nearly reaches the linear configuration (Boese et al., 1994). The 180° angle at the sp carbon atoms of alkynes is of course well-known by the students ((cycloprop-1-en-3-yl)ethyne, Figure 2c), again, and rather obvious deviations found in ring systems have not been discussed with printed models. The 180° C=C=C angle in the case of allenes and the corresponding dihedral angle of 90° of the substituents at the terminal carbon atoms is visualized by 1,3-dichloropropa-1,2-diene (Figure 2g). As an interesting aspect the possibly bent structure of acyclic allenes with a push-push substitution pattern (∠C=C=C = 135°) (Dyker, Lavallo, Donnadieu, & Bertrand, 2008) may be discussed here in the context of the electronic situation of the π-bond (Patel & Bharatam, 2011).
Subsequently, bond lengths have been introduced as most helpful parameter for the discussion of structural details. The measuring of bond lengths needs to be performed more accurate by the students in comparison to bond angles since the center point of the atom is a critical point. Additionally, the scaling factor needs to be applied here. First, the standard CC single bond length of 1.53 Å is discussed (Allen et al., 1987). A very strong shortening of the CC bond to 1.46 Å is found in the exotic structure of cubylcubane (Figure 3) and easily derived from the model by the students (1.3 mm shorter than the standard bond length) (Gilardi, Maggini, & Eaton, 1988).
At a first look, this is reported to be rather strange by the students, as the structure seems to be very crowded. Looking at the structure more closely reveals the opposite effect. The cubic structure pulls back the three substituents of the bridging carbon atom leading to an opening of the tetrahedral angle to 125°. The electronic effect of more p-type orbitals inside the orthogonal cage structure and consequently more s-type orbitals at the exocyclic bonds allows explaining the bond shortening (Gilardi et al., 1988). Additionally, the nice synthesis of cubylcubane is worth to be discussed in this context (Eaton & Maggini, 1988). At this point, smaller deviations from the standard bond length caused by substituent effects has been discussed, too. The bond shortening by electron withdrawing groups is visualized by the comparison of the H2C-CH2 bond length in chlorocyclopropane with the H2C-CHCl bond in dichlorocyclopropane (Figure 2f). The explanation can be given by an increased s-character of the C-C bond, again. Additionally, orbital contraction at the carbon atom by an increasing net positive charge caused by the electron withdrawing groups leads to a shorter CC bond length (Mack, Dakkouri, & Oberhammer, 1991). These deviations from the standard bond length are too small to be measured in the 3D-printed models, which is readily accepted by the students and emphasizes the differences of small (electronic/substituent) effects and larger (steric) effects. The opposite case, bond elongation of CC carbon bonds, is nicely discussed on recent online blogs and publications. The basic idea discussed in the course of this lecture is the minimization of the bond dissociation energy partly by stabilization of the resulting fragments, typically by three aryl moieties as substituents at both connected carbon atoms. Very recent approaches include ring strain, negative hyperconjugation and other effects (Bradley, 2018; Li et al., 2019). Since the resulting structures are large, this discussion has not been supported with scale models in the scope of this lecture until know.
For the C=C bond length, a minimization from the standard value (Allen et al., 1987) of 1.32 Å has been demonstrated with the structure of cycloprop-1-en-3-yl)ethyne (Figure 2c), which represents the shortest reported C=C bond length. With 1.26 Å the bond length is midway between a CC double and CC triple bond. The detailed influence of the ethynyl substituent, which plays a major role in the final shortening of the bond, has not been fully elucidated in literature yet (Baldridge et al., 1998).
Elongation of the Csp2=Csp2 bond leads to aromatic systems with a standard bond length of 1.38 Å and 1.39 Å in benzene, respectively (model No. 33) (Allen et al., 1987). Substituent effects can lead to further bond elongation. At this point, the concept of bond orders has been introduced. Coronene has been taken as an example which represents a series of varying bond orders from roughly 30 to 70 % double bond character (Fawcett & Trotter, 1966; Robertson & White, 1945). A large set of resonance structures can be drawn for coronene to explain the differing bond orders (Robertson & White, 1945). By slow and partial hydrogenation, the strong differences in the bonds have been proven experimentally. Looking at the scale model of coronene (Figure 4a) at least the strongly differing six outer bonds with 1.34 Å and inner bonds with 1.41–1.42 Å are readily identified by the students. For the conversion to the corresponding double-bond character, a scaled Pauling-Brockway (Pauling & Brockway, 1937) like relation with correction for smaller bonds (Fawcett & Trotter, 1966) has been applied (Figure 4c). This relation is readily accepted by the students and applied for several other structures discussed in the course.
The differences of the inner bond length in coronene are very small (Figure 4b). Although the flat structure of coronene simplifies the exact measurement, it is not possible to distinguish between bonds, which differ by 0.3 mm (0.02 Å). Even in plotted cross-sections of the STL file the differences remain small (Figure 4b). Consequently, this aspect has been used to start a discussion on accuracy of the real measured bond length by X-ray crystal structure determination. An extremely high accuracy is needed to distinguish between rather similar bonds. This leads to a discussion of the possible error in the context of the two slightly varying crystal structures for coronene given in literature which have been used as basis here (Fawcett & Trotter, 1966; Robertson & White, 1945).
In the context of resonance structures and the aromaticity of coronene, sydnones have been introduced as a very exotic example of potentially aromatic structures (Simas, Miller, & de Athayde Filho, 1998; Wiechmann et al., 2014). N-(2,6-Diisopropylphenyl)sydnone (Figure 5) has been chosen as stable example. Especially, the impossibility to write a resonance structure without charge separation attracts attention (Figure 5a). Although zwitterionic structures are well-known by the students, for example from amino acids, usually a corresponding neutral form is imaginable. Since this is not possible here, the “touchable” scaled model of the true structure helps to emphasize that the resonance structures are just a (very helpful) imagination and the real binding situation and electron distribution is somewhere in between. As mentioned above, students get readily used to autonomously measure parameters from the models to answer questions concerning molecular properties. At this point, the students are usually capable to develop a strategy to answer the question whether sydnones are aromatic or not. At least some students refer to the differing resonance structures, point out the missing delocalization in one case and suggest to look at the exocyclic C-O bond length, which is readily measured from the scale model. The bond length is determined to 1.21 Å, consequently a true C=O double bond (Allen et al., 1987), which indicates non-aromaticity. Of course, this is just one aspect and can be used as a starting point for the discussion of other indicators for aromaticity (Simas et al., 1998; Wiechmann et al., 2014).
As a further exotic structure in this context, diademane (see model No. 31) has been introduced. The idea of cis-tris-σ-homobenzene is represented by endo,endo-tetracyclo[6.1 .0.02,4.05,7]-nonane, which is based on the structure of benzene with alternating cyclopropane moieties instead of alternating double bonds. While this structural motif is not stable itself, the corresponding diademane which is in possession of an additional bridging carbon atom for the three cyclopropane units can be isolated (Kaufmann et al., 1983). The students are quite impressed by the perfectly planar cyclohexane ring (see model No. 31), which is in strong contrast to all conformations of non-aromatic six membered rings. In these cases, the carbon atoms of the flat cyclohexane ring are described as a structural intermediate between sp2 and sp3 hybridization (Kabuto, Yagihara, Asao, & Kitahara, 1973). 1JC,H coupling constants from magnetic resonance spectroscopy may be introduced here as analytical method to characterize the hybridization. The structure of diademane is used to discuss the concept of homoaromaticity and furthermore the synthetic pathway towards diademane as well as its decomposition are an interesting aspect (Kaufmann et al., 1983).
Static stereochemistry – chirality
As mentioned above, the E/Z nomenclature of olefins had not been supported by 3D-printed structures. These structures are readily discussed in the 2D space. The priority ranking of substituents is repeated in this context. Central chirality and the CIP (Cahn, Ingold, Prelog) system, which is well-known by the students on this level of education, is used as an introduction to more complex stereochemical phenomena and is visualized by (R/S)-bromochlorofluoromethane (see Figure 2e, top). Looking at the scale models (model No. 2 and 3) more closely, the bond angles show slight deviations from the tetrahedral bond angle due to sterical hindrance and van der Waals attraction. (S,S)-Lactide has been 3D-printed as the chiral monomer of PLA (Figure 2a) which was the 3D-printing material for all structures. As a first aspect, adamantanes have been introduced as rather uncommon motif for central chirality (Prelog, 2006). The adamantane cage (Figure 2d) matches the tetrahedral bond angle of 109° at every carbon center quite exactly. Consequently, the four off-standing substituents at the four tertiary carbon atoms of adamantane form a geometric structure, which resembles a stretched methane molecule with a virtual central bonding point (Figure 6b). The bond angles FXCl, FXBr and ClXBr (X = center of chirality) are quite close to the tetrahedral bond angle, again. Slight deviations to bromochlorofluoromethane can be explained by the absence of steric hindrance of the four substituents towards each other. The concept of central chirality detached from a four-coordinated carbon atom demonstrated with the two mirrored adamantane structures (Figure 6a) attracts great interest by the students.
Phosphorous-chiral (P-chiral) compounds have been introduced next. P-chirality is based on the large inversion barrier >100 kJ/mol at the phosphorous center (compared to ∼20 kJ/mol for nitrogen) (Bader, Cheeseman, Laidig, Wiberg, and Breneman 1990). For visualization, the enantiomers of chloro(methyl)phosphane have been printed as scale models (see Figure 2e, bottom). Although too reactive in reality (instable P-Cl bond) this DFT-calculated structure has been chosen for some reasons. First, the fourth “substituent” (with lowest priority) is the lone pair at the central P atom, which is quite uncommon for chiral molecules. Second, the choice of H and Cl as substituents allows comparing the structure with bromochlorofluoromethan and to discuss the spatial requirements of the lone pair (∠HCCl vs. ∠HPCl, see Figure 2e). Third, even small phosphanes such as PH3 show high inversion barriers of 130–140 kJ/mol, i.e. they are stereochemically stable (Bader et al., 1990). Finally, the methyl substituent is an example for substituents commonly found in phosphanes. Ethylpropylphenylphosphine is discussed as a stable and practically usable example for P-chiral compounds. This leads to the application of ethylpropylphenylphosphine as chiral ligand in enantioselective rhodium-catalyzed hydrogenation reactions (Knowles & Sabacky, 1968) and subsequently the great importance of P-chiral ligands in catalysis (Grabulosa, 2011).
After central chirality has been completed, axial chirality has been introduced with the structure of allenes (Hauptmann & Mann, 1996; Ye & Ma, 2014). The enantiomers of 1,3-dichloropropa-1,2-diene (see Figure 2g, model No. 7, 8) easily allow determining their axial chirality. The interesting synthesis of chiral allenes and their occurrence and applications has been discussed in this context (Ye & Ma, 2014). Stepwise exchange of the C=C unit by cyclobutane moieties (see model No. 26–29) leads to spiro compounds with axial chirality. Here, a deviation of the dihedral ClCCCl angle from 90° to 125° in case of 2,6-dichlorospiro[3.3]heptane complicates the visual determination of the correct chirality. The students had some problems to identify the axis in the scale model and to find the similarity between (aS)-1,3-dichloropropa-1,2-diene and (aS)-2,6-dichlorospiro[3.3]heptane (see Figure 2h). This is a nice example to demonstrate that in reality, i.e. with true bond length and angles, the situation that is well understood in theory and easily applied to simple models may need some training for complex structures. The chirality of spiro[3.3]heptanes has been discussed further with Fecht’s acid. The determination of the absolute configuration of Fecht’s acids is a very nice example and can be used as a starting point to discuss the complexity of absolute structure determination, the problems of empirical rules and theoretical models and the introduction of heavy atoms (barium salt) for the analysis via anomalous dispersion in X-ray structure determination (Hulshof et al., 1976). Sterically hindered biphenyls may be discussed as example for axial chirality at this point, too.
Planar chirality has been explained with the structure of paracyclophanes. The enantiomers of 4,7,12,15-tetrachloro[2,2]paracyclophane (see Figure 2i) and the non-chiral 4,12-dichloro[2,2]paracyclophane (model No. 14 in the Supplementary material) have been printed as examples which have been synthesized (Pan, Wang, & Xiao, 2016). The mirrored (pR/pS)-tetrachloroparacyclophanes attract students’ interest and they try a couple of times to match the structures in any orientation. The 3D structure allows straightforward teaching of the determination of planar chirality. An interesting aspect is the deviation of the connection of the two benzene planes from orthogonality. The two bridging carbon atoms are slightly tilted by 19° from a vertical axis (Figure 2i). This is in contrast to the structure of 4,12-dichloro[2,2]paracyclophane and in contrast to a structural model which would have been obtained from standardized modelling kits. The deviation is readily explained by the sterical hindrance of the chlorine atoms. Although rather obvious, students expressed their astonishment that “even the tilted bond” is mirrored in the enantiomers. The determination of the absolute configuration of paracyclophanes has been used as a second nice example to discuss the problems of chiral structure determination (Furo, Mori, Wada, & Inoue, 2005).
The X-ray structures of (P)-Helicene and (M)-Helicene have been printed for the visualization of helical chirality (see Figure 7). The distortion from planarity of polycyclic aromatic hydrocarbons based on ortho-fused benzene rings starts with four connected rings (Shen & Chen, 2012). Six rings would be sufficient to cover a full 360° turn (compare to coronene) and consequently the structure based on 7 rings leads to a complete benzene ring on top of the first one. The P/M-notation is easily understood by the students. Again, an interesting structural discussion is combined with the stereochemical aspect. Looking at the scale model more closely, the students identify strongly differing bond length and transfer them into single/double bond character according to the scaled Pauling-Brockway relation discussed above. The structure is readily explained by appropriate resonance structures and torsional strain. Furthermore, the pitch of the helix is discussed (Figure 7b) (Shen & Chen, 2012).
Stereochemistry is always connected to the discussion of point groups. The application of 3D-printed structures for teaching symmetry is discussed in literature (Casas & Estop, 2015; Rodenbough et al., 2015; Scalfani & Vaid, 2014). The set of structures presented above can be used to train point groups as well, since they cover a broad range of different symmetry elements. Some additional models have been printed in this context to emphasize the connection of point groups and chirality. A special focus is given to the point groups Cn and Dn, which can provide chirality beyond the asymmetric carbon center with C1 symmetry. The introduction of symmetry elements such as mirror planes and inversion centers within the molecule naturally destroys chirality. Structures discussed in this context include the chiral methanes, adamantanes and phosphanes (C1, Figure 2e and Figure 6); 4,7,12,15-tetrachloro[2,2]paracyclophane (D2, Figure 2i) in contrast to 4,12-dichloro[2,2]paracyclophane (Ci, see model No. 14) and the capped cubane structure octahydro-1H-1,3,4-(epimethanetriyl)cyclobuta[cd]pentalene (D2h, see model No. 10); 1-chloroadamantane (C3v, Figure 2d) and cubylcubane (D3d, Figure 3) in contrast to the rare example of chirality in point group C3 represented by (1E,3R*,5E,7R*,9E,11R*)-3,7,11-trimethylcyclododeca-1,5,9-triene (C3, see model No. 19,20); and the chiral allenes (C2, Figure 2g). Additionally, substituted cyclopropanes are introduced. trans-1,2-Dichlorocyclopropane (C2, Figure 2f) is chiral in contrast to chlorocyclopropane (Cs, Figure 2f) and the determination of the absolute configuration of the comparable trans-1,2-dimethylcyclopropane is a nice synthetic and analytic story in this context (von E. Doering & Kirmse, 1960). trans-(R*,R*)-1,2-Dichlorocyclopropane (Figure 2f) with 2 stereogenic centers is a good starting point for the disscussion of the reduction of the number of isomers due to intramolecular symmetrie in achiral meso-compounds (cis-(R,S)-1,2-dichlorocyclopropane, see model No. 32) which leads to the topic of chiral sugar molecules. Due to their large structures, no 3D models have been printed in the context of sugar chemistry.
Finally, the lecture course moves over to stereochemical syntheses. While the introduction based on general concepts such as Walden inversion can be repeated as by the help of bromochlorofluoromethane (Figure 2e) and the inversion of chloro(methyl)phosphane (Figure 2e) the full synthetic pathways and more complex aspects such as stereochemical induction and catalysis had not been supported by scale models any longer.
The application of scale models for oral exams is rather straightforward. In our case, the lectures have been finalized with written exams. In this case, it would be necessary to hand out one model to each student. Due to the resulting printing time, this has not been realized yet. Until now, only the very simple structures of benzene (model No. 33) and methane (model No. 34) are intended as helpful tool for the exams. From these small structures and depending on the scaling factor, ∼10 pieces/24 h can be printed (in a batch). The students acknowledge the structures as very helpful for the spatial orientation, e.g. to correctly assign point groups of substituted benzenes or the chirality of carbon centers. Due to the reproducibility and low costs (∼ 50 ct/model), the structures can be taken home by the students. In future, it is planned to print sufficient amounts of scale models which can be handed out to the students and to include some questions which can be answered from the geometric details.
The lecture course and exercises have been evaluated by the Clausthal University of Technology Center for Quality Management in study and teaching before and after introduction of the scale models. The course has been given to small groups of 20–30 students, consequently the results of evaluation can’t be expected to be too reliable. The overall rating (1 = best, 5 = worst) of the combined course/exercise improved from 1.74 (before) to 1.33 (after). The acquirement of skills improved from 2.27 to 1.62. The most positive feedback is received from the free comment section of the evaluation sheets (see Supplementary material). The evaluation has been performed according to a standard questionnaire, i.e. without any mention of the scale models. From 21 students who returned the questionnaire, five added a personal comment and all five comments refer to the 3D-printed models. The students highlighted “touchable structures”, “molecules from a 3D-printer”, “the possibility to use 3D-printed structures to understand the context”, “illustrative explanation”, “printed models for visualization” and “the pleasant working atmosphere”.
The students’ scores of the written exams improved after introduction of the scale models. It must be noted again, that the small groups involved in this course must lead to significant fluctuations of the grades. Still, the improvement of the scores by 9.1 percentage points after introduction of the models can be seen as an indication for the positive effect on students’ learning. From the perspective of the lecturer, the students were much more active and involved in the discussion. At least partially, we conclude the positive effect to be based on the students’ group staying more focused on the topic by hands-on measuring and discussing the results of the scale models.
Scale models of chemical structures attract students’ interest and are easily applied to beginners’ courses. Beyond that, the scale models have the potential to be applied in more advanced courses, too. The exact scaling and high resolution of 3D-printed structures allows determining bond length and angles with an accuracy of 0.05 Å and 1°. We equipped a lecture course/exercise in organic chemistry/stereochemistry for second/third-year undergraduates with a set of 37 models based on X-ray structures and quantum chemical calculations. The scale models have been introduced from the beginning of the course and students readily recognized the discussion of geometry and stereochemistry with the scale models. A fixed scaling factor of 1 : 1.8·108 was used for all models to facilitate the discussions. Students readily start to evaluate various properties of the structures autonomously. The working atmosphere in the course was very vivid and students stay focused on the discussion passing the models to each other, measuring distances, calculating bond orders and comparing the results. Furthermore, the scaled models emphasize the importance of X-ray structures for organic chemists. Measuring geometric parameters from the models takes some time and is well-suited for exercises, but not a pure lecture course. Here, a group of 20–30 students has been taught, which is the upper limit with one set of structures. In larger courses, multiple sets of structures would need to be prepared. Future work will concentrate on the implementation of scale models in further advanced lecture courses on quantum chemistry as well as written exams.
Supplementary material contains summary of all structures, PDB codes, assignment of filenames and results of evaluation (PDF) as well as all scaled models ready for 3D-printing (ZIP Container with 37 STL files).
We sincerely thank Prof. Dr. Andreas Schmidt for the suggestion of various structures and helpful discussions. We gratefully acknowledge financial support of the Clausthal University of Technology fund for the improvement of study conditions (project: visualization of complex structures). We sincerely thank Marina Schmitt for her patient support during the coloring of the 3D-printed models.
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The online version of this article offers supplementary material (DOI: https://doi.org/10.1515/cti-2019-0006).