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Journal articles on the topic 'Molecular symmetry'

Author: Grafiati

Published: 4 June 2021

Last updated: 19 February 2022

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1

Pidcock, Elna, W. D. Samuel Motherwell, and Jason C. Cole. "A database survey of molecular and crystallographic symmetry." Acta Crystallographica Section B Structural Science 59, no. 5 (September 25, 2003): 634–40. http://dx.doi.org/10.1107/s0108768103012278.

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The point of contact between molecular and crystallographic symmetries is that of the Wyckoff position, the position at which a molecule resides in a crystal structure. These Wyckoff positions may have the same symmetry as the molecules, some symmetry in common with the molecules or no symmetry at all. Using CSDSymmetry [Yao et al. (2002). Acta Cryst. B58, 640–646], a relational database containing information pertaining to the symmetry of molecules and the crystal structures that play host to them, the distribution of molecules over Wyckoff positions and the occupancy of Wyckoff positions in crystal structures is presented. Analysis of these data has led to the characterization of some relationships between molecular and crystallographic symmetry.

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2

Bai, Wen-Ju, and Xiqing Wang. "Appreciation of symmetry in natural product synthesis." Natural Product Reports 34, no. 12 (2017): 1345–58. http://dx.doi.org/10.1039/c7np00045f.

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3

Ivanov, Julian. "Molecular Symmetry Perception." Journal of Chemical Information and Computer Sciences 44, no. 2 (March 2004): 596–600. http://dx.doi.org/10.1021/ci0341868.

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4

Barón, Máximo, Alex D. Bain, and Romina S. Conde. "A dynamic look on molecular symmetry." Canadian Journal of Chemistry 95, no. 7 (July 2017): 736–43. http://dx.doi.org/10.1139/cjc-2016-0657.

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J.H. van’t Hoff’s seminal paper variously titled as either: Chemistry in Space, The Placement of Atoms in Space or other with similar wording, depending on the language it was published in, suggested that the structure of a molecule would be independent of its physical state: solid, liquid, vapor, gaseous, or in solution. However, this is definitely not true so much so that during the last decades many examples have accumulated showing that the structure of a molecule in a crystalline solid can differ substantially from its structure in solution. This would have important consequences not only on how molecules are structurally described and the way they react, but also that molecular symmetry may not be a static property and has to be considered from a dynamic point of view. To add additional evidence to this conception, we took advantage of a family of trans-1,4-di- and tetra-substituted cyclohexane derivatives that appear to have a centre of symmetry but show a substantial dipole moment in solution. In the present work, we used the trans-1,4-dicarboxymethylcyclohexane and its 1,4-dibrominated derivative and were able, through dipole moment determinations IR, Raman, NMR studies, and computational calculations with the SpinWorks, MOPAC, and MOLDEN programs, to confirm our assumption that the molecular symmetry and the molecular structure are dependent on the environment.

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5

Dekhtyar, M. L., V. M. Rozenbaum, N. G. Shkoda, and M. I. Ikim. "Ratchet effect in brownian photomotors: symmetry constraints and going beyond them." Himia, Fizika ta Tehnologia Poverhni 12, no. 2 (June 30, 2021): 124–34. http://dx.doi.org/10.15407/hftp12.02.124.

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The symmetry conditions have been derived for the occurrence of the ratchet effect in Brownian photomotors. To this end, spatiotemporal symmetry operations in vector transformations, coordinate and time shifts, and in the overdamped regime were applied to the average photomotor velocity taken as a functional of the coordinate- and time-dependent potential energy. As established, individual Brownian particles (molecules) can move directionally only provided a symmetrically distributed charge fluctuates in them and they are placed on the substrates with an antisymmetric charge distribution or, vice versa, they are characterized by antisymmetrically distributed charge fluctuations and are placed on symmetric substrates. The collective directed motion of orientation-averaged particles is possible only in the former case. If a particle charge distribution is described by a time dependence with the universal type of symmetry (i.e., simultaneously symmetric, antisymmetric, and shift-symmetric), an additional symmetry constraint on the ratchet functioning arises: the ratchet effect is ruled out in the overdamped regime but allowed for inertial moving particles if the charge distributions in both the particle and the substrate are neither symmetric nor antisymmetric. The effect of the universal type of symmetry is exemplified by dipole photomotors derived from donor-acceptor conjugated organic molecules. With a specific type of molecular photoexcitation and a specific relationship of the dipole moments in the ground and excited states, the ratchet effect becomes symmetry-forbidden. The forbiddenness can be removed by molecular polarization effects, which in this case become the predominant factor governing the direction of the motion and average velocity of photomotors. The estimated velocities of polarization photomotors are an order of magnitude larger than for known motor proteins and dipole Brownian photomotors. These results can be helpful in the purposeful molecular design of dipole photomotors.

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6

HARGITTAI, MAGDOLNA, and ISTVÁN HARGITTAI. "Symmetry in chemistry." European Review 13, S2 (August 22, 2005): 61–75. http://dx.doi.org/10.1017/s1062798705000669.

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Symmetry and chemistry have been in a fruitful interplay, initially in spectroscopy and crystallography, lately in more traditional domains of chemistry, such as reactivity and conformational analysis. A simple phenomenological approach suffices to get an idea about the symmetries of molecules whereas group theoretical approach greatly facilitates the understanding of molecular vibrations, electronic structure, and the mechanism of chemical reactions. In our discussion, the multi-level relationship between symmetry and chemistry is demonstrated by a sampler of examples, including the variations of symmetry of free molecules and molecular packing in crystals. Symmetry considerations continue to assist chemistry in systematizing and interpreting observations and also in discovering new reactions, molecules, and other materials.

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7

Cao, Xiaoping. "Molecular symmetry andab initio calculations. I. Symmetry-matrix and symmetry-supermatrix." Journal of Computational Chemistry 10, no. 7 (October 1989): 957–62. http://dx.doi.org/10.1002/jcc.540100714.

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8

HU, ZHAN-NING, and V. C. LO. "CHIRAL LIPID BILAYERS WITH CYLINDRICAL SYMMETRY." International Journal of Modern Physics B 19, no. 18 (July 20, 2005): 2999–3011. http://dx.doi.org/10.1142/s0217979205030827.

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In this paper, we have studied the chiral lipid bilayers with the tilted fluid phase where the orientation of the molecular tilt varies as a function of the cylindrical coordinates. The rigorous solution of the equation related to the orientation of the long molecular axis is obtained, which describes the property of the tubules with a modulation in the tilt. When the angle of the molecular director is independent of the cylindrical coordinates θ, z, the patterns formed by chiral molecules can be degenerated to the right-handed helix, the left-handed helix, the straight lines, and the circles. The curvature and torsion of the corresponding curves are given explicitly, which denotes the winding of the molecules around the cylinder. We find also that the angle between the director of the molecule and the local normal direction of the cylinder increases if the radius of the cylinder reduces when the tilted angle ϕ from the equator of the cylinder is uniform.

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9

Xue-Zhuang, Zhao, and Xu Xiu-Fang. "The Molecular Fuzzy Symmetry." Acta Physico-Chimica Sinica 20, no. 10 (2004): 1175–78. http://dx.doi.org/10.3866/pku.whxb20041001.

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10

Fritzer, Harald P. "Molecular symmetry with quaternions." Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 57, no. 10 (September 2001): 1919–30. http://dx.doi.org/10.1016/s1386-1425(01)00477-2.

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11

Barron, L. D. "Symmetry and molecular chirality." Chemical Society Reviews 15, no. 2 (1986): 189. http://dx.doi.org/10.1039/cs9861500189.

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12

Bunker, Philip R., Per Jensen, and Christian Jungen. "Molecular Symmetry and Spectroscopy." Physics Today 52, no. 9 (September 1999): 63–64. http://dx.doi.org/10.1063/1.882827.

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13

Michelot, F., and T. Schwartzmann. "Symmetry of molecular properties." Molecular Physics 80, no. 6 (December 20, 1993): 1269–96. http://dx.doi.org/10.1080/00268979300103031.

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14

Sold�n, Pavel. "Extended molecular symmetry groups." Journal of Mathematical Chemistry 20, no. 2 (1996): 331–49. http://dx.doi.org/10.1007/bf01165352.

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15

Cole, Jason C., Jing Wen Yao, Gregory P. Shields, W. D. S. Motherwell, Frank H. Allen, and Judith A. K. Howard. "Automatic detection of molecular symmetry in the Cambridge Structural Database." Acta Crystallographica Section B Structural Science 57, no. 1 (February 1, 2001): 88–94. http://dx.doi.org/10.1107/s010876810001380x.

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A method for the detection of approximate molecular symmetry in crystal structures has been developed. The point-group symmetry is assigned to each molecule and the relevant symmetry elements can be visualized, superimposed on the molecule. The method has been validated against reference structures with exact symmetry subjected to small random perturbation.

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16

Wilson, A. J. C. "Space groups rare for organic structures. III. Symmorphism and inherent molecular symmetry." Acta Crystallographica Section A Foundations of Crystallography 49, no. 6 (November 1, 1993): 795–806. http://dx.doi.org/10.1107/s0108767393003319.

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To a close approximation, the relative frequency of the space groups of molecular organic compounds is determined by ease of packing. When the molecules are in general Wyckoff positions, the relative frequency anticorrelates with the degree of symmorphism. Somewhat different considerations apply if the molecule possesses and uses some inherent symmetry (\overline 1, 2, m, 2/m, 222, mm, ...) [Kitaigorodskii (1955); Kitaigorodskii (1961). Organic Chemical Crystallography. New York: Consultants Bureau]. The observed frequencies are analysed in the light of the degree of symmorphism and molecular symmetry.

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17

Shi, Ping-Ping, Yuan-Yuan Tang, Peng-Fei Li, Wei-Qiang Liao, Zhong-Xia Wang, Qiong Ye, and Ren-Gen Xiong. "Symmetry breaking in molecular ferroelectrics." Chemical Society Reviews 45, no. 14 (2016): 3811–27. http://dx.doi.org/10.1039/c5cs00308c.

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Symmetry breaking occurs between the high-temperature, high-symmetry paraelectric phase and the low-temperature, low-symmetry ferroelectric phase along with a reduction in the number of symmetry elements, obeying the Curie symmetry principle and relating to the ferroelectricity.

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18

Zyss, J., and S. Brasselet. "Multipolar Symmetry Patterns in Molecular Nonlinear Optics." Journal of Nonlinear Optical Physics & Materials 07, no. 03 (September 1998): 397–439. http://dx.doi.org/10.1142/s0218863598000302.

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Organic materials for quadratic nonlinear optics generally follow the basic pattern of strongly dipolar quasi one-dimensional intramolecular charge transfer molecules organized in macroscopic crystalline or statistical polar lattices. This restriction has been lifted by the introduction of the much broader class of multipolar materials whereby efficient two- and three-dimensional molecules can be fruitfully exploited in self assembled or externally engineered multipolar macroscopic structures. At the molecular level, polarized harmonic scattering permits to evaluate the invariant irreducible components of the molecular quadratic tensor. Its anisotropy and dispersion can be accounted for by a three-quantum model in agreement with linear spectroscopy on poled samples, whereas the validity of the two-level model is restricted to one-dimensional systems. Permanent macroscopic multipolar organization can be implemented by purely optical photoinduced processes. Adequate choice of the polarization of "write" beams permits to imprint any desired symmetry pattern onto the (non)linear material. Photonic engineering thus complements and considerably broadens the more traditional scope of molecular engineering.

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19

Voges, K., J. Gripp, H. Hartwig, and H. Dreizler. "Analysis of Torsion in a Three-Top Molecule. Torsional Barrier and Moment of Inertia of Trimethyl Ethynyl Germane." Zeitschrift für Naturforschung A 51, no. 4 (April 1, 1996): 299–305. http://dx.doi.org/10.1515/zna-1996-0409.

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Internal rotation effects for a large number of molecules containing one or two symmetric internal rotors have been investigated using microwave spectroscopy. The high resolution of molecular beam Fourier transform microwave spectroscopy revealed now the internal rotation fine structure in the rotational spectrum of trimethyl ethynyl germane, (CH3)3GeC=CH. After assigning the rotational transition J = 1 → 0 in the vibrational and torsional ground state to the symmetry species of the molecular symmetry group G162 , the torsional barrier V3 and the rotational constant B0 could be determined to (4.5±0.2) kJ/mol and (1823.370±0.010) MHz, respectively.

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20

Mellor, Thomas M., Sergei N. Yurchenko, and Per Jensen. "Artificial Symmetries for Calculating Vibrational Energies of Linear Molecules." Symmetry 13, no. 4 (March 26, 2021): 548. http://dx.doi.org/10.3390/sym13040548.

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Linear molecules usually represent a special case in rotational-vibrational calculations due to a singularity of the kinetic energy operator that arises from the rotation about the a (the principal axis of least moment of inertia, becoming the molecular axis at the linear equilibrium geometry) being undefined. Assuming the standard ro-vibrational basis functions, in the 3N−6 approach, of the form ∣ν1,ν2,ν3ℓ3;J,k,m⟩, tackling the unique difficulties of linear molecules involves constraining the vibrational and rotational functions with k=ℓ3, which are the projections, in units of ℏ, of the corresponding angular momenta onto the molecular axis. These basis functions are assigned to irreducible representations (irreps) of the C2v(M) molecular symmetry group. This, in turn, necessitates purpose-built codes that specifically deal with linear molecules. In the present work, we describe an alternative scheme and introduce an (artificial) group that ensures that the condition ℓ3=k is automatically applied solely through symmetry group algebra. The advantage of such an approach is that the application of symmetry group algebra in ro-vibrational calculations is ubiquitous, and so this method can be used to enable ro-vibrational calculations of linear molecules in polyatomic codes with fairly minimal modifications. To this end, we construct a—formally infinite—artificial molecular symmetry group D∞h(AEM), which consists of one-dimensional (non-degenerate) irreducible representations and use it to classify vibrational and rotational basis functions according to ℓ and k. This extension to non-rigorous, artificial symmetry groups is based on cyclic groups of prime-order. Opposite to the usual scenario, where the form of symmetry adapted basis sets is dictated by the symmetry group the molecule belongs to, here the symmetry group D∞h(AEM) is built to satisfy properties for the convenience of the basis set construction and matrix elements calculations. We believe that the idea of purpose-built artificial symmetry groups can be useful in other applications.

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21

Chen, Guo-Qiang. "Symmetry elements and molecular achirality." Journal of Chemical Education 69, no. 2 (February 1992): 159. http://dx.doi.org/10.1021/ed069p159.

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22

Whiffen, D. H. "Ensemble averages and molecular symmetry." Molecular Physics 63, no. 6 (April 20, 1988): 1053–69. http://dx.doi.org/10.1080/00268978800100761.

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23

Brown, R. J. C., and R. F. C. Brown. "Melting Point and Molecular Symmetry." Journal of Chemical Education 77, no. 6 (June 2000): 724. http://dx.doi.org/10.1021/ed077p724.

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24

Dannenfelser, R. M., N. Surendran, and S. H. Yalkowsky. "Molecular Symmetry and Related Properties." SAR and QSAR in Environmental Research 1, no. 4 (December 1993): 273–92. http://dx.doi.org/10.1080/10629369308029892.

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25

Royer, W. E., and W. A. Hendrickson. "Molecular symmetry of Lumbricus erythrocruorin." Journal of Biological Chemistry 263, no. 27 (September 1988): 13762–65. http://dx.doi.org/10.1016/s0021-9258(18)68307-3.

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26

Delaney, P., M. Nolan, and J. C. Greer. "Symmetry, delocalization, and molecular conductance." Journal of Chemical Physics 122, no. 4 (January 22, 2005): 044710. http://dx.doi.org/10.1063/1.1836754.

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27

Balasubramanian, K. "Computer Perception of Molecular Symmetry." Journal of Chemical Information and Modeling 35, no. 4 (July 1, 1995): 761–70. http://dx.doi.org/10.1021/ci00026a015.

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28

Martin, A. Scott, and J. Roy Sambles. "Molecular rectification, photodiodes and symmetry." Nanotechnology 7, no. 4 (December 1, 1996): 401–5. http://dx.doi.org/10.1088/0957-4484/7/4/017.

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29

Liu, Jun. "Hidden symmetry in molecular graphs." Journal of the Chemical Society, Faraday Transactions 93, no. 1 (1997): 5–9. http://dx.doi.org/10.1039/a602071b.

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30

Schlame, Michael, Mindong Ren, Yang Xu, Miriam L. Greenberg, and Ivan Haller. "Molecular symmetry in mitochondrial cardiolipins." Chemistry and Physics of Lipids 138, no. 1-2 (December 2005): 38–49. http://dx.doi.org/10.1016/j.chemphyslip.2005.08.002.

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31

Fieck, Gerhard. "Permutation representations in molecular symmetry." Theoretica Chimica Acta 73, no. 4 (April 1988): 247–77. http://dx.doi.org/10.1007/bf00527414.

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32

Cammi, R., L. Oleari, and C. Oleari. "Symmetry descent in molecular systems." Il Nuovo Cimento D 8, no. 1 (July 1986): 1–18. http://dx.doi.org/10.1007/bf02450462.

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33

Baburin, Igor A., and Vladislav A. Blatov. "Three-dimensional hydrogen-bonded frameworks in organic crystals: a topological study." Acta Crystallographica Section B Structural Science 63, no. 5 (September 14, 2007): 791–802. http://dx.doi.org/10.1107/s0108768107033137.

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1551 homomolecular single hydrogen-bonded frameworks in organic crystals have been classified into 148 topological types of three-periodic nets. Different representations of hydrogen-bonded frameworks as nets of molecular centroids, edge or ring nets are discussed. To study the influence of hydrogen bonds on the topology of molecular packings, 42 270 molecular crystals without hydrogen bonds have been considered. The topologies of molecular packings are found to be independent of hydrogen bonding. Analysis of 231 homomolecular frameworks composed of crystallographically different molecules shows that molecules not related by symmetry tend to form the same hydrogen-bond pattern. The relations between net topological types, space-group symmetry of crystals, site symmetry and point-group symmetry of molecules are discussed. As a result, a set of rules for the crystal design of molecular frameworks is proposed.

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34

Redžepović, Izudin, Slavko Radenković, and Boris Furtula. "Effect of a Ring onto Values of Eigenvalue–Based Molecular Descriptors." Symmetry 13, no. 8 (August 18, 2021): 1515. http://dx.doi.org/10.3390/sym13081515.

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The eigenvalues of the characteristic polynomial of a graph are sensitive to its symmetry-related characteristics. Within this study, we have examined three eigenvalue–based molecular descriptors. These topological molecular descriptors, among others, are gathering information on the symmetry of a molecular graph. Furthermore, they are being ordinarily employed for predicting physico–chemical properties and/or biological activities of molecules. It has been shown that these indices describe well molecular features that are depending on fine structural details. Therefore, revealing the impact of structural details on the values of the eigenvalue–based topological indices should give a hunch how physico–chemical properties depend on them as well. Here, an effect of a ring in a molecule on the values of the graph energy, Estrada index and the resolvent energy of a graph is examined.

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35

Wilhelm, Philipp, Jakob Schedlbauer, Florian Hinderer, Daniel Hennen, Sigurd Höger, Jan Vogelsang, and John M. Lupton. "Molecular excitonic seesaws." Proceedings of the National Academy of Sciences 115, no. 16 (April 2, 2018): E3626—E3634. http://dx.doi.org/10.1073/pnas.1722229115.

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The breaking of molecular symmetry through photoexcitation is a ubiquitous but rather elusive process, which, for example, controls the microscopic efficiency of light harvesting in molecular aggregates. A molecular excitation within a π-conjugated segment will self-localize due to strong coupling to molecular vibrations, locally changing bond alternation in a process which is fundamentally nondeterministic. Probing such symmetry breaking usually relies on polarization-resolved fluorescence, which is most powerful on the level of single molecules. Here, we explore symmetry breaking by designing a large, asymmetric acceptor–donor–acceptor (A1-D-A2) complex 10 nm in length, where excitation energy can flow from the donor, a π-conjugated oligomer, to either one of the two boron-dipyrromethene (bodipy) dye acceptors of different color. Fluorescence correlation spectroscopy (FCS) reveals a nondeterministic switching between the energy-transfer pathways from the oligomer to the two acceptor groups on the submillisecond timescale. We conclude that excitation energy transfer, and light harvesting in general, are fundamentally nondeterministic processes, which can be strongly perturbed by external stimuli. A simple demonstration of the relation between exciton localization within the extended π-system and energy transfer to the endcap is given by considering the selectivity of endcap emission through the polarization of the excitation light in triads with bent oligomer backbones. Bending leads to increased localization so that the molecule acquires bichromophoric characteristics in terms of its fluorescence photon statistics.

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36

Maruani, Jean, and Alejandro Toro-Labbé. "Conjugate symmetry of molecular systems and determination of their conformations." Canadian Journal of Chemistry 66, no. 8 (August 1, 1988): 1948–56. http://dx.doi.org/10.1139/v88-314.

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In nonrigid molecules and molecular aggregates, the dependence of a property on conformation may be expressed in the form of a limited expansion in terms of appropriate harmonics. The use of the conjugate symmetry of the molecular groups to reduce such an expansion may have several advantages: (i) it helps decrease, sometimes drastically, the time required to calculate the conformational dependence of the considered property; (ii) it provides a parameterized functional form that can be used by experimentalists to rationalize their results. The symmetry rules that define the distinct non-zero harmonics are determined by a set of indices that depend on both the form and type of the property (scalar, polar, axial, tensorial; aggregate, mononuclear, binuclear) and the nature of the isodynamic operations characterizing the system. We have applied Altmann's isodynamic groups to the analysis of Wigner's harmonic expansions of dynamical, electric, and magnetic properties of various molecular structures: binary molecular associations, quasi-atoms in molecular fields, rigid molecules in crystal lattices, and non-rigid molecules involving one to three rotors. A few examples are given to illustrate these considerations.

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37

Kudlicki, Andrzej, Małgorzata Rowicka, Mirosław Gilski, and Zbyszek Otwinowski. "An efficient routine for computing symmetric real spherical harmonics for high orders of expansion." Journal of Applied Crystallography 38, no. 3 (May 13, 2005): 501–4. http://dx.doi.org/10.1107/s0021889805007685.

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A numerically efficient method of constructing symmetric real spherical harmonics is presented. Symmetric spherical harmonics are real spherical harmonics with built-in invariance with respect to rotations or inversions. Such symmetry-invariant spherical harmonics are linear combinations of non-symmetric ones. They are obtained as eigenvectors of an appropriate operator, depending on symmetry. This approach allows for fast and stable computation up to very high order symmetric harmonic bases, which can be used in e.g. averaging of non-crystallographic symmetry in protein crystallography or refinement of large viruses in electron microscopy.

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38

Miao, Le-Ping, Lin-Lin Chu, Xiang-Bin Han, Bei-Dou Liang, Chao-Yang Chai, Chang-Chun Fan, Xiao-Xu Wang, Ye-Feng Yao, and Wen Zhang. "A ferroelastic molecular rotor crystal showing inverse temperature symmetry breaking." Inorganic Chemistry Frontiers 8, no. 11 (2021): 2809–16. http://dx.doi.org/10.1039/d1qi00309g.

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A molecular rotor crystal shows a ferroelastic phase transition with unique inverse temperature symmetry breaking which is a result of concerted molecular movement triggered by anisotropic steric repulsion among adjacent molecules.

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39

Rossmann, M. G., R. McKenna, L. Tong, D. Xia, J. Dai, H. Wu, H. K. Choi, and R. E. Lynch. "Molecular replacement real-space averaging." Journal of Applied Crystallography 25, no. 2 (April 1, 1992): 166–80. http://dx.doi.org/10.1107/s002188989101141x.

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Structure determination of macromolecules often depends on phase improvement and phase extension by use of real-space averaging of electron density related by noncrystallographic symmetry. Although techniques for such procedures have been described previously [Bricogne (1976). Acta Cryst. A32, 832–847; Johnson (1978). Acta Cryst. B34, 576–577], modern computer architecture and experience with these methods have suggested changes and improvements. Two unit cells are considered: (1) the p-cell corresponding to the actual crystal structure(s) being determined (there would be more than one of these if the molecule crystallizes in more than one crystal form) and (2) the h-cell corresponding to the molecule in a standard orientation with respect to which the molecular symmetry axes are defined. Averaging can proceed entirely within the p-cell, referring to the h-cell only in as far as knowledge of the molecular symmetry is required. It is also possible to place the averaged molecule back into the h-cell, where it can be used to redefine the molecular envelope or for displaying a suitably chosen asymmetric unit of the molecule. Techniques are discussed for automatically selecting a molecular envelope which is consistent with packing considerations within the p-cell and which retains the symmetry of the molecular point group. The electron density map to be averaged is divided into bricks for storage in virtual memory. Roughly as many bricks as there are noncrystallographic asymmetric units per crystallographic asymmetric unit need to be retained in memory at one time. This procedure minimizes paging problems and avoids double sorting. Use of eight-point interpolation permits storing the map at grid points separated by no more than 1/2.5 of the resolution limit to obtain rapid convergence.

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40

Del Bene, Janet E., Kyungsun Kim, and Isaiah Shavitt. "An ab initio study of symmetry breaking in calculations on the first excited singlet state of N2H2." Canadian Journal of Chemistry 69, no. 2 (February 1, 1991): 246–50. http://dx.doi.org/10.1139/v91-039.

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Calculation of the vertically excited singlet n → π* state of trans-N2H2 carried out in Cs symmetry at the RHF and RHF-CISD levels results in a broken symmetry solution in which the wave function does not reflect the C2h symmetry of the molecular framework. The excited state RHF energy computed in Cs symmetry is lower than the corresponding energy computed in C2h symmetry, but the single-reference CISD energy based on the Cs RHF configuration is higher than the corresponding C2h result. The symmetry breaking leads to difficulties in the description of the excited state potential energy surface, including the location of stationary points and the calculation of vibrational frequencies, and in the treatment of complexes of excited N2H2 with other molecules. The molecular symmetry of the vertically excited state can be restored in Cs calculation by the use of a four-configuration MCSCF wave function. The MCSCF procedure provides consistent data and leads to the prediction that the relaxed excited state has C2 molecular symmetry. Unlike the RHF case, the UHF wave function does not display symmetry breaking at the C2h geometry, and agrees with the MCSCF model in predicting an equilibrium structure of C2 symmetry. A low-energy structure of C2 symmetry has also been found with the UMP2 model, although it could not be positively confirmed that it corresponds to an equilibrium structure. The symmetry-breaking dilemma is not unique to the excited n → π* state of N2H2, but arises in other molecules in which the two chromophores are similarly symmetry related. Key words: symmetry breaking, excited state, MCSCF, N2H2.

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41

Koç, Ramazan, Hayriye Tütüncüler, and Atalay Küçükbursa. "Symmetry and Molecular Orbitals of C60." Mathematical and Computational Applications 2, no. 2 (August 1, 1997): 91–100. http://dx.doi.org/10.3390/mca2020091.

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42

Fedosky, Edward W., and William F. Coleman. "Teaching Molecular Symmetry with JCE WebWare." Journal of Chemical Education 82, no. 11 (November 2005): 1741. http://dx.doi.org/10.1021/ed082p1741.1.

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43

Balasubramanian, K. "Graph theoretical perception of molecular symmetry." Chemical Physics Letters 232, no. 5-6 (January 1995): 415–23. http://dx.doi.org/10.1016/0009-2614(94)01382-6.

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Gong, Juliane Q., Ludovic Favereau, Harry L. Anderson, and Laura M. Herz. "Breaking the Symmetry in Molecular Nanorings." Journal of Physical Chemistry Letters 7, no. 2 (January 8, 2016): 332–38. http://dx.doi.org/10.1021/acs.jpclett.5b02617.

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Tsoucaris, G., and G. Le Bas. "Symmetry and molecular recognition in clathrates." Acta Crystallographica Section A Foundations of Crystallography 49, s1 (August 21, 1993): c198. http://dx.doi.org/10.1107/s0108767378094362.

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Baikalov, Igor, and Richard E. Dickerson. "Molecular Replacement Using DNA Helical Symmetry." Acta Crystallographica Section D Biological Crystallography 54, no. 3 (May 1, 1998): 324–33. http://dx.doi.org/10.1107/s0907444997010512.

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Abstract:

The efficiency of molecular-replacement methods in the structure analysis of B-DNA is markedly increased if a knowledge of the structural properties and helical symmetry of B-DNA is incorporated into molecular-replacement procedures. The separation of the most significant or most robust parameters, such as the location of helices in the unit cell, from the less well defined parameters, such as rotation around the helix axis, further improves the reliability of molecular replacement and avoids frameshift errors in the positioning of the model. This approach has been applied successfully to solve novel structures of four B-DNA decamers in various space groups.

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Lafortune, S., S. Tremblay, and P. Winternitz. "Symmetry classification of diatomic molecular chains." Journal of Mathematical Physics 42, no. 11 (November 2001): 5341–57. http://dx.doi.org/10.1063/1.1398583.

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Yan, Linghao, Muqing Hua, Qiushi Zhang, Tsz Ue Ngai, Zesheng Guo, Tsz Chun Wu, Tong Wang, and Nian Lin. "Symmetry breaking in molecular artificial graphene." New Journal of Physics 21, no. 8 (August 5, 2019): 083005. http://dx.doi.org/10.1088/1367-2630/ab34a6.

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Zhan, Chang-Guo. "Maximum overlap symmetry molecular orbital model." International Journal of Quantum Chemistry 44, no. 2 (September 5, 1992): 123–40. http://dx.doi.org/10.1002/qua.560440205.

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Flurry, R. L. "Site symmetry in molecular point groups." International Journal of Quantum Chemistry 6, S6 (June 18, 2009): 455–58. http://dx.doi.org/10.1002/qua.560060654.

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