Website | Home URL |
Division | Physical |
Title |
|
Specialties |
|
wmg@chem.ucla.edu | |
Office | Young Hall 3047 |
Office Phone | (310) 825-2005 |
Lab | Young Hall 3107 |
Office Lab | (310) 825-6790 |
Biography
B.S., Harvard University (1967); Ph.D., University of Chicago (1970); NSF Postdoctoral Fellow, University of Paris-Orsay (1971); Miller Institute Fellow, University of California, Berkeley (1971-1972); Alfred P. Sloan Research Fellow (1974); Camille and Henry Dreyfus Teacher-Scholar Award (1976); Glenn T. Seaborg Award (1981); Hanson-Dow Distinguished Teaching Award (1986); American Physical Society Fellow (1987); Herbert Newby McCoy Award (1988); Brotherton Professor, University of Leeds (1988); Royal Society of Chemistry/Lennard-Jones Medal (1991); University Distinguished Teaching Award (1996); J. S. Guggenheim Fellowship (1998-1999); Rothschild Professor, Institut Curie, Paris (1999); American Chemical Society “Liquids” (Hildebrand) Prize (2001); Laughlin Professor, Cornell University (2006); Fellow of American Academy of Arts and Sciences (2009); Festschrift issue of J. Phys. Chem. (2016); Glenn T. Seaborg Medal (2017).
Research Interests
After 25 years of theoretical work in statistical mechanics, focusing on structure and phase transitions involving increasingly complex fluids – e.g., liquid crystals, self-assembling amphiphilic molecules, polymer solutions, and colloidal suspensions – I became seduced by viruses around 20 years ago and have been working ever since on trying to understand how they “work”. Collaborating with Avi Ben-Shaul on theory predicting high pressures in DNA viruses and various aspects of the self-assembly of RNA viruses, I started a lab with my colleague Chuck Knobler to carry out experiments on a broad range of physical aspects of viruses. We performed the first measurement of the pressure (~50 atm) in a DNA virus, and started taking simple RNA viruses apart and trying to put them back together again. We also made the first structure determinations of RNA viral genomes in their native state in solution, using synchrotron small-angle X-ray scattering, fluorescence correlation spectroscopy, and cryo-electron microscopy. Over the past 10 years we have included plant, insect, and mammalian viruses in our menagerie of RNA genome viruses, and have moved from exclusively in vitro work (purified viral components in test tubes) to studying how these viruses work in host cells. We have also begun to collaborate with pharmaceutical and biotech companies, and with medical research teams, on using our in vitro self-assembled virus-like particles containing therapeutic mRNA for gene and vaccine delivery purposes.
Honors & Awards
- Cornell University Laughlin Lecturer
- UCLA H. N. McCoy Award
- Case Western Reserve University Bikerman Lecturer
- American Chemical Society “Liquids” (Hildebrand) Prize
- Institut Curie Rothschild Lecturer
- J. S. Guggenheim Fellowship
- UCLA Luckman Distinguished Teaching Award
- British Royal Society Lennard-Jones Medal
- UCLA H. N. McCoy Award
- University of Leeds Brotherton Lecturer
- American Physical Society Fellow
- UCLA Hanson-Dow Distinguished Teaching Award
- UCLA Glenn T. Seaborg Award
- Camille and Henry Dreyfus Teacher-Scholar Award
- Alfred P. Sloan Fellowship
- Elected to Michigan Society of Fellows
- Miller Institute Fellowship at Berkeley
- N.S.F. – N.A.T.O. Postdoctoral Fellowship
- N.S.F. Traineeship
- Harvard College Scholarship
- American Academy of Arts and Sciences
Representative Publications
- Knobler, C. M., Gelbart, W. M. (2022) How and why RNA genomes are (partially) ordered in viral capsids. Curr. Opin. Virol. 52:203-210.
- Tanimoto, C. R., Thurm, A. R., Brandt, D. S., Knobler, C. M., Gelbart, W. M. (2022) The Nonmonotonic Dose Dependence of Protein Expression in Cells Transfected with Self-Amplifying RNA. J. Virol. 96 (7). doi: 10.1128/jvi.01858-21.
- Duran-Meza, A. L., Villagrande-Escareno, M. V., Ruiz-Garcia, J., Knobler, C. M., Gelbart, W. M. (2021) Controlling the surface charge of simple viruses. PLoS ONE, 16(9): e0255820.
- Beren, C., Cui, Y., Chakravarty, A., Yang, X., Knobler, C. M, Zhou, Z. H., Gelbart, W. M. (2020) Genome organization and interaction with capsid protein in a multipartite RNA virus. PNAS, 117 (20), 10673-80.
- Thurm, A. R., Beren, C., Duran-Meza, A. L., Knobler, C. M., Gelbart, W. M. (2019) RNA homopolymers form higher-curvature virus-like particles than do normal-composition RNAs. Biophysical Journal, 117 (7), 1331-41.
- Chung, S., Lerner, E., Jin, Y., Kim, S., Alhadid, Y., Grimaud, L. W., Zhang, I. X., Knobler, C. M., Gelbart, W. M., Weiss, S. (2019) The effect of macromolecular crowding on single-round transcription by Escherichia coli RNA polymerase. Nucleic Acids Research, 47 (3), 1440-50.
- Biddlecome, A., Habte, H. H., McGrath, K. M, Sambanthamoorthy, S., Wurm, M., Sykora, M. M., Knobler, C. M., Lorenz, I. C., Lasaro, M., Elbers, K., Gelbart, W. M. (2019) Delivery of self-amplifying RNA vaccines in in vitro reconstituted virus-like particles. PLoS ONE, 14 (6): e0215031.
- Beren, C. B., Liu, K. N., Dreesens, L. L., Knobler, C. M., Gelbart, W. M. (2018) Enzymatic Synthesis and Fractionation of Fluorescent PolyU RNAs. Bio-protocols, 8 (17) e2988.
- Garmann R. F., Knobler C. M., Gelbart W. M. (2018) Protocol for Efficient Cell-Free Synthesis of Cowpea Chlorotic Mottle Virus-Like Particles Containing Heterologous RNAs. In: Wege C., Lomonossoff G. (eds) Virus-Derived Nanoparticles for Advanced Technologies. Methods in Molecular Biology, vol 1776. Humana Press, New York, NY
- Chen, Y. J., Wu, D., Gelbart, W. M., Knobler, C. M., Phillips, R., Kegel, W. K. (2018) Two-Stage Dynamics of In Vivo Bacteriophage Genome Ejection. Phys. Rev. X, American Physical Society, 8, 021029.
- Beren, C., Dreesens, L. L., Liu, K. N., Knobler, C. M., & Gelbart, W. M. (2017). The effect of RNA secondary structure on the self-assembly of viral capsids. Biophysical journal, 113, 339-347.
- Chung, S., Lerner, E., Jin, Y., Kim, S., Alhadid, Y., Grimaud, L. W., . . . Weiss, S. (2017). The effect of macromolecular crowding on single-round transcription by E. coli RNA polymerase. bioRxiv, 218321.
- Borodavka, A., Singaram, S. W., Stockley, P. G., Gelbart, W. M., Ben-Shaul, A., & Tuma, R. (2016). Sizes of long RNA molecules are determined by the branching patterns of their secondary structures. Biophysical journal, 111, 2077-2085.
- Garmann, R. F., Gopal, A., Athavale, S. S., Knobler, C. M., Gelbart, W. M., & Harvey, S. C. (2015). Visualizing the global secondary structure of a viral RNA genome with cryo-electron microscopy. Rna, 21(5), 877-86.
- Ben-Shaul, A., & Gelbart, W. M. (2015). Viral ssRNAs are indeed compact. Biophysical journal, 108, 14-16.
- Garmann, R. F., Comas-Garcia, M., Knobler, C. M., & Gelbart, W. M. (2015). Physical principles in the self-assembly of a simple spherical virus. Accounts of chemical research, 49, 48-55.
- Jin, Y., Sdao, S. M., Dover, J. A., Porcek, N. B., Knobler, C. M., Gelbart, W. M., & Parent, K. N. (2015). Bacteriophage P22 ejects all of its internal proteins before its genome. Virology, 485, 128-134.
- Singaram, S. W., Garmann, R. F., Knobler, C. M., Gelbart, W. M., & Ben-Shaul, A. (2015). Role of RNA branchedness in the competition for viral capsid proteins. The Journal of Physical Chemistry B, 119, 13991-14002.
- Jin, Y., Knobler, C. M., & Gelbart, W. M. (2015). Controlling the extent of viral genome release by a combination of osmotic stress and polyvalent cations. Physical Review E, 92, 022708.
- Gelbart, W. M. (2015). DNA–peptide complexes: Regulation of interferon production. Nature materials, 14, 661.
- Garmann, R. F., Sportsman, R., Beren, C., Manoharan, V. N., Knobler, C. M., & Gelbart, W. M. (2015). A simple RNA-DNA scaffold templates the assembly of monofunctional virus-like particles. Journal of the American Chemical Society, 137, 7584-7587.
- Gopal, A., Egecioglu, D. E., Yoffe, A. M., Ben-Shaul, A., Rao, A. L., Knobler, C. M., & Gelbart, W. M. (2014). Viral RNAs are unusually compact. PLoS One, 9, e105875.
- Comas-Garcia, M., Garmann, R. F., Singaram, S. W., Ben-Shaul, A., Knobler, C. M., & Gelbart, W. M. (2014). Characterization of viral capsid protein self-assembly around short single-stranded RNA. The Journal of Physical Chemistry B, 118, 7510-7519.
- Garmann, R. F., Comas-Garcia, M., Koay, M. S., Cornelissen, J. J., Knobler, C. M., & Gelbart, W. M. (2014). The role of electrostatics in the assembly pathway of a single-stranded RNA virus. Journal of virology, JVI–01044.
- Garmann, R. F., Comas-Garcia, M., Gopal, A., Knobler, C. M., & Gelbart, W. M. (2014). The assembly pathway of an icosahedral single-stranded RNA virus depends on the strength of inter-subunit attractions. Journal of molecular biology, 426, 1050-1060.
- Vega-Acosta, J. R., Cadena-Nava, R. D., Gelbart, W. M., Knobler, C. M., & Ruiz-Garcı́a, J. (2014). Electrophoretic mobilities of a viral capsid, its capsid protein, and their relation to viral assembly. The Journal of Physical Chemistry B, 118, 1984-1989.
- Azizgolshani, O., Garmann, R. F., Cadena-Nava, R., Knobler, C. M., & Gelbart, W. M. (2013). Reconstituted plant viral capsids can release genes to mammalian cells. Virology, 441, 12-17.
- Cadena-Nava, R. D., Comas-Garcia, M., Garmann, R. F., Rao, A. L., Knobler, C. M., & Gelbart, W. M. (2012). Self-assembly of viral capsid protein and RNA molecules of different sizes: requirement for a specific high protein/RNA mass ratio. Journal of virology, 86, 3318-3326.
- Gopal, A., Zhou, Z. H., Knobler, C. M., & Gelbart, W. M. (2012). Visualizing large RNA molecules in solution. Rna, 18, 284-299.
- Gelbart, W. M., Ben-Shaul, A., & Roux, D. (2012). Micelles, membranes, microemulsions, and monolayers. Springer Science & Business Media.
- Comas-Garcia, M., Cadena-Nava, R. D., Rao, A. L., Knobler, C. M., & Gelbart, W. M. (2012). In vitro quantification of the relative packaging efficiencies of single-stranded RNA molecules by viral capsid protein. Journal of virology, JVI–01695.
- Fang, L. T., Gelbart, W. M., & Ben-Shaul, A. (2011). The size of RNA as an ideal branched polymer. The Journal of chemical physics, 135, 10B616.
- Snyder, J. E., Azizgolshani, O., Wu, B., He, Y., Lee, A. C., Jose, J., Suter, D. M., Knobler, C. M., Gelbart, W. M., Kuhn, R. J. (2011). Rescue of Infectious Particles from Pre-assembled Alphavirus Nucleocapsid Cores. Journal of virology.
- Fang, L. T., Yoffe, A. M., Gelbart, W. M., & Ben-Shaul, A. (2011). A sequential folding model predicts length-independent secondary structure properties of long ssRNA. The Journal of Physical Chemistry B, 115, 3193-3199.
- Cadena-Nava, R. D., Hu, Y., Garmann, R. F., Ng, B., Zelikin, A. N., Knobler, C. M., & Gelbart, W. M. (2011). Exploiting fluorescent polymers to probe the self-assembly of virus-like particles. The Journal of Physical Chemistry B, 115, 2386-2391.
- Qiu, X., Rau, D. C., Parsegian, V. A., Fang, L. T., Knobler, C. M., & Gelbart, W. M. (2011). Salt-dependent DNA-DNA spacings in intact bacteriophage λ reflect relative importance of DNA self-repulsion and bending energies. Physical review letters, 106, 028102.
- Yoffe, A. M., Prinsen, P., Gelbart, W. M., & Ben-Shaul, A. (2010). The ends of a large RNA molecule are necessarily close. Nucleic acids research, 39, 292-299.
- Prinsen, P., Schoot, P., Gelbart, W. M., & Knobler, C. M. (2010). Multishell structures of virus coat proteins. The Journal of Physical Chemistry B, 114, 5522-5533.
- Knobler, C. M., & Gelbart, W. M. (2010). What Determines the Size of an RNA Virus? In Emerging Topics in Physical Virology (pp. 185-215). World Scientific.
- Knobler, C. M.Gelbart, W. M. Physical chemistry of DNA viruses Annu Rev Phys Chem, 2009; 60: 367-83.
- Gelbart WM, Knobler CM Presssurized Viruses Science, 2009; 323(5922): 1682-1683.
- Prinsen P, Fang LT, Yoffe AM, Knobler CM, Gelbart WM The Force Acting on a Polymer Partially confined in a Tube J Phys Chem B, 2009; 113(12): 3873-3879.
- Chang, C. B.Knobler, C. M.Gelbart, W. M.Mason, T. G. Curvature dependence of viral protein structures on encapsidated nanoemulsion droplets ACS Nano, 2008; 2(2): 281-6.
- Evilevitch, A., Fang, L.-T., Yoffe, A. M., Castelnuovo, M., Rau, D. C., Parsegian, Gelbart W. M. and Knobler,. C. M. Effects of Salt Concentrations and Bending Energy on the Extent of Ejection of Phage Genomes Biophys. J., 2008; 94(3): 1110-1120.
- Ng, B.C.; Yu, M.; Gopal, A.; Rome, L.H.; Monbouquette, H.G.; and Tolbert, S.H. Encapsulation of Semiconducting Polymers in Vault Protein Cages Nano Letters, 2008; 8(10): 3503?3509.
- Hu, Y.Zandi, R.Anavitarte, A.Knobler, C. M.Gelbart, W. M. Packaging of a polymer by a viral capsid: the interplay between polymer length and capsid size Biophys J, 2008; 94(4): 1428-36.
- Yoffe, A. M.Prinsen, P.Gopal, A.Knobler, C. M.Gelbart, W. M.Ben-Shaul, A. Predicting the sizes of large RNA molecules Proc Natl Acad Sci U S A, 2008; 105(42): 16153-8.
- Knobler, C.M. and W.M. Gelbart The Physics of Phages Physics Today, 2008; 61(1): 42-47.
- Johnson RR, Watt R, Kovac B, Zyuzin A, Van Lier E, Erdman KL, Gyles W, Sabaiduc V, McQuarrie SA, Wilson J, Backhouse C, Gelbart W, Kuo T Advances in intense beams, beam delivery, targetry, and radiochemistry at advanced cyclotron systems NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH SECTION B-BEAM INTERACTIONS WITH MATERIALS AND ATOMS , 2007; 261(1-2): 803-808.
- Lobo NF, Campbell KS, Thaner D, deBruyn B, Koo H, Gelbart WM, Loftus BJ, Severson DW, Collins FH Analysis of 14 BAC sequences from the Aedes aegypti genome: a benchmark for genome annotation and assembly Genome Biology, 2007; 8(5): r88.
- Bhutkar A, Russo SM, Smith TF, Gelbart WM Genome-scale analysis of positionally relocated genes Genome Research, 2007; 17(12): 1880-1887.
- Lin MF, Carlson JW, Crosby MA, Matthews BB, Yu C, Park S, Wan KH, Schroeder AJ, Gramates LS, Pierre SES, Roark M, Wiley KL, Kulathinal RJ, Zhang PL, Myrick KV, Antone JV, Celniker SE, Gelbart WM, Kellis M Revisiting the protein-coding gene catalog of Drosophila melanogaster using 12 fly genomes Genome Research, 2007; 17(12): 1823-1836.
- Nguyen, T. T. Bruinsma, R. F. Gelbart, W. M. Continuum theory of retroviral capsids Phys Rev Lett, 2006; 96(7): 078102.
- Inamdar MM, Gelbart WM, Phillips R Dynamics of DNA ejection from bacteriophage Biophysical Journal, 2006; 91(2): 411-420.
- Grayson, P. Evilevitch, A. Inamdar, M. M. Purohit, P. K. Gelbart, W. M. Knobler, C. M. Phillips, R. The effect of genome length on ejection forces in bacteriophage lambda Virology, 2006; 348(2): 430-436.
- Nguyen, T. T. Bruinsma, R. F. and Gelbart, W. M. Elasticity theory and shape transitions of viral shells Phys Rev E Stat Nonlin Soft Matter Phys, 2005; 72(5 Pt 1): 051923.
- Evilevitch, A. Gober, J. W. Phillips, M. Knobler, C. M. and Gelbart, W. M. Measurements of DNA lengths remaining in a viral capsid after osmotically suppressed partial ejection Biophys J, 2005; 88(1): 751-756.
- Bagatella-Flores, N., H. Schiessel and W. M. Gelbart Statics and Dynamics of Polymer-Wrapped Colloids J. Phys. Chem B, 2005; 109(45): 21305-21312.
- Borukhov, I. Bruinsma, R. F. Gelbart, W. M. Liu, A. J. Structural polymorphism of the cytoskeleton: a model of linker-assisted filament aggregation Proc Natl Acad Sci U S A, 2005; 102(10): 3673-3678.
- Tzlil, S. Deserno, M. Gelbart, W. M. and Ben-Shaul, A. A statistical-thermodynamic model of viral budding Biophys J, 2004; 86(4): 2037-2048.
- Lee, K. C. Borukhov, I. Gelbart, W. M. Liu, A. J. and Stevens, M. J. Effect of mono- and multivalent salts on angle-dependent attractions between charged rods Phys Rev Lett, 2004; 93(12): 128101.
- Evilevitch, A. Martin Castelnovo, C.M. Knobler and W.M. Gelbart Measuring the Force Ejecting DNA from Phage J. Phys. Chem B, 2004; 108(21): 6838?6843.
- Zandi, R. Reguera, D. Bruinsma, R. F. Gelbart, W. M. and Rudnick, J. Origin of icosahedral symmetry in viruses Proc Natl Acad Sci U S A, 2004; 101(44): 15556-15560.
- Castelnovo, M. and W.M. Gelbart Semiflexible Chain Condensation by Neutral Depleting Agents: Role of Correlations between Depletants Macromolecules, 2004; 37(9): 3510?3517.
- Tzlil, S. Kindt, J. T. Gelbart, W. M. Ben-Shaul, A. Forces and pressures in DNA packaging and release from viral capsids Biophys J, 2003; 84(3): 1616-1627.
- Castelnovo, M. Bowles, R. K. Reiss, H. Gelbart, W. M. Osmotic force resisting chain insertion in a colloidal suspension Eur Phys J E Soft Matter, 2003; 10(2): 191-197.
- Evilevitch, A. Lavelle, L. Knobler, C. M. Raspaud, E. Gelbart, W. M. Osmotic pressure inhibition of DNA ejection from phage Proc Natl Acad Sci U S A, 2003; 100(16): 9292-9295.
- Cordova, A. Deserno, M. Gelbart, W. M. and Ben-Shaul, A. Osmotic shock and the strength of viral capsids Biophys J, 2003; 85(1): 70-74.
- Bruinsma, R. F. Gelbart, W. M. Reguera, D. Rudnick, and J. Zandi, R. Viral self-assembly as a thermodynamic process Phys Rev Lett, 2003; 90(24): 248101.
- Zandi, R. Reguera, D. Rudnick, J. and Gelbart, W. M. What drives the translocation of stiff chains? Proc Natl Acad Sci U S A, 2003; 100(15): 8649-8653.
- Huet, F. Lu, J. T. Myrick, K. V. Baugh, L. R. Crosby, M. A. and Gelbart, W. M. A deletion-generator compound element allows deletion saturation analysis for genomewide phenotypic annotation Proc Natl Acad Sci U S A, 2002; 99(15): 9948-9953.
- Deserno, M. and W.M. Gelbart Adhesion and Wrapping in Colloid-Vesicle Complexes J. Phys. Chem B, 2002; 106(21): 5543?5552.
- Borukhov, I., K.C. Lee, R.F. Bruinsma, W.M. Gelbart, A.J. Liu and M.J. Stevens Association of Two Semi-flexible Polyelectrolytes by Interchain Linkers: Theory and Simulations J.Chem Phys, 2002; 117(1): 462.
- Myrick, K. V., and W.M. Gelbart Universal Fast Walking for direct and versatile determination of flanking sequence Gene, 2002; 284(1-2): 125-131.
- Kindt, J. and W.M. Gelbart Chain Self-Assembly and Phase Transitions in Semi-flexible Polymer Systems J.Chem, 2001; Phys(114): 1432-1439.
- Gelbart, W.M Condensation and Complexation of DNA in Aqueous Solution: Biological Implications, Electrostatic Effects in Soft Matter and Biophysics, 2001; ed. by C. Holm, P. Kekicheff and R. Podgornik: .
- Schiessel, H., W.M. Gelbart and R.F. Bruinsma DNA Folding: Structural and Mechanical Properties of the Two-angle Model for Chromatin Biophys, 2001; J(80): 1940-1956.
- Kindt, J.Tzlil, S.Ben-Shaul, A.Gelbart, W. M. DNA packaging and ejection forces in bacteriophage Proc Natl Acad Sci U S A, 2001; 98(24): 13671-4.
- Borukhov, I.Bruinsma, R. F.Gelbart, W. M.Liu, A. J. Elastically driven linker aggregation between two semiflexible polyelectrolytes Phys Rev Lett, 2001; 86(10): 2182-5.
- Schiessel, H., R.F. Bruinsma and W.M. Gelbart Electrostatic Complexation of Spheres and Chains under Elastic Stress, J.Chem, 2001; Phys(115): 7545.
- Schiessel, H., J. Widom, R.F. Bruinsma and W.M. Gelbart Polymer Reptation and Nucleosome Repositioning Phys, 2001; Rev(Letters 86): 4414-4417.
- Lambert, O., L. Letellier, W.M. Gelbart and J.L. Rigaud DNA Delivery by Phage as a Strategy for Encapsulating Toroidal Condensates of Arbitrary Size into Liposomes Proc Natl Acad Sci U S A, 2000; USA(97): 7248.
- Gelbart, W.M., R.F. Bruinsma, P.A. Pincus and V.A. Parsegian DNA-Inspired Electrostatics Physics Today, 2000; (September): .
- Schiessel, H., J. Rudnick, R.F. Bruinsma and W.M. Gelbart Organized Condensation of Worm-Like Chains Europhys, 2000; Letters 51: 237.
- Gelbart, W.M., R.P. Sear, J.R. Heath and S. Chaney Array Formation in Nano-colloids: Theory and Experiment in 2D Faraday Discussions, 1999; 112: 299-307.
- Sear, R. and W.M. Gelbart Microphase Separation vs the Vapor-Liquid Transition in Systems of Spherical Particles J.Chem, 1999; Phys(110): 4582.
- Park, S.Y., R.F. Bruinsma and W.M. Gelbart Spontaneous Overcharging of Macro-ion Complexes, Europhys, 1999; Letters(46): 454.
- Sear, R., S.W. Chung, G. Markovich, W.M. Gelbart and J.R. Heath Spontaneous Patterning of Quantum Dots at the Air-Water Interface Phys, 1999; Rev(E.59): R6255.
- Noro, M.G. and W.M. Gelbart Theory of Lamellar-Lamellar Phase Transition in Pure and Mixed Surfactant Solutions J.Chem, 1999; Phys(111): 1.
- Ohara, P.C. and W.M. Gelbart Interplay between Hole Instability and Nanoparticle Array Formation in Ultrathin Liquid Films Langmuir, 1998; 14: 3418.
- Harries, D., S. May, W.M. Gelbart and A. Ben-Shaul Structure, Stability and Thermodynamics of Lamellar DNA-Lipid Complexes Biophys, 1998; J(75): 159.
- Vossmeyer, T., S.W. Chung, W.M. Gelbart and J.R. Heath Surprising Superstructures: Rings, Advanced Materials, 1998; 10: 351.
- Park, S.Y., D. Harries and W.M. Gelbart Topological Defects and the Optimum Size of DNA Condensates Biophys, 1998; J(75): 714.
- Gelbart, W.M. and R.F. Bruinsma Compositional-Mechanical Instability of Interacting Mixed Lipid Membranes Phys, 1997; Rev(E55): 831.
- Gronbech-Jensen, N., R.J. Mashl, R.F. Bruinsma and W.M. Gelbart Counterion-Induced Attraction between Rigid Polyelectrolytes Phys, 1997; Rev(Letters 78): 2477.
- Noro, M.G., and W.M. Gelbart Micellar Shape and Long-Range Ordering Transitions in Ternary Surfactant Solutions J. Phys. Chem, 1997; (101): 8642.
- Ohara, P.C., J.R. Heath and W.M. Gelbart Self-Assembly of Sub-micrometer Rings of Particles from Solutions of Nanoparticles, Angew, Chem. Int. Ed. Engl, 1997; 36: 1077.
- Ben-Shaul, A., W.M. Gelbart The ‘New Science’ of Complex Fluids J. Phys. Chem, 1996; (100): 13169.
- Sharlow, M.F., R.B. Selinger, A. Ben-Shaul and W.M. Gelbart Cell Model and Computer Simulation Studies of Layered and Hexagonal States of Hard, Aligned, Rods vs Disks J. Phys. Chem, 1995; (99): 2907.
- Ohara, P.C., D.V. Leff, J.R. Heath and W.M. Gelbart Crystallization of Opals from Polydisperse Nanoparticles Phys, 1995; Rev(Letters 75): 3466.
- Weakliem, C.L., G. Fujii, J.E. Cheng, A. Ben-Shaul and W.M. Gelbart Effect of Tension on Pore Formation in Drug-Containing Vesicles J. Phys. Chem, 1995; (99): 7694.
- Bohbot, Y., A. Ben-Shaul, R. Granek and W.M. Gelbart Monte Carlo and Mean-Field Studies of Phase Evolution in Concentrated Surfactant Solutions J.Chem, 1995; Phys(103): 8764.
- Boden, N., R. Harding, W.M. Gelbart, P. Ohara, K. W. Jolley, A.P. Heerdegen and A. N. Parbhu On the nature of the intramicellar and intermicellar forces governing the liquid crystalline phase behavior of aqueous solutions of disklike micelles J.Chem, 1995; Phys(103): 5712.
- Leff, D.V., P.C. Ohara, J.R.Heath and W.M. Gelbart Thermodynamic Control of Gold Nanocrystal Size: Experiment and Theory Journal of Physical Chemistry, 1995; (99): 7036.
- Gelbart, W.M., A. Ben-Shaul and D. Roux, ed Micelles, Membranes, Microemulsions and Monolayers , , 1994; .
- Whetten, R.L., and W.M. Gelbart Nanocrystal Microemulsions: Surfactant-Stabilized Size and Shape J. Phys. Chem, 1994; (98): 3544.
- Granek, R., W.M. Gelbart, Y. Bohbot and A. Ben-Shaul Smectic-A to Bilayer Evolution in Concentrated Surfactant Solutions: The Role of Spontaneous Curvature J.Chem, 1994; Phys(101): 4331.
- Ben-Shaul, A., W.M. Gelbart Statistical Thermodynamics of Amphiphilic Self-Assembly: Structure and Phase Transitions in Micellar Solutions, Micelles, Membranes, Microemulsions and Monolayers, 1994; ed. by W.M. Gelbart, A. Ben-Shaul, and D. Roux: .
- Wang, Z.G., M.E. Costas and W.M. Gelbart Flexible Micelles and the n ? 0 Vector Spin Model J. Phys. Chem, 1993; (97): 1237.
- Selinger, R.B., R.E. Lynden-Bell, and W.M. Gelbart Stress-induced Failure and Melting of Ideal Solids J.Chem, 1993; Phys(98): 9808.
- Gelbart, W.M., S.Q. Wang, A. Ben-Shaul and R. Bruinsma Effects of Flow Fields on Self-Assembly in Micellized Surfactant Solutions, Proceedings of the 8th International Symposium on Surfactants in Solution, 1992; ed. by M. L. Mittal and D. O. Shah : .
- Bruinsma, R., W.M. Gelbart and A. Ben-Shaul Flow-Induced Gelation of Living (Micellar) Polymers J.Chem, 1992; Phys(96): 7710.
- Kramer, D., A. Ben-Shaul and W.M. Gelbart Monte Carlo and Mean-Field Studies of Successive Phase Transitions in Rod Monolayers J.Chem, 1992; Phys(96): 2236.
- Sharlow, Mark F., and W.M. Gelbart On the Parallel-Perpendicular Transition for a Nematic Phase at a Wall, Liquid Crystals, 1992; 11: 25.
- Costas, M.E., Z.-G. Wang and W. M. Gelbart Spin-Hamiltonian Analyses of Grafted Rod Phase Transitions J.Chem, 1992; Phys(96): 2288.
- Bagdassarian, C., D. Roux, A. Ben-Shaul and W. M. Gelbart Curvature Defects in Lamellar Phases of Amphiphile-Water Systems J.Chem, 1991; Phys(94): 3030.
- Selinger, R.B, Z.G. Wang, and W.M. Gelbart Effect of Temperature and Small-Scale Defects on the Strength of Solids J.Chem, 1991; Phys(95): 9128.
- Wang, Z.G., U. Landman, R. B. Selinger, and W. M. Gelbart Molecular Dynamics Study of Elasticity and Failure of Ideal Solids Phys, 1991; Rev(B44): 378.
- Selinger, R.B, Z.G. Wang, and W.M. Gelbart Solids under Stress: The Statistical Mechanics of Failure, Lectures on Thermodynamics and Statistical Mechanics, 1991; ed. by M. Lopez de Haro and C. Varea (World Scientific): .
- Selinger, R.B, Z.G. Wang, A. Ben-Shaul, and W.M. Gelbart Statistical Thermodynamic Approach to Fracture Phys, 1991; Rev(A43): 4396.
- Szleifer, I., A. Ben-Shaul and W. M. Gelbart Chain Packing Statistics and Thermodynamics of Amphiphilic Monolayers J. Phys. Chem, 1990; (94): 5081.
- Wang, S.Q., A. Ben-Shaul and W. M. Gelbart Flow Effects on Micellar Size Distribution, J.Chem, 1990; Chem(94): 2219.
- Szleifer, I., D. Kramer, A. Ben-Shaul, W. M. Gelbart and S. Safran Molecular Theory of Curvature Elasticity in Surfactant Films J.Chem, 1990; Phys(92): 6800.
- Wang, S.Q. and W. M. Gelbart Effect of Elongational Flow on the Orientational Order Phase Transitions and Viscosity of Hard Rod Fluids J.Chem, 1989; Phys(90): 597.
- W.M. Gelbart The Molecular world, Microverse, 1989; ed. by W. Alschuler: .
- Szleifer, I., D. Kramer, A. Ben-Shaul, D. Roux, and W. M. Gelbart Curvature Elasticity of Pure and Mixed Surfactant Films, Phys, 1988; Rev(Letters 60): 1966.
- Bagdassarian, C., W. M. Gelbart, and A. Ben-Shaul Liquid Crystalline States of Surfactant Solutions of Isotropic Micelles J.Stat, 1988; Phys(52): 1307.
- Chen, Z.Y., J. Talbot, W. M. Gelbart, and A. Ben-Shaul Phase Transitions in Systems of Grafted, Rigid Rods Phys, 1988; Rev(Letters 61): 1376.
- Ben-Shaul, A., W.M. Gelbart, and I. Szleifer Chain Packing and the Compressional Elasticity of Surfactant Films, Physics of Amphiphiles , 1987; ed. by D Langevin and J. Meunier: .
- Ben-Shaul, A., W.M. Gelbart, and I. Szleifer Molecular Theory for Amphiphile Packing and Elastic Properties of Monolayers and Bilayers, Physics of Amphiphiles , 1987; ed. by D Langevin and J. Meunier: .
- Ben-Shaul, A., W.M. Gelbart, and J.L. Viovy Scaling Properties of Chain Interactions in Amphiphilic Aggregates J.Chem, 1987; Phys(87): 41144.
- Chen, Z.Y., W.M. Gelbart, P. Meakin, and P. Weakliem Second-Order Light Scattering and Local Anisotropy of Diffusion-Limited Aggregates and Bond-Percolation Clusters Phys, 1987; Rev.(Letters 58): 1996-2000.
- Ben-Shaul, A., W.M. Gelbart, and I. Szleifer Statistical Thermodynamics of Molecular Organization in Mixed Micelles and Bilayers J.Chem, 1987; Phys(86): 7094.
- Ben-Shaul, A., W.M. Gelbart, and I. Szleifer Chain Statistics in Micelles and Bilayers: Effects of Surface Roughness and Internal Energy J.Chem, 1986; Phys(85): 5345-5359.
- Chen, Z.Y., W.M. Gelbart, and M.R. Kuzma Comment on the Concentration Dependence of Isotropic/Nematic Transition Temperatures in Micellar Systems Phys, 1986; Rev(A34): 2531-2534.
- Ben-Shaul, A., W.M. Gelbart, and I. Szleifer Packing of Chain-Like Molecules at Interfaces, Proceedings of the 15th Mexican Statistical Physics Meeting, Kinam, 1986; 7(Serie A): 5-20.
- Ben-Shaul, A., W.M. Gelbart, G.V. Hartland, and D.H. Rorman Size Distribution of Mixed Micelles: Rodlike Surfactant-Alcohol Aggregates J. Phys. Chem, 1986; (90): 5277-5287.
- Rosenfeld, Y., W.M. Gelbart, and W.E. McMullen Spontaneous Alignment in Charged-Particle Systems: Fixed-Length vs. Micellar Situations J.Chem, 1986; Phys(85): 1088-1097.
- Ben-Shaul, A., W.M. Gelbart, and W.E McMullen Theory of Micellar Stability in Isotropic and Nematic Phases, Mol. Cryst. Liq., 1986; Chem(132): 325-338.
- Ben-Shaul, A., W.M. Gelbart, and I. Szleifer Chain Organization and Thermodynamics in Micelles and Bilayers: I. Theory J.Chem, 1985; Phys(83): 3597-3612.
- Ben-Shaul, A., W.M. Gelbart, and I. Szleifer Chain Organization and Thermodynamics in Micelles and Bilayers: II. Model Calculations J.Chem, 1985; Phys(83): 3612-3621.
- Ben-Shaul, A., W.M. Gelbart, and W.E McMullen Isotropic-Nematic Transition in Micellized Solutions J.Chem, 1985; Phys(46): 5616-5624.
- Ben-Shaul, A., W.M. Gelbart, and W.E McMullen Nematic Stability and the Alignment-Induced Growth of Anisotropic Micelles, J. de Phys., 1985; 46: 1137-1145.
- Ben-Shaul, A., W.M. Gelbart, A. Masters, and W.E. McMullen On the Partitioning of Cosurfactant in Mixed Micelles: Size Enhancement and Nematic Stability, Langmuir, 1985; 1: 101-104.
- Ben-Shaul, A., W.M. Gelbart, and W.E McMullen On the Theory of Micellar Size in Isotropic and Nematic Surfactant Solutions Proceedings of the 5th International Symposium on Surfactants in Solution, ed. by P. Botherel and K. L. Mittal , 1985; .
- Ben-Shaul, A., W.M. Gelbart, and I. Szleifer Statistical-Thermodynamic Theory of Surfactant Organization in Micelles and Bilayers, Proceedings of the 5th International Symposium on Surfactants in Solution, ed. by P. Botherel and K. L. Mittal , 1985; .
- Ben-Shaul, A., W.M. Gelbart, and I. Szleifer Theory of Chain Packing in Amphiphile Aggregates Ann.Rev.Phys.Chem, 1985; 36: 179-212.
- Ben-Shaul, A., W.M. Gelbart, and I.Szleifer Amphiphile Chain Organization in Micelles of Different Geometries, Physics of Amphiphiles: Micelles, Vesicles, and Microemulsions, 1984; .
- Ben-Shaul, A., W.M. Gelbart, and Y. Rabin Anisotropy Induced in a Semi-Flexible Polymer by a Liquid-Crystalline Solvent, Liquid Crystals and Ordered Fluids, 1984; 4: .
- Ben-Shaul, A., W.M. Gelbart, A. Masters, and W.E. McMullen Effects of Inter-aggregate Forces on Micellar Size in Isotropic and Aligned Phases, Physics of Amphiphiles: Micelles, Vesicles, and Microemulsions, 1984; .
- Ben-Shaul, A., and W.M. Gelbart Micellar Growth due to Inter-aggregate Interactions J. Phys. Chem, 1984; (88): 861-867.
- Rosenfeld, Y., and W.M. Gelbart On the Statistical Thermodynamics of Interacting Charged Particles of Arbitrary Shape and Concentration J.Chem, 1984; Phys(81): 4574-4584.
- Ben-Shaul, A., W.M. Gelbart, and W.E McMullen Rod/Disk Co-existence in Dilute Soap Solutions, J.Colloid and Interface Sci, 1984; 98: 523-537.
- Ben-Shaul, A., W.M. Gelbart, and I. Szleifer Statistical Thermodynamics of Amphiphile Chains in Micelles Proc. Nat. Acad. Sci., 1984; 81: 4601-4606.
- Ben-Shaul, A., W.M. Gelbart, and W.E. McMullen Translational and Rotational Contributions to the Size of Micelles in Dilute Soap Solutions J. Phys. Chem, 1984; 88: 6649-6655.
- Ben-Shaul, A., W.M. Gelbart, and Y. Rabin On the Stretching of Alkyl Chains by Nematics J.Chem, 1983; Phys(78): 4303-4309.
- Ben-Shaul, A., and W.M. Gelbart Effect of Inter-aggregate Forces on the Size Distribution of Micelles J.Chem, 1982; Phys(86): 316-319.
- Gelbart, W.M Molecular Theory of Nematic Liquid Crystals J. Phys. Chem, 1982; (86): 4298-4308.
- Ben-Shaul, A., and W.M. Gelbart Molecular Theory of the Elastic Constants of Nematic Liquids, J.Chem, 1982; Phys(77): 916-934.
- McMullen, W.E., Y. Rabin, and W.M. Gelbart Phase Diagram Behaviors for Rod/Plate Liquid Crystal Mixtures, Mol. Cryst. Liq., 1982; Cryst(89): 67-77.
- Stannard, P.R., and W.M. Gelbart Intramolecular Vibrational Energy Redistribution, J.Chem, 1981; Phys(85): 3592-3600.
- Elert, M.L., W.M. Gelbart, and P.R. Stannard On the Overtone-Combination Spectra of XY2 Molecules J.Chem, 1981; Phys(74): 6050-6063.
- Beswick, J.A., W.M. Gelbart, and G. Delgado-Barrio Vibrational Dephasing in Liquids–Analogy with Molecular Electronic Lineshapes, Can.J, 1981; Phys(59): 1514-1532.
- Barboy, Boris, and W.M. Gelbart A Van der Waals Picture of the Isotropic-Nematic Liquid Crystal Phase Transition Accts. Chem, 1980; Res(13): 290-297.
- Beswick, J.A., and W.M. Gelbart Bending Contribution to Rotational Distributions in the Photodissociation of Polyatomic Molecules J.Chem, 1980; Phys(84): 3148-3152.
- Barboy, Boris, and W.M. Gelbart Hard Particle Fluids: I. General Scaled-Particle-Like Descriptions J.Stat, 1980; Phys(22): 685-708.
- Barboy, Boris, and W.M. Gelbart Hard Particle Fluids: II. General y-expansion-Like Descriptions J.Stat, 1980; Phys(22): 709-742.
- Heller, Eric J., and W.M. Gelbart Normal Mode Spectra of Local Mode Molecules, J.Chem, 1980; Phys(73): 626-629.
- Elert, Mark L., W.M. Gelbart, and Donald F. Heller Photodissociation of the Formaldehyde Molecule: Does It or Doesn’t It? Chem, 1980; Revs.(80): 403-417.
- Dujardin, Gerald, W.M. Gelbart, Sydney Leach, John P. Maier, and Guy Taieb Radiationless Transitions in Molecular Ions: Mono- and Di-chloroacetylene Cations J.Chem, 1980; Phys(73): 4987-4998.
- Gelbart, W.M. Collision-Induced and Multiple Light Scattering by Simple Fluids Philosophical Transactions of The Royal Society, 1979; Lond (A293): 359-376.
- Barboy, Boris, and W.M. Gelbart On the Form of the Free Energy for Uniaxially Ordered Liquids, Mol. Cryst. Liq., 1979; Cryst(55): 209-235.
- Barboy, Boris, and W.M. Gelbart Series Representation of the Equation of State for Hard Particle Fluids J.Chem, 1979; Phys(71): 3053-3063.
- Gelbart, W.M. ‘Collision-Induced Scattering,’ in Correlation Functions and Quasiparticle Interactions in Condensed Matter, Proceedings of the NATO Advanced Study Insitute held in Minneapolis, Minnesota, 1978; 1997 ed(ed. by J.W. Halley): .
- Gelbart, W.M. ‘Double Light Scattering by Critical Fluids,’ in Correlation Functions and Quasiparticle Interactions in Condensed Matter, Proceedings of the NATO Advanced Study Insitute held in Minneapolis, Minnesota, 1978; 1977(ed. by J.W. Halley): .
- Gelbart, W.M. ‘Intermolecular Spectroscopy,’ Intermolecular Spectroscopy and Dynamical Properties of Dense Systems, Proceedings of the Enrico Fermi International School of Physics held in Varenna, Italy, 1978; (ed. by J.van Kranendonk): .
- Leach, Sydney, Paul R. Stannard, and W.M. Gelbart Interelectronic-state Perturbation Effects on Photoelectron Spectra and Emission Quantum Yields. Application to CO2+, Mol, 1978; Phys(36): 1119-1132.
- Elert, Mark L., W.M. Gelbart, and Donald F. Heller Photodissociation Dynamics of Small Polyatomics J.Chem, 1978; Phys(69): 4061-4068.
- Elert, Mark L., W.M. Gelbart, and Paul R. Stannard Some Symmetry Aspects of the Local Mode Description of Vibrational Structure, Int. J. , 1978; Quantum Chem(14): 703-709.
- Baram, Asher, and W.M. Gelbart Angular Correlation Ranges in Flexible Polymer Chains J.Chem, 1977; Phys(66): 617-623.
- Baram, Asher, and W.M. Gelbart Continuum Limit of the Rotational Isomeric State Model J.Chem, 1977; Phys(66): 466.
- Gelbart, Abe, and W.M. Gelbart Effective One-Body Potentials for Orientationally Anisotropic Fluids, Mol, 1977; Phys(33): 1387-1399.
- Baron, Barbara A, and W.M. Gelbart Generalized van der Waals Theory of the Isotropic-Nematic Phase Transition J.Chem, 1977; Phys(66): 207-214.
- Elert, Mark L., W.M. Gelbart, and Paul R. Stannard Local Mode Structure of the Water Molecule, J.Chem, 1977; Phys(67): 5395-5397.
- Baron, Barbara A., and W.M. Gelbart Molecular Shape and Volume Effects on Orientational Ordering in Simple Liquid Crystals J.Chem, 1977; Phys(67): 5795-5802.
- Avouris, P., W.M. Gelbart, and M.A. Sayed Nonradiative Electronic Relaxation Under Collision-Free Conditions Chemical Reviews, 1977; 77: 793-833.
- Gelbart, W.M Photodissociation Dynamics of Polyatomic Molecules, Ann, 1977; Rev. Phys. Chem(28): 323-348.
- Kuhn, Ingred, Donald F. Heller, and W.M. Gelbart Relative Rate Calculations for Intramolecular Radiationless Transitions Chem, 1977; Phys(22): 435-452.
- Baram, Asher, and W.M. Gelbart Theory of Krishnan Effect: Application to Dilute Colloidal Suspensions J.Chem, 1977; Phys(66): 1188-1202.
- Oxtoby, David W., and W.M. Gelbart Collisional Polarizabilities of the Inert Gases: Second-order Overlap, Exchange, and Correlation Effects, Mol, 1975; Phys(30): 535-547.
- Oxtoby, David W., and W.M. Gelbart Collisional Polarizability Anisotropies of the Noble Gases, Mol, 1975; Phys(29): 1569-1577.
- Elert, Mark L., W.M. Gelbart, and Donald F. Heller Decays, Recurrences, and Large Molecule Behavior in the Theory of Radiationless Transitions Chem, 1975; Phys(7): 116-123.
- Harris, Robert A., Donald F. Heller, W.M. Gelbart Density Functional Formulation of Collisional Polarizabilities J.Chem, 1975; Phys(62): 1947-1954.
- Oxtoby, David W., and W.M. Gelbart Three-Body Potential Energies and Crystal Binding Energies in an Electron Gas Approximation, Phys, 1975; Rev(A12): 227-230.
- Harris, Robert A., Donald F. Heller, and W.M. Gelbart A Priori Calculation of Collisional Polarizabilities: (He)2, (Ne)2, and (Ar)2, J.Chem, 1974; Phys(61): 3854-3856.
- Oxtoby, David W., and W.M. Gelbart Depolarized Light Scattering Near the Gas-Liquid Critical Point J.Chem, 1974; Phys(60): 3359-3368.
- Oxtoby, David W., and W.M. Gelbart Double-Scattering-Induced Deviations from Ornstein-Zernike Behavior Near the Critical Point Phys, 1974; Rev(A10): 738-741.
- Oxtoby, David W., and W.M. Gelbart Shear Viscosity and Order Parameter Dynamics of Fluids Near the Critical Point J.Chem, 1974; Phys(61): 2957-2964.
- Heller, Donald F., and W.M. Gelbart Short Range Electronic Distortion and the Density Dependent Dielectric Function of Simple Gases, Chem, 1974; Phys(Letters 27): 359-365.
- Baron, Barbara A., and W.M. Gelbart The Triplet Polarizability and Depolarization Virial Data for Atomic Gases Chem, 1974; Phys(6): 140-144.
- Gelbart, W.M. Depolarized Light Scattering by Simple Fluids Advan. Chem, 1973; Phys.(26): 1-107.
- Freed, Karl F., and W.M. Gelbart Intramolecular Perturbations and the Quenching of Luminescence in Small Molecules Chem, 1973; Phys(Letters 18): 470-476.
- Gelbart, W.M. On the Transitional Raman Effect, Mol, 1973; Phys(26): 873-889.
- Gelbart, W.M. Second Harmonic Generation by Atomic Fluids Chem, 1973; Phys(Letters 23): 53-56.
- Freed, Karl F., W.M. Gelbart, and Donald F. Heller The Role of Accepting Modes in Theory of Nonradiative Transitions Chem, 1973; Phys(Letters 23): 56-65.
- Cazes, Danielle, and W.M. Gelbart Comment on Collision Induced Electronic Relaxation Chem, 1972; Phys(Letters 15): 37-41.
- Gelbart, W.M. Many-Body Effects and the Depolarization of Light by Simple Gases J.Chem, 1972; Phys(57): 699-672.
- Freed, Karl F., W.M. Gelbart, and Stuart A. Rice Random Matrix Theory and the Master Equation for Finite Systems J.Chem, 1972; Phys.(57): 4699-4712.
- Freed, Karl F., Donald F. Heller, and W.M. Gelbart The Dependence of Radiationless Decay Rates in Polyatomic Molecules upon the Initially Selected Vibronic State: General Theory and Application J.Chem, 1972; Phys(56): 2309-2327.
- Jortner, Joshua, and W.M. Gelbart On Observing ‘New’ States in Small Molecules J.Chem, 1971; Phys(54): 2070-2077.
- Freed, Karl F, and W.M. Gelbart On the Born-Oppenheimer Separation and the Calculation of Nonradiative Transition Rates Chem, 1971; Phys.(Letters 10): 187-192.
- Rice, Stuart A., and W.M. Gelbart Relaxation Phenomena in Excited Molecules, J.Pure and Applied Chem, 1971; 27: 361-387.
- Freed, Karl F., W.M. Gelbart, Joshua Jortner, Stuart A. Rice, and Kenneth G Spears. Boltzmann Statistics and Radiationless Decay in Large Molecules: Optical Selection Studies Chem, 1970; Phys(Letters 6): 345-352.
- Freed, Karl F, W.M. Gelbart, and Stuart A. Rice Internal Rotation and the Breakdown of the Adiabatic Approximation: Many-Phonon Radiationless Transitions J.Chem, 1970; Phys.(50): 4775 -4786.
- Freed, Karl F, W.M. Gelbart, and Stuart A. Rice. Scholastic Theory of Vibrational Relaxation and Dissociation, J.Chem, 1970; Phys(52): 5718-5732.
- Rice, Stuart A, and W.M. Gelbart Some Formal Results in a Theory of Molecular Rearrangements: Photoisomerism J.Chem, 1969; Phys.(52): 2460-2473.