In more detail, this consists of the following:

• application of quantum chemical methods in the use of semiempirical theories for the calculation of spectra of medium to large molecular systems and the study of reactions on surfaces of extended systems to gain insight into the formation of ceramics (silicon carbide) and diamond coatings;

• the numerical study of precursor reactions in the formation of soot in hydrocarbon fuel combustion using Ab Initio quantum chemical methods;

• development of methods to obtain local minima and saddle points on potential energy surfaces in order to characterize stable and transition structures in chemical reactions;

• the use of the time dependent variational principle and coherent states to study dynamics of exciton propagation, chemical reactions and squeezed light.

• the analyses of the connection between various holomorphic representations of quantum mechanics and group representations, based on structures induced by generalised coherent states.

  In still more detail

• Numerical quantum chemical calculations on

  • medium to large molecular systems using semiempirical methods embodied in the intermediate neglect of differential overlap (INDO) program developed at the Quantum Theory Project, University of Florida

  • on small systems using Ab initio propagator methods to calculate spectra

• The use of coherent states and the Time Dependent Variation Principle in the structure of quantum mechanical approximation theory with application to reaction dynamics. In particular, the time dependent Hartree Fock Bogoluibov and Time Dependent Antisymmetrized Geminal Power approximations for electronic systems and gaussian wave packets for nuclear motion;

• The N representability problem, i.e. determining the conditions needed to ensure that a given second order reduced density matrix for a systems of N electrons can be derived from the full density matrix of the system;

• The use of holomorphic representations of quantum mechanics in the solution of the N representability problem;

• Nonlinear optimization theory, designing and implementing effective algorithms for finding local minima and the saddle points between these minima. If the objective function is the energy of a system of atoms with respect to internuclear distance, then such points correspond to stable geometries and transition states;

• Application of computational quantum chemistry to the study of precursor reactions in the formation of soot;

• Numerical studies (molecular dynamic and static) of the properties of silicon and silicon carbide surfaces and reactions on these surfaces;

• Numerical studies (molecular dynamic and static) of the properties of diamond surfaces and reactions on diamond surfaces

  ---

  Publications

  1 B. Weiner, Probability in Theoretical Chemistry, Thesis University of Leicester (1970).
  
  2 T. A. Claxton and B. Weiner, The MCSCF Method, Trans. Farad. Soc., 66, 2113 2119 (1970).
  
  3 T. A. Claxton, M. J. Godfrey and B. Weiner, Ab Initio UHF Calculations, J. Chem. Soc. Farad. Trans. II, 68, 566 574 (1972).
  
  4 B. Weiner and O. Goscinski, The Fundamentals of Propagator Approximations and the GNS Construction, Int. J. Quantum Chem. 12, S1, 289 306 (1977).
  
  5 O. Goscinski and B. Weiner,The role of Algebraic Formulations of Approximate Greens Functions for Systems with a Finite Number of Electrons, Physica Scripta, 21, 385 393 (1980).
  
  6 B. Weiner and O. Goscinski, The Self Consistent Approximation to the Polarization Propagator, Int, J. Quantum Chem. 18, 1109 1131 (1980).
  
  7 B. Weiner And O. Goscinski, Calculation of Optimal Antisymmetrized Geminal Power (Projected BCS) Functions and Their Associated Excitation Spectrum, Phys. Rev. A 22, 2374 2391 (1980).
  
  8 R. L. Lozes, B. Weiner and Y. Ohrn, Invariance Transformations and AGP Optimization, Int. J. Quantum Chem. S15, 129 131 (1981).
  
  9 J. V. Ortiz, B. Weiner and Y. Ohrn, The AGP Wavefunction and Its Relation to Other Descriptions of Electronic Structure, Int. J. Quantum Chem. S15, 113 128 (1981).
  
  10 B. Weiner and O. Goscinski, Superoperator Approach to Propagator Approximation, Int. J. Quantum Chem. 21, 369 398 (1982).
  
  11 B. Weiner, The General Linear Group Approach to Bivariational Problems, Int. J. Quantum Chem. 21, 591 610 (1982).
  
  12 O. Goscinski and B. Weiner, The Excited Spectrum Associated with a Generalized Antisymmetrized Geminal Power (GAGP) Ground State, Phys. Rev. A 25, 650 657 (1982).
  
  13 O. Goscinski, B. Weiner and N. Elander, Oscillator Strength Anomalies as Described by the AGP Model, J. Chem. Phys. 77, 2445 2447 (1982).
  
  14 H. J. Aa. Jensen, B. Weiner, J. V. Ortiz and Y. Ohrn, A Powerful Procedure for Optimizing AGP States, Int. J. Quantum Chem. S16, 615 128 (1982).
  
  15 B. Weiner and O. Goscinski, Excitation Operators Associated with Antisymmetrized Geminal Power States, Phys. Rev. A 27, 57 71 (1983).
  
  16 H. J. Aa Jensen, B. Weiner and Y. Ohrn, AGP Calculations, Int. J. Quantum Chem. 23, 65 70 (1983).
  
  17 B. Weiner, Superoperator Perturbation Theory for Propagators, J. Math Phys. 24, 1791 1796 (1983).
  
  18 H.A. Kurtz, B. Weiner and H. J. Aa Jensen, The Polarization Propagator Based on an AGP State: Theory and Application to the Helium Atom, Int. J. Quantum Chem. S17, 415 423 (1983).
  
  19 B. Weiner, H. J. Aa Jensen and Y. Ohrn, Polarization Propagator Calculation with an AGP Reference State, J. Chem. Phys. 80, 2009 2021 (1984).
  
  20 B. Weiner and Y. Ohrn, Comment on the Radiative Lifetimes of the B3∏g State of N2, J. Chem. Phys. , 5866 5867 (1984).
  
  21 B. Weiner, Representability Problem in Quantum Mechanics, Phys. Rev. A. 30, 2922 2931 (1984).
  
  22 W. D. Edwards, B. Weiner. M. Zerner and Y. Ohrn, Semi Empirical Antisymmetrized Geminal Power Calculation for Molecular Spectra, Int.J. Quantum Chem. S18, 507 517 (1984).
  
  23 B. Weiner and H. Kurtz, The Antisymmetrized Geminal Power (AGP) Approximation to the Excitation Propagator, Int. J. Quantum Chem. 27, 769 780 (1985).
  
  24 B. Weiner Consistent Propagator Approximations, Int. J. Quantum Chem. 28, 61 84 (1985).
  
  25 B. Weiner, H. Kurtz and Y. Ohrn, in Comparison of Ab Initio Calculations with Experiment: State of the Art, ed. R. J. Bartlett, 339 355 (Reidel Dordrecht, the Netherlands, 1985).
  
  26 B. Weiner and Y. Ohrn, Calculations of Spectroscopic Properties of the Ground and Excited States of Be2, J. Chem. Phys. , 2965 2971 (1985).
  
  27 W. D. Edwards, B. Weiner and M. C. Zerner, On the Low Lying States and Electronic Spectroscopy of Fe(II) Porphine, J. Am. Chem. Soc. 108, 2196 2204 (1986).
  28 E. Deumens, B. Weiner and Y. Ohrn, Time Dependent Antisymmetrized Geminal Power Theory Using a Coherent State Formulation, in Density Matrices and Density Functionals proceedings of the A.J. Coleman symposium, edited by R. Erdahl and V. Smith, (Reidel Dordrecht, the Netherlands), 167 191 (1987).
  
  29 R. Roy Chowdhury, E. Sangfelt and B. Weiner, Generalized Tamm Dancoff Approximation (GTDA) and Random Phase Approximation (GRPA) Calculations on LiH, Be and Li2, J. Chem. Phys., 4523 4530 (1987).
  
  30 B. Weiner and Y. Ohrn, Correlated Electronic States the LiH Molecule Studied with the Polarization Propagator, J. Phys. Chem, 91, 563 569 (1987).
  
  31 E. Deumens, B. Weiner and Y. Ohrn, Time Dependent Variational Principle on the Group SO(2r): Generalizations of Time Dependent Hartree Fock, Nucl. Phys. A 446, 85 108 (1987).
  
  32 P. Froelich, E. Sangfelt and B. Weiner, New Implementation of the Complex Coordinate Method for Molecular Resonances and Photo ionization Cross Sections, Int. J. Quantum Chem. 31, 823 (1987).
  
  33 J. D. Head, B. Weiner and M. C. Zerner, A Survey of Optimization Procedures for Stable Structures and Transition States, Int. J. Quantum Chem., 33, 177 186 (1988).
  
  34 W. D. Edwards, B. Weiner and M. C. Zerner, The Electronic Structure of various Spin States of Porphinato Iron(III) Chloride, J.Phys. Chem. 92, 6188 6197 (1988).
  
  35 B. Weiner, The Lie Algebraic Structure of the Set of One Particle Fermion Operators, Int.J.Quantum Chem. S22, 407 424 (1988).
  
  36 B. Weiner, A. Cameron, J. Leszczynski and M. C. Zerner, A Theoretical study of the Tautomers of C3H3, J. Phys. Chem. , 139 144 (1989).
  
  37 J. Fonslick, B. Weiner and A. Khan, On the Question of Hypoidite Ion Formation in the Aqueous Solution of Iodine: Theoretical and Experimental Study of H2OI2 Complex, J. Chem. Phys. , 3836 3838 (1989).
  
  38 B. Weiner, Coherent State Approach to the N Representability Problem, J. Mol. Struct. (Theochem), 199, 119 135 (1989).
  
  
  39 B. Weiner, J. Feng, J. Leszczynski and M. C. Zerner,A study of the reaction C3H3+ + C2H2 and the tautomers of C5H5+, J. Am. Chem. Soc., 111, 4648 4655 (1989).
  
  40 B. Weiner, P. Shaw and B. Mechtly, Variational evolution on a Davydov Lattice using Generalized Coherent Trial States, Phys. Rev.A, 40, 7275 7285 (1989).
  
  41 B. Weiner, D. Heaney, C. Williams and M. C. Zerner, Structures of C5H3,J.Phys. Chem.,94 ,7001 7007 (1990).
  42 B. Weiner, C. Carmer and M. Frenklach, Reaction of C2H2 on Silicon (111) surface, Phys. Rev. B, 1678 1684 (1990).
  
  43 B. Weiner, E. Deumens,and Y. Ohrn, Coherent State Formulation of Multi Configurational States, J. Math. Phys.,32, 1166 1175 (1991).
  
  44 B. Weiner, E. Deumens,and Y. Ohrn, Spin Projections of Fermion Coherent States, J. Math Phys., 32, 2413 2426 (1991).
  
  45 B. Weiner, Time Dependent Quantum Mechanics with Correlated Coherent States, Proceedings of NATO Advanced Research Workshop on Time Dependent Quantum Mechanics: Theory and Experiment, Snowbird 1992, 413 434 (Plenum 1992).
  
  46 X. G. Zhao, C. S. Carmer, B. Weiner and M. Frenklach, Molecular Dynamics with the AM1 Potential: Reactions on Diamond Surfaces, J. Phys. Chem. 97, 1639 1648 (1993).
  
  47 C. S. Carmer, B. Weiner and M. Frenklach, Molecular Dynamics with Combined Quantum and Empirical Potentials: Adsorption on Si(100) J. Chem. Phys. 99, 1356 1372 (1993).
  
  48. H. Wang, B. Weiner, and M. Frenklach, A Theoretical Study of Reactions between Phenylvinyleum and Acetylene, J. Phys. Chem. 97, 10364 10371 (1993).
  
  49. B. Weiner, P Representations of Operators, Proceedings of International Symposium on Coherent States: Past, Present, and Future, edited by D. H. Feng and J. R. Klauder, Singapore, 1994, Oak Ridge Associated Universities World Scientific.
  
  50. B. Weiner, E. Deumens, and Y. Ohrn, Coherent State Approach to Electron Nuclear Dynamics with an Antisymmetrized Geminal Power State, J. Math. Phys. 35, 1139 1170 (1994).
  
  51. S. Skokov, B. Weiner and M. Frenklach, Elementary Reaction Mechanism of Diamond Growth from Acetylene, J. Phys. Chem. 98, 8 11 (1994).
  
  52. S. Skokov, C. S. Carmer, B. Weiner and M. Frenklach, Reconstruction of (100) Diamond Surface using Molecular Dynamics with Combined Quantum and Empirical Forces., Phys. Rev. B. 49, 5662 5671 (1994).
  
  53. S. Skokov, B. Weiner and M. Frenklach, Molecular Dynamics of Oxygenated (100) Diamond Surfaces, Phys. Rev B. 49, 11374 11382 (1994).
  
  54. S. Skokov, B. Weiner and M. Frenklach, Elementary Reaction Mechanism of Diamond Growth from Methyl, J. Phys. Chem. 98, 7073 7082 (1994).
  
  55. M. Frenklach, S. Skokov and B. Weiner, An Atomistic Model for Stepped Diamond Growth, Nature. 372, 535-537 (1994)
  
  56. B. Weiner, S. Skokov and M. Frenklach, A Theoretical analysis of a diamond (100) (2X1) dimer bond, J. Chem. Phys. 102, 5486-5491, (1995)
  
  57. S. Skokov, B. Weiner and M. Frenklach, Chemistry of Acetylene on Diamond (100) Surfaces, J. Phys. Chem. 99, 5616-5625 (1995)
  
  58. S. Skokov, B. Weiner and M. Frenklach, Th Frauenheim and M. Sternberg, Dimer-row pattern formation in diamond (100) growth, Phys. Rev B. 52, 5486-5491, (1995)
  
  59. B. Weiner, S. Skokov and M. Frenklach, Transformation of Monatomic Steps on (100) Diamond Surfaces, Proceedings of the Fourth International Symp. on Diamond Angus, J. C. editor, 1995, pp.546-51. The Electrochemical Society, Pennington, NJ.
  
  60. M. Frenklach, S. Skokov and B. Weiner, “On the Role of Surface Diffusion in Diamond Growth”, Proceedings of the Fourth International Symp. on Diamond Angus, J. C. editor, 1995, pp.1-12. The Electrochemical Society, Pennington, NJ.
  
  61. R.M. Herman, B. Weiner and P.B. Shaw, “Line shapes of the fundamental vibration-rotation-phonon and pure rotation-phonon spectra in HD”, AIP Conference Proceedings, 12th International Conference on Spectral Line Shapes, 13-17 June 1994; 1995, pp 357-8.
  
  62. S. Skokov, B. Weiner and M. Frenklach, A Theoretical Study of the Energetics and Vibrational Spectra of Oxygenated (100) Diamond Surfaces, Proceedings of the Mat. Res. Soc.Symp. Proc. 1996, vol. 416.
  
  63. S. Skokov, B. Weiner and M. Frenklach, "A Theoretical Study of Oxygenated (100) Diamond Surfaces, in the presence of hydrogen". Phys. Rev. B , 55, 1895, (1997)
  
  64. B. Weiner and S. B. Trickey, “Fukutome Symmetry Classification of the Kohn-Sham Auxiliary One-Matrix and its Associated State or Ensemble”, IJQC, 69, 451-460, (1998)
  
  65. B. Weiner and S. B. Trickey, “Time-Dependent Variational Principle in Density Functional Theory, Adv. Quantum Chemistry (Academic Press, San Diego, 1999), 35, 217-47.
  
  66. B. Weiner and S. B. Trickey, “State Energy Functionals and Variational Equations in Density Functional Theory”, Theochem, 501-502, 65-83 (2000)
  
  67. B. Weiner and J. V. Ortiz, “Effective Procedure for Energy Optimizing Antisymmetric Geminal Power States”, J. Chem. Phys., 117, 5135-5154 (2002)