Abstract
The working equations of auxiliary density functional theory (ADFT) and auxiliary density perturbation theory (ADPT) are derived in the framework of the linear combination of Gaussian type orbital expansion. The ADFT and ADPT implementations in the density functional theory program deMon2k are discussed. The use of ADFT and ADPT in first-principle Born–Oppenheimer molecular dynamics at the pico- to nanosecond time scale is reviewed. In particular, the long-standing mystery of the discrepancy between experiment and computations for the polarizability of small sodium clusters is resolved. Applications of the parallel deMon2k ADFT implementation to systems on the nanometer scale are reviewed. This includes Al-zeolites and giant fullerenes. It is shown that structures as large as C540m can be fully optimized without any symmetry constrains in the ADFT framework employing all-electron basis sets within a few days.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Alberti, A. (1997). Location of Brønsted sites in mordenite. Zeolites, 19, 411.
Alberti, A., Davoli, P., & Vezzalini, G. (1986). The crystal-structure refinement of a natural modernite. Zeitschrift fur Kristallograhie, 175, 249.
Almbladh, C. O., & Pedroza, A. C. (1984). Density-functional exchange-correlation potentials and orbital eigenvalues for light atoms. Physical Review A, 29, 2322.
Andreoni, W. (2007). The physics of fullerene-based and fullerene-related materials. Dordrecht: Kluwer Academic Publishers.
Andzelm, J., & Wimmer, E. (1992). Density functional Gaussian-type-orbital approach to molecular geometries, vibrations, and reaction energies. Journal of Chemical Physics, 96, 1280.
Andzelm, J., Radzio, E., & Salahub, D. R. (1985). Compact basis sets for LCAO-LSD calculations. Part I: Method and bases for Sc to Zn. Journal of Computational Chemistry, 6, 520.
Andzelm, J., Russo, N., & Salahub, D. R. (1987). Ground and excited states of group IVA diatomics from local-spin-density calculations: Model potentials for Si, Ge, and Sn. Journal of Chemical Physics, 87, 6562.
Anquetil, R., Saussey, J. C., & Lavalley, J. C. (1999). Confinement effect on the interaction of hydroxy groups contained in the side pockets of H-mordenite with nitriles; a FT-IR study. Physical Chemistry Chemical Physics, 1, 555.
Baerends, E. J., Ellis, D. E., & Ros, P. (1973). Self-consistent molecular Hartree–Fock–Slater calculations I. The computational procedure. Chemical Physical, 2, 41.
Bakowies, D., Bühl, M., & Thiel, W. (1995). Can large fullerenes be spherical? Journal of the American Chemical Society, 117, 10113.
Bates, K. R., & Scuseria, G. E. (1998). Why are buckyonions round? Theoretica Chimica Acta, 99, 29.
Becke, A. D. (1987). A multicenter numerical integration scheme for polyatomic molecules. Journal of Chemical Physics, 88, 2547.
Becke, A. D. (1993a). A new mixing of Hartree–Fock and local density-functional theories. Journal of Chemical Physics, 98, 1372.
Becke, A. D. (1993b). Density-functional thermochemistry. III. The role of exact exchange. Journal of Chemical Physics, 98, 5648.
Belpassi, L., Tarantelli, F., Sgamellotti, A., & Quiney, H. M. (2006). Electron density fitting for the Coulomb problem in relativistic density-functional theory. Journal of Chemical Physics, 124, 124104.
Bergeron, D. E., Castleman, A. W., Jr., Morisato, T., & Khanna, S. N. (2004). Formation of Al13I−: Evidence for the superhalogen character of Al13. Science, 304, 84.
Bergeron, D. E., Roach, P. J., Castleman, A. W., Jr., Jones, N. O., & Khanna, S. N. (2005). Al cluster superatoms as halogens in polyhalides and as alkaline earths in iodide salts. Science, 307, 231.
Bertran, O., Trickey, S. B., & Torras, J., (2010). Incorporation of deMon2k as a new parallel quantum mechanical code for the PUPIL system. Journal of Computational Chemistry, 31, 2669.
Binkley, J. S., Pople, J. A., & Dobosh, P. A. (1974). The calculation of spin-restricted single-determinant wavefunctions. Molecular Physics, 28, 1423.
Birkenheuer, U., Gordienko, A. B., Nasluzov, V. A., Fuchs-Rohr, M. K., & Rösch, N. (2005). Model density approach to the Kohn-Sham problem: Efficient extension of the density fitting technique. International Journal of Quantum Chemistry, 102, 743.
Blundell, S. A., Guet, C., & Zope, R. R. (2000). Temperature dependence of the polarizability of sodium clusters. Physical Review Letters, 84, 4826.
Boltalina, O. V., Ioffe, I. N., Sidorov, L. N., Seifert, G., & Vietze, K. (2000). Ionization energy of fullerenes. Journal of the American Chemical Society, 122, 9745.
Bonin, K. D., & Kresin, V. V. (1997). Electric-dipole polarizabilities of atoms, molecules and clusters. Singapore: World Scientific.
Bühl, M., & Hirsch, A. (2001). Spherical aromaticity of fullerenes. Chemical Review, 101, 1153.
Calaminici, P., Jug, K., & Köster, A. M. (1998). Density functional calculations of molecular polarizabilities and hyperpolarizabilities. Journal of Chemical Physics, 109, 7756.
Calaminici, P., Jug, K., & Köster, A. M. (1999). Static polarizabilities of Na n (n < 9) clusters: An all-electron density functional study. Journal of Chemical Physics, 111, 4613.
Calaminici, P., Köster, A. M., Vela, A., & Jug, K. (2000). Comparison of static polarizabilities of Cu n , Na n , and Li n (n < 9) clusters. Journal of Chemical Physics, 113, 2199.
Calaminici, P., Köster, A. M., Carrington, T., Roy, P. N., Russo, N., & Salahub, D. R. (2001). V3: Structure and vibrations from density functional theory, Franck–Condon factors, and the pulsed-field ionization zero-electron-kinetic energy spectrum. Journal of Chemical Physics, 114, 4036.
Calaminici, P., Köster, A. M., & Salahub, D. R. (2003). Negative ion photoelectron spectra simulation of V3O from a density functional study. Journal of Chemical Physics, 118, 4913.
Calaminici, P., Flores-Moreno, R., & Köster, A. M. (2005). A density functional study of structures and vibrations of Ta3O and Ta3O−. Computing Letters, 1, 164.
Calaminici, P., Dominguez-Soria, V. D., Geudtner, G., Hernandez-Marin, E., & Köster, A. M. (2006). Parallelization of three-center electron repulsion integrals. Theoretica Chimica Acta, 115, 221.
Calaminici, P., Janetzko, F., Köster, A. M., Mejia-Olvera, R., & Zuniga-Gutierrez, B. (2007a). Density functional theory optimized basis sets for gradient corrected functionals: 3d transition metal systems. Journal of Chemical Physics, 126, 044108.
Calaminici, P., Köster, A. M., & Gamboa Martinez, G. U. (2007b). Temperature dependence of the polarizability of sodium clusters: An all-electron density functional study. In G. Maroulis & T. Simos (Eds.), Computational methods in science and engineering, theory and computation: Old problems and new challenges (Vol. 1, pp. 207–211). New York: AIP Conference Proceedings Melville.
Calaminici, P., Geudtner, G., & Köster, A. M. (2009). First-principle calculations of large fullerenes. Journal of Chemical Theory and Computation, 5, 29.
Campana, L., Selloni, A., Weber, J., & Goursot, A. (1997). Cation siting and dynamical properties of zeolite offretite from first-principles molecular dynamics. Journal of Physical Chemistry, 101, 9932.
Carmona-Espíndola, J., Flores-Moreno, R., & Köster, A. M. (2010). Time-dependent auxiliary density perturbation theory. Journal of Chemical Physics, 133, 084102.
Casida, M. E. (1995). Time-dependent density functional response theory for molecules. In P. D. Chong (Ed.), Recent advances in density functional methods. Singapore: World Scientific Publishing Co.
Casida, M. E., Daul, C., Goursot, A., Köster, A. M., Petterson, L. G. M., Proynov, E., St.-Amant, A., Salahub, D. R., Duarte, H., Godbout, N., Guan, J., Jamorski, C., Leboeuf, M., Malkin, V., Malkina, O., Sim, F., & Vela, A. (1996). deMon-KS Version 3.4, deMon Software. Montréal: Université de Montréal.
Cerius2 (2005). Version 4.10. San Diego: Accelrys Inc.
Chacko, S., Kanhere, D. G., & Blundell, S. A. (2005). First principles calculations of melting temperatures for free Na clusters. Physical Review B, 71, 155407.
Chandrakumar, K. R. S., Ghanty, T. K., & Ghosh, S. K. (2004). Static dipole polarizability and binding energy of sodium clusters Na n (n = 1–10): A critical assessment of all-electron based post-Hartree-Fock and density functional methods. Journal of Chemical Physics, 120, 6487.
Cioslowski, J. (1995). Electronic structure calculations on fullerenes and their derivatives. New York: Oxford University Press.
del Campo, J. M., & Köster, A. M. (2008). A hierarchical transition state search algorithm. Journal of Chemical Physics, 129, 024107.
Delley, B. (1990). An all-electron numerical method for solving the local density functional for polyatomic molecules. Journal of Chemical Physics, 92, 508.
Demuth, T., Benco, L., Hafner, J., Toulhouat, H., & Hutschka, F. (2001). Ab initio investigation of the adsorption of benzene in mordenite. Journal of Chemical Physics, 114, 3703.
Dérouane, E. G., André, J. M., & Lucas, A. A. (1988). Surface curvature effects in physisorption and catalysis by microporous solids and molecular sieves. Journal of Catalysis, 110, 58.
Diercksen, G. H. F., & McWeeny, R. (1966). Self-consistent perturbation theory. I. General formulation and some applications. Journal of Chemical Physics, 44, 3554.
Dirac, P. A. M. (1930). Note on exchange phenomena in the Thomas atom. Proceedings of the Cambridge Philosophical Society, 26, 376.
Dodds, J. L., McWeeny, R., Raynes, W. T., & Riley, J. P. (1977). SCF theory for multiple perturbations. Molecular Physics, 33, 611.
Dominguez-Soria, V. D., Calaminici, P., & Goursot, A. (2007). Theoretical study of the structure and properties of Na-MOR and H-MOR zeolite models. Journal of Chemical Physics, 127, 154710.
Dominguez-Soria, V. D., Calaminici, P., & Goursot, A. (2008). Theoretical study of the structure and properties of Na-MOR and H-MOR zeolite models. In A. Gedeon, P. Massiani, & F. Babonneau (Eds.), Studies in surface science and catalysis, zeolites and related materials: Trends, targets and challenges, Proceedings of 4th International FEZA Conference (Vol. 174, p. 717). Amsterdam: Elsevier.
Dominguez-Soria, V. D., Geudtner, G., Morales, J. L., Calaminici, P., & Köster, A. M. (2009). Robust and efficient density fitting. Journal of Chemical Physics, 131, 124102.
Dreizler, R. M., & Gross, E. K. U. (1990). Density functional theory. Berlin: Springer.
Dunlap, B., & Boettger, J. C. (1996). Local-density-functional study of the fullerenes, graphene and graphite. Journal of Physics B, 29, 4907.
Dunlap, B. I., & Rösch, N. (1990). The Gaussian-type orbitals density-functional approach to finite systems. Advances in Quantum Chemistry, 21, 317.
Dunlap, B. I., & Zope, R. R. (2006). Efficient quantum-chemical geometry optimization and the structure of large icosahedral fullerenes. Chemical Physics Letters, 422, 451.
Dunlap, B. I., Connolly, J. W. D., & Sabin, J. R. (1979). On first-row diatomic molecules and local density models. Journal of Chemical Physics, 71, 4993.
Dunlap, B. I., Brenner, D. W., Mintmire, J. W., Mowrey, R. C., & White, C. T. (1991). Local density functional electronic structures of three stable icosahedral fullerenes. Journal of Physical Chemistry, 95, 8737.
Fermi, E. (1927). A statistical method for the determination of some atomic properties. Rendiconti Accademia Lincei, 6, 602.
Fermi, E. (1928 a). A statistical method for the determination of some properties of the atom and its application to the theory of the periodic system of the elements. Zeitschrift für Physik, 48, 73.
Fermi, E. (1928 b). On the statistical deduction of some atomic properties. Application to the theory of the periodic system of the elements. Rendiconti Accademia nazionale dei Lincei, 7, 342.
Flores-Moreno, R. (2010). Symmetry conservation in Fukui functions. Journal of Chemical Theory and Computation, 6, 48.
Flores-Moreno, R., & Köster, A. M. (2008). Auxiliary density perturbation theory. Journal of Chemical Physics, 128, 134105.
Flores-Moreno, R., & Ortiz, J. V. (2009). Integral approximations in ab initio electron propagator calculations. Journal of Chemical Physics, 131, 124110.
Flores-Moreno, R., Melin, J., Ortiz, J. V., & Merino, G. (2008). Efficient evaluation of analytic Fukui functions. Journal of Chemical Physics, 129, 224105.
Fournier, R. (1990). Second and third derivatives of the linear combination of Gaussian type orbitals–local spin density energy. Journal of Chemical Physics, 92, 5422.
Gamboa Martinez, G., Calaminici, P., & Köster, A. M. (2008). How important are temperature effects for cluster polarizabilities? Journal of Physical Chemistry A, 112, 11969.
Gaspar, R. (1954). Uber eine Approximation des Hartreefogkschen Potentials durch eine Universelle Potentialfunktion. Acta Physica Academiae Scientiarum Hungaricae, 3, 263.
Gel’fand, I. M., & Fomin, S. V. (1963). Calculus of variations. Englewood Cliffs: Prentice Hall.
Geudtner, G., Janetzko, F., Köster, A. M., Vela, A., & Calaminici, P. (2006). Parallelization of the deMon2k code. Journal of Computational Chemistry, 27, 483.
Godbout, N., Salahub, D. R., Andzelm, J., & Wimmer, E. (1992). Optimization of gaussian-type basis-sets for local spin-density functional calculations. 1. Boron through neon, optimization technique and validation. Canadian Journal of Physics, 70, 560.
Goursot, A., Fajula, F., Daul, C., & Weber, J. (1998). Study of the molecular electrostatic potentials of zeolites: the acidity in offretite. Journal of Physical Chemistry, 92, 4456.
Guan, J. G., Casida, M. E., Köster, A. M., & Salahub, D. R. (1995). All-electron local and gradient-corrected density-functional calculations of Na n dipole polarizabilities for n = 1–6. Physical Review B, 52, 2184.
Haddon, R. C., Scuseria, G. E., & Smalley, R. E. (1997). C240 – The most chemically inert fullerene? Chemical Physics Letters, 272, 38.
Hall, G. G. (1951). The molecular orbital theory of chemical valency. 8. A method of calculating ionization potentials. Proceedings of the Royal Society of London Series B, 205, 541.
Hamel, S., Casida, M. E., & Salahub, D. R. (2001). Assessment of the quality of orbital energies in resolution-of-the-identity Hartree–Fock calculations using deMon auxiliary basis sets. Journal of Chemical Physics, 114, 7342.
Heggie, M. I., Terrones, M., Eggen, B. R., Jungnickel, G., Jones, R., Latham, C. D., & Briddon, P. R. (1998). Quantitative density-functional study of nested fullerenes. Physical Review B, 57, 13339.
Hohenberg, P., & Kohn, W. (1964). Inhomogeneous electron gas. Physical Review, 136, B864.
Hoover, W. G. (1985). Canonical dynamics: Equilibrium phase-space distributions. Physical Review A, 31, 1695.
Iijima, S. (1980). Direct observation of the tetrahedral bonding in graphitized carbon-black by high-resolution electron-microscopy. Journal of Crystal Growth, 50, 675–683.
Ito, M., & Saioto, Y. (1985). The crystal-structure of ion-exchanged mordenite. Bulletin of the Chemical Society of Japan, 58, 3035.
Itoh, S., Ordejon, P., Drabold, D. A., & Martin, R. M. (1996). Structure and energetics of giant fullerenes: An order-N molecular-dynamics study. Physical Review B, 53, 2132.
Jacobs, P. A., & Martens, G. A. (1987). Synthesis in highsilica aluminosilicate zeolites. Amsterdam: Elsevier.
Jamorski, C., Casida, M. E., & Salahub, D. R. (1996). Dynamic polarizabilities and excitation spectra from a molecular implementation of time-dependent density-functional response theory: N2 as a case study. Journal of Chemical Physics, 104, 5134.
Janetzko, F., Köster, A. M., & Salahub, D. R. (2008). Development of the cyclic cluster model formalism for Kohn-Sham auxiliary density functional theory methods. Journal of Chemical Physics, 128, 024102.
Johnson, K. H. (1966). “Multiple-Scattering” model for polyatomic molecules. Journal of Chemical Physics, 45, 3085.
Johnson, K. H., & Messmer, R. P. (1974). Clusters, chemisorption and catalysis. Journal of Vacuum Science & Technology, 11, 236.
Johnson, K. H., & Smith, F. C. (1970). Cluster-wave approach to the electronic structures of complex molecules and solids. Physical Review Letters, 24, 139.
Johnson, K. H., & Smith, F. C. (1971). Scattered-wave model for the electronic structure and optical properties of the permanganate ion. Chemical Physics Letters, 10, 219.
Johnson, K. H., & Smith, F. C. (1972). Chemical bonding of a molecular transition-metal ion in a crystalline environment. Physical Review B, 5, 831.
Kadish, K. M., & Ruoff, R. S. (2007). Fullerenes: Chemistry, physics, and technology. New York: Wiley.
Knickelbein, M. B. (2001). Electric dipole polarizabilities of Ni12 − 58. Journal of Chemical Physics, 115, 5957.
Knickelbein, M. B. (2003). Electric dipole polarizabilities of Nb2 − 27. Journal of Chemical Physics, 118, 6230.
Knickelbein, M. B. (2004). Electric dipole polarizabilities of copper clusters. Journal of Chemical Physics, 120, 10450.
Knight, W. D., Clemenger, K., de Heer, W. A., Saunders, W. A., Chou, M. Y., & Cohen, M. L. (1984). Electronic shell structure and abundances of sodium clusters. Physical Review Letters, 52, 2141.
Knight, W. D., Clemenger, K., de Heer, A. W., & Saunders, W. A. (1985). Polarizability of alkali clusters. Physical Review B, 31, 2539.
Kohn, W., & Sham, L. J. (1965). Self-consistent equations including exchange and correlation effects. Physical Review, 140, A1133.
Komornicki, A., & Fitzgerald, G. (1993). Molecular gradients and hessians implemented in density functional theory. Journal of Chemical Physics, 98, 1398.
Köster, A. M. (1996). Efficient recursive computation of molecular integrals for density functional methods. Journal of Chemical Physics, 104, 4114.
Köster, A. M. (1998). Habilitation thesis. Universität Hannover.
Köster, A. M. (2003). Hermite Gaussian auxiliary functions for the variational fitting of the Coulomb potential in density functional methods. Journal of Chemical Physics, 118, 9943.
Köster, A. M., Calaminici, P., Gómez, Z., & Reveles, J. U. (2002). Density functional theory calculations of transition metal clusters. In K. Sen (Ed.), Reviews of modern quantum chemistry, a celebration of the contribution of Robert G. Parr. River Edge: World Scientific.
Köster, A. M., Goursot, A., & Salahub, D. R. (2003). DeMon. In J. McCleverty, T. J. Meyer, & B. Lever (Eds.), Comprehensive coordination chemistry-II, from biology to nanotechnology (Vol. 1). Amsterdam: Elsevier.
Köster, A. M., Flores-Moreno, R., & Reveles, J. U. (2004a). Efficient and reliable numerical integration of exchange-correlation energies and potentials. Journal of Chemical Physics, 121, 681.
Köster, A. M., Reveles, J. U., & del Campo, J. M. (2004b). Calculation of exchange-correlation potentials with auxiliary function densities. Journal of Chemical Physics, 121, 3417.
Köster, A. M., Calaminici, P., Casida, M. E., Flores-Moreno, R., Geudtner, G., Goursot, A., Heine, T., Ipatov, A., Janetzko, F., del Campo, J. M., Patchkovskii, S., Reveles, J. U., Salahub, D. R., & Vela, A. (2006). The deMon developers. Mexico-City: Cinvestav. http://www.demon-software.com.
Köster, A. M., del Campo, J. M., Janetzko, F., & Zuniga-Gutierrez, B. (2009). A MinMax self-consistent-field approach for auxiliary density functional theory. Journal of Chemical Physics, 130, 114106.
Köster, A. M., Geudtner, G., Calaminici, P., Casida, M. E., Flores-Moreno, R., Goursot, A., Janetzko, F., Reveles, J. U., Vela, A., & Salahub, D. R. (2010). The deMon2k user’s guide. http://www.demon-software.com.
Krack, M., & Köster, A. M. (1998). An adaptive numerical integrator for molecular integrals. Journal of Chemical Physics, 108, 3226.
Krishnamurty, S., Heine, T., & Goursot, A. (2003). Influence of dynamics on the structure and NMR chemical shift of a zeolite precursor. Journal of Physical Chemistry B, 104, 5728.
Krishnamurty, S., Stefano, M., Mineva, T., Bégu, S., Devoisselle, J. M., Goursot, A., Zhu, R., & Salahub, D. R. (2008 a). Lipid thermodynamics: Melting is molecular. ChemPhysChem, 9, 2321.
Krishnamurty, S., Stefano, M., Mineva, T., Bégu, S., Devoisselle, J. M., Goursot, A., Zhu, R., & Salahub, D. R. (2008 b). Density functional theory-based conformational analysis of a phospholipid molecule (Dimyristoyl Phosphatidylcholine). Journal of Physical Chemistry B, 112, 13433.
Kronik, L., Vasiliev, I., & Chelikowsky, J. R. (2000). Ab initio calculations for structure and temperature effects on the polarizabilities of Na n (n < ∼ 20) clusters. Physical Review B, 62, 9992.
Kroto, H. W., & McKay, K. (1988). The formation of quasi-icosahedral spiral shell carbon particles. Nature, 331, 328.
Kroto, H. W., Heath, J. R., O’Brien, S. C., Curl, R. F., & Smalley, R. E. (1985). C60: Buckminsterfullerene. Nature (London), 318, 162.
Kümmel, S., Akola, J., & Manninen, M. (2000). Temperature dependence of the polarizability of sodium clusters. Physical Review Letters, 84, 4826.
Laikov, D. N. (1997). Fast evaluation of density functional exchange-correlation terms using the expansion of the electron density in auxiliary basis sets. Chemical Physics Letters, 281, 151.
Lev, B., Zhang, R., de la Lande, A., Salahub, D. R., & Noskov, S. Y. (2010). The QM-MM interface for CHARMM-deMon. Journal of Computational Chemistry, 31, 1015.
Levy, M. (1979). Universal variational functionals of electron densities, first-order density matrices, and natural spin-orbitals and solution of the v-representability problem. Proceedings of the National Academy of Sciences, 76, 6062.
Levy, M., & Perdew, J. P. (1985). In R. M. Dreizler & J. da Providencia (Eds.), Density functional methods in physics. New York: Plenum.
Li, H., & Jensen, G. H. (2002). Partial Hessian vibrational analysis: The localization of the molecular vibrational energy and entropy. Theoretica Chimica Acta, 107, 211.
Malkin, V. G., Malkina, O. L., & Salahub, D. R. (1993 a). Calculations of NMR shielding constants by uncoupled density functional theory. Chemical Physics Letters, 204, 80.
Malkin, V. G., Malkina, O. L., & Salahub, D. R. (1993 b). Calculations of NMR shielding constants beyond uncoupled density functional theory. IGLO approach. Chemical Physics Letters, 204, 87.
Malkin, V. G., Malkina, O. L., Casida, M. E., & Salahub, D. R. (1994). Nuclear magnetic resonance shielding tensors calculated with a sum-over-states density functional perturbation theory. Journal of the American Chemical Society, 116, 5898.
Marie, O., Thibault-Starzyk, F., & Lavalley, J. C. (2000). Confirmation of the strongest nitriles–hydroxy groups interaction in the side pockets of mordenite zeolites. Physical Chemistry Chemical Physics, 2, 5341.
Marie, O., Massiani, P., & Thibault-Starzyk, F. (2004). Infrared evidence of a third Brønsted site in mordenites. Journal of Physical Chemistry B, 108, 5073.
Martyna, G. J., Klein, M. L., & Tuckerman, M. (1992). Nosé-Hoover chains: The canonical ensemble via continuous dynamics. Journal of Chemical Physics, 97, 2635.
McWeeny, R. (1962). Perturbation theory for the Fock-Dirac density matrix. Physical Review, 126, 1028.
McWeeny, R. (2001). Methods of molecular quantum mechanics (2nd reprinting). London: Academic.
McWeeny, R., & Diercksen, G. H. F. (1968). Self-consistent perturbation theory. II. Extension to open shells. Journal of Chemical Physics, 49, 4852.
McWeeny, R., Dodds, J. L., & Sadlej, A. J. (1977). Generalization for perturbation-dependent non-orthogonal basis set. Molecular Physics, 34, 1779.
Meier, W. M. (1961). The crystal structure of mordenite (ptilolite). Zeitschrift fur Kristallograhie, 115, 439.
Messmer, R. P., Tucker, C. W., & Johnson, K. H. (1975). A comparison of SCF-Xα and extended Hückel methods for metal clusters. Chemical Physics Letters, 36, 423.
Messmer, R. P., Salahub, D. R., & Davenport, J. W. (1978). Calculation of angular dependence of photoemission for the Al(100) + O system using a simple molecular orbital cluster model. Chemical Physics Letters, 57, 29.
Mintmire, J. W., & Dunlap, B. I. (1982). Fitting the Coulomb potential variationally in linear-combination-of-atomic-orbitals density-functional calculations. Physical Review A, 25, 88.
Mintmire, J. W., Sabin, J. R., & Trickey, S. B. (1982). Local-density-functional methods in two-dimensionally periodic systems. Hydrogen and beryllium monolayers. Physical Review B, 26, 1743.
Molof, R. W., Miller, T. M., Schwartz, H. L., Benderson, B., & Park, J. T. (1974 a). Measurements of the average electric dipole polarizabilities of the alkali dimers. Journal of Chemical Physics, 61, 1816.
Molof, R. W., Schwartz, H. L., Miller, T. H., & Bederson, B. (1974 b). Measurements of electric dipole polarizabilities of the alkali-metal atoms and the metastable noble-gas atoms. Physical Review A, 10, 1131.
Nosé, S. (1984). A unified formulation of the constant temperature molecular dynamics methods. Journal of Chemical Physics, 81, 511.
Parr, R. G., & Yang, W. (1989). Density-functional theory of atoms and molecules. New York: Oxford University Press.
Passaglia, E. (1975). Crystal-chemistry of mordenites. Contributions to Mineralogy and Petrology, 50, 65.
Pearson, R. G. (1973). Hard and soft acids and bases. Journal of the American Chemical Society, 85, 3533.
Perdew, J. P., Burke, K., & Ernzerhof, M. (1996). Generalized gradient approximation made simple. Physical Review Letters, 77, 3865.
Politzer, P. (1987). A relationship between the charge capacity and the hardness of neutral atoms and groups. Journal of Chemical Physics, 86, 1072.
Pople, J. A., & Nesbet, R. K. (1954). Self-consistent orbitals for radicals. Journal of Chemical Physics, 22, 571.
Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. (1992). Numerical recipes in FORTRAN (2nd ed.). Cambridge: Cambridge University Press.
Rayane, D., Allouche, A. R., Benichou, E., Antoine, R., Aubert-Frecon, M., Dugourd, P., Broyer, M., Ristori, C., Chandezon, F., Hubert, B. A., & Guet, C. (1999). Static electric dipole polarizabilities of alkali clusters. The European Physical Journal D, 9, 243.
Reveles, J. U., & Köster, A. M. (2004). Geometry optimization in density functional methods. Journal of Computational Chemistry, 25, 1109.
Roothaan, C. C. J. (1951). New developments in molecular orbital theory. Reviews of Modern Physics, 23, 69.
Roothaan, C. C. J. (1960). Self-consistent field theory for open shells of electronic systems. Reviews of Modern Physics, 32, 179.
Rozanska, X., van Santen, R. A., Demuth, T., Hutschka, F., & Hafner, J. (2003). A periodic DFT study of isobutene chemisorption in proton-exchanged zeolites: Dependence of reactivity on the zeolite framework structure. Journal of Physical Chemistry B, 107, 1309.
Rozanska, X., Barbosa, L. A. M. M., & van Santen, R. A. (2005). A periodic density functional theory study of cumene formation catalyzed by H-Mordenite. Journal of Physical Chemistry B, 109, 2203.
Rungsirisakun, R., Jansang, B., Pantu, P., & Limtrakul, J. (2005). The adsorption of benzene on industrially important nanostructured catalysts (H-BEA, H-ZSM-5, and H-FAU): Confinement effects. Journal of Molecular Structure, 239, 733.
Salahub, D. R. (1978). Electronic-structure of B4H8Fe(CO)3 – comparison of SCF-Xα-SW molecular orbital theory with ultraviolet photoelectron-spectrum. Journal of the Chemical Society, Chemical Communications, 9, 385.
Salahub, D. R., Weber, J., Goursot, A., Köster, A. M., & Vela, A. (2005). Applied density functional theory and the deMon codes 1964 to 2004. In C. E. Dykstra, G. Frenking, K. S. Kim, & G. Scuseria (Eds.), Theory and applications of the computational chemistry: The first 40 years. Amsterdam: Elsevier.
Sambe, H., & Felton, R. H. (1975). A new computational approach to Slater’s SCF–Xα equation. Journal of Chemical Physics, 62, 1122.
Saunders, V. R. (1983). Methods in computational physics (p. 1). Dordrecht: Reidel.
Schlenker, J. L., Pluth, J. J., & Smith, J. V. (1979). Positions of cations and molecules in zeolites with the mordenite framework. 9. Dehydrated H-mordenite via acid exchange. Materials Research Bulletin, 14, 849.
Schwarz, K. (1972). Optimization of the statistical exchange parameter α for the free atoms H through Nb. Physical Review B, 5, 2466.
Scuseria, G. E. (1995). The equilibrium structures of giant fullerenes: Faceted or spherical shape? An ab initio Hartree-Fock study of icosahedral C240 and C540. Chemical Physics Letters, 243, 193.
Scuseria, G. E. (1996). Ab Initio calculations of fullerenes. Science, 271, 942.
Seifert, G., Vietze, K., & Schmidt, R. (1996). Ionization energies of fullerenes – size and charge dependence. Journal of Physics B, 29, 5183.
Shao, N., Gao, Y., Yoo, S., An, W., & Zeng, X. C. (2006). Search for lowest-energy fullerenes: C98 to C110. Journal of Physical Chemistry A, 110, 7672.
Shao, N., Gao, Y., & Zeng, X. C. (2007). Search for lowest-energy fullerenes 2: C38 to C80 and C112 to C120. Journal of Physical Chemistry C, 111, 17671.
Shedge, S. V., Carmona-Espíndola, J., Pal, S., & Köster, A. M. (2010). Comparison of the auxiliary density perturbation theory and the noniterative approximation to the coupled perturbed Kohn-Sham method: Case study of the polarizabilities of disubstituted azoarene molecules. Journal of Physical Chemistry A, 114, 2357.
Sim, F., Salahub, D. R., & Chin, S. (1992). The accurate calculation of dipole moments and dipole polarizabilities using Gaussian-based density functional methods. International Journal of Quantum Chemistry, 43, 463.
Simoncic, P., & Armbruster, T. (2004). Peculiarity and defect structure of the natural and synthetic zeolite mordenite: A single-crystal X-ray study. American Mineralogist, 89, 421.
Slater, J. C. (1951). A simplification of the Hartree-Fock method. Physical Review, 81, 385.
Smirnov, K., & Thibault-Starzyk, F. (1999). Confinement of acetonitrile molecules in mordenite. A computer modeling study. Journal of Physical Chemistry B, 103, 8595.
St-Amant, A., & Salahub, D. R. (1990). New algorithm for the optimization of geometries in local density functional theory. Chemical Physics Letters, 169, 387.
Thibault-Starzyk, F., Travert, A., Saussey, J. C., & Lavalley, J. C. (1998). Correlation between activity and acidity on zeolites: A high temperature infrared study of adsorbed acetonitrile. Topics in Catalysis, 6, 111.
Thomas, L. H. (1927). The calculation of atomic fields. Mathematical Proceedings of the Cambridge Philosophical Society, 23, 542.
Tikhonov, G., Kasperovich, V., Wong, K., & Kresin, V. V. (2001). A measurement of the polarizability of sodium clusters. Physical Review A, 64, 063202.
Trickey, S. B., Müller-Plate, F., Diercksen, G. H. F., & Boettger, J. C. (1992). Interplanar binding and lattice relaxation in a graphite dilayer. Physical Review B, 45, 4460.
Trickey, S. B., Alford, J. A., & Boettger, J. C. (2004). Methods and implementation of Robust, high-precision Gaussian basis DFT calculations for periodic systems: The GTOFF code. In J. Leszczynski (Ed.), Computational materials science, theoretical and computational chemistry (Vol. 15, p. 171). Amsterdam: Elsevier.
Triguero, L., & Pettersson, L. G. M. (1998). MO and DFT approaches to the calculation of X-ray absorption/emission spectra of nitrogen atom adsorbed on Cu(100). Surface Science, 398, 70.
Triguero, L., Pettersson, L. G. M., & Ågren, H. (1998). Calculations of X-ray emission spectra of molecules and surface adsorbates by means of density functional theory. Journal of Physical Chemistry A, 102, 10599.
Ugarte, D. (1992). Curling and closure of graphitic networks under electron-beam irradiation. Nature, 359, 707i–709i.
Ugarte, D. (1995). Onion-like graphitic particles. Carbon, 33, 989–993.
Vahtras, O., Almlöf, J., & Feyereisen, M. W. (1993). Integral approximations for LCAO-SCF calculations. Chemical Physics Letters, 213, 514.
Valerio, G., Goursot, A., Vetrivel, R., Malkina, O., & Malkin, V. (1998). Calculation of 29Si and 27Al MAS NMR chemical shifts in zeolite-β using density functional theory: Correlation with lattice structure. Journal of the American Chemical Society, 120, 11426.
Vásquez-Pérez, J. M., Gamboa Martinez, G. U., Köster, A. M., & Calaminici, P. (2009). The discovery of unexpected isomers in sodium heptamers by Born–Oppenheimer molecular dynamics. Journal of Chemical Physics, 131, 124126.
Velde, G. T., Bickelhaupt, F. M., Baerends, E. J., Guerra, C. F., Van Gisbergen, S. J. A., Snijders, J. G., & Ziegler, T. (2001). Chemistry with ADF. Journal of Computational Chemistry, 22, 931.
Vos, A. M., Rozanska, X., Schoonheydt, R. A., van Santen, R. A., Hutschka, F., & Hafner, J. (2001). A theoretical study of the alkylation reaction of toluene with methanol catalyzed by acidic mordenite. Journal of the American Chemical Society, 123, 2799.
Vosko, S. H., Wilk, L., & Nusair, M. (1980). Accurate spin-dependent electron liquid correlation energies for local spin-density calculations – a critical analysis. Canadian Journal of Physics, 58, 1200.
Weber, J., Berthou, H., & Jorgensen, C. K. (1977). Application of the MS Xα method to the understanding of satellite excitations in inner shell photoelectron spectra of lanthanide trifluorides. Chemical Physics Letters, 45, 1.
Wei, D. Q., & Salahub, D. R. (1994). Hydrated proton clusters and solvent effects on the proton transfer barrier: A density functional study. Journal of Chemical Physics, 101, 7633.
Wei, D. Q., & Salahub, D. R. (1997). Hydrated proton clusters: Ab initio molecular dynamics simulation and simulated annealing. Journal of Chemical Physics, 106, 6086.
Wei, D. Q., Proynov, E. I., Milet, A., & Salahub, D. R. (2000). Solvation of the hydroxide anion: A combined DFT and molecular dynamics study. Journal of Physical Chemistry A, 104, 2384.
Xu, C. H., & Scuseria, G. E. (1996). An O(N) tight-binding study of carbon clusters up to C8640: The geometrical shape of the giant icosahedral fullerenes. Chemical Physics Letters, 262, 219.
Yang, D. S., Zgierski, M. Z., Berces, A., Hackett, P. A., Roy, P. N., Martinez, A., Carrington, T., Salahub, D. R., Fournier, R., Pang, T., & Chen, C. F. (1996). Vibrational and geometric structures of Nb3C2 and \({\mathrm{Nb}}_{3}{\mathrm{C}}_{2}^{+}\) from pulsed field ionization-zero electron kinetic energy photoelectron spectra and density functional calculations. Journal of Chemical Physics, 105, 10663.
Yang, Y., Trafford, K., Kresnawahjuesa, O., Sepa, J., Gorte, R. J., & White, D. (2001). An examination of confinement effects in high-silica zeolites. Journal of Physical Chemistry B, 105, 1935.
York, D., Lu, J. P., & Yang, W. (1994). Density-functional calculations of the structure and stability of C240. Physical Review B, 49, 8526.
Zhao, Q., & Parr, R. G. (1992). Quantities T s [n] and T c [n] in density-functional theory. Physical Review A, 46, 2337.
Zhao, Q., & Parr, R. G. (1993). Constrained-search method to determine electronic wave functions from electronic densities. Journal of Chemical Physics, 98, 543.
Zhao, Q., Morrison, R. C., & Parr, R. G. (1994). From electron densities to Kohn-Sham kinetic energies, orbital energies, exchange-correlation potentials, and exchange-correlation energies. Physical Review A, 50, 2138.
Zope, R. R., Baruah, T., Pederson, M. R., & Dunlap, B. I. (2008). Static dielectric response of icosahedral fullerenes from C60 to C2160 characterized by an all-electron density functional theory. Physical Review B, 77, 115452.
Acknowledgments
Financial support from CONACYT (U48775, 60117-F and 130726), ICYTDF (PIFUTP08-87 and PICCO-10-47), and CIAM (107310) is gratefully acknowledged. Parts of this chapter have been realized with the help of the bilateral CONACYT-CNRS project 16871.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer Science+Business Media B.V.
About this entry
Cite this entry
Calaminici, P. et al. (2012). Auxiliary Density Functional Theory: From Molecules to Nanostructures. In: Leszczynski, J. (eds) Handbook of Computational Chemistry. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0711-5_16
Download citation
DOI: https://doi.org/10.1007/978-94-007-0711-5_16
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-0710-8
Online ISBN: 978-94-007-0711-5
eBook Packages: Chemistry and Materials ScienceReference Module Physical and Materials ScienceReference Module Chemistry, Materials and Physics