QUANTUM SYSTEMS IN CHEMISTRY AND PHYSICS Basic Problems and Model Systems Progress in Theoretical Chemistry and Physics Volume Honorary Editors: William N Lipscomb (Harvard, MA, USA) Ilya Prigogine (Brussels, Belgium) ExecutiveEditors : Jean Maruani (Paris, France) Stephen Wilson (Oxon, UK) Advisory Editors: Hans Agren (Stockholm, Sweden) David Avnir (Jerusalem, Israel) Jerzy Cioslowski (Tallahassee, FL, USA) Raymond Daudel (Paris, France) K.U Gross (Würzburg, Germany) W.F van Gunsteren (Zürich, Switzerland) Kimihiko Hirao (Tokyo, Japan) Ivan Hubaỗ (Bratislava, Slovakia) Melvyn P Levy (New Orleans, LA, USA) Gulzari L Malli (Burnaby, Canada) Roy McWeeny (Pisa, Italy) Paul G Mezey (Saskatoon, Canada) M.A.C Nascimento (Rio, Brazil) Jacek Rychlewski (Poznan, Poland) Steven D Schwartz (New York, NY, USA) Yves G Smeyers (Madrid, Spain) Sandor Suhai (Heidelberg, Germany) Orlando Tapia (Uppsala, Sweden) Peter R Taylor (San Diego, CA, USA) R Guy Woolley (Nottingham, UK) Quantum Systems in Chemistry and Physics Volume Basic Problems and Model Systems Granada, Spain, 1998 Edited by Alfonso Hernández-Laguna Estación Experimental del Zaidín (C.S.I.C.), Granada, Spain Jean Maruani Laboratoire de Chimie Physique (C.N.R.S.), Paris, France Roy McWeeny Universita di Pisa, Pisa, Italy and Stephen Wilson Rutherford Appleton Laboratory, Oxfordshire, United Kingdom KLUWER ACADEMIC PUBLISHERS NEW YORK / BOSTON / DORDRECHT / LONDON / MOSCOW eBook ISBN: Print ISBN: 0-306-46941-3 0-792-35969-0 ©2002 Kluwer Academic Publishers New York, Boston, Dordrecht, London, Moscow Print ©2000 Kluwer Academic Publishers London All rights reserved No part of this eBook may be reproduced or transmitted in any form or by any means, electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America Visit Kluwer Online at: and Kluwer's eBookstore at: http://kluweronline.com http://ebooks.kluweronline.com Progress in Theoretical Chemistry and Physics A series reporting advances in theoretical molecular and material sciences, including theoretical, mathematical and computational chemistry, physical chemistry and chemical physics Aim and Scope Science progresses by a symbiotic interaction between theory and experiment: theory is used to interpret experimental results and may suggest new experiments; experiment helps to test theoretical predictions and may lead to improved theories Theoretical Chemistry (including Physical Chemistry and Chemical Physics) provides the conceptual and technical background and apparatus for the rationalisation of phenomena in the chemical sciences It is, therefore, a wide ranging subject, reflecting the diversity of molecular and related species and processes arising in chemical systems The book series Progress in Theoretical Chemistry and Physics aims to report advances in methods and applications in this extended domain It will comprise monographs as well as collections of papers on particular themes, which may arise from proceedings of symposia or invited papers on specific topics as well as initiatives from authors or translations The basic theories of physics – classical mechanics and electromagnetism, relativity theory, quantum mechanics, statistical mechanics, quantum electrodynamics – support the theoretical apparatus which is used in molecular sciences Quantum mechanics plays a particular role in theoretical chemistry, providing the basis for the valence theories which allow to interpret the structure of molecules and for the spectroscopic models employed in the determination of structural information from spectral patterns Indeed, Quantum Chemistry often appears synonymous with Theoretical Chemistry: it will, therefore, constitute a major part of this book series However, the scope of the series will also include other areas of theoretical chemistry, such as mathematical chemistry (which involves the use of algebra and topology in the analysis of molecular structures and reactions); molecular mechanics, molecular dynamics and chemical thermodynamics, which play an important role in rationalizing the geometric and electronic structures of molecular assemblies and polymers, clusters and crystals; surface, interface, solvent and solid-state effects; excited-state dynamics, reactive collisions, and chemical reactions Recent decades have seen the emergence of a novel approach to scientific research, based on the exploitation of fast electronic digital computers Computation provides a method of investigation which transcends the traditional division between theory and experiment Computer-assisted simulation and design may afford a solution to complex problems which would otherwise be intractable to theoretical analysis, and may also provide a viable alternative to difficult or costly laboratory experiments Though stemming from Theoretical Chemistry, Computational Chemistry is a field of research v Progress in Theoretical Chemistry and Physics in its own right, which can help to test theoretical predictions and may also suggest improved theories The field of theoretical molecular sciences ranges from fundamental physical questions relevant to the molecular concept, through the statics and dynamics of isolated molecules, aggregates and materials, molecular properties and interactions, and the role of molecules in the biological sciences Therefore, it involves the physical basis for geometric and electronic structure, states of aggregation, physical and chemical transformations, thermodynamic and kinetic properties, as well as unusual properties such as extreme flexibility or strong relativistic or quantum-field effects, extreme conditions such as intense radiation fields or interaction with the continuum, and the specificity of biochemical reactions Theoretical chemistry has an applied branch – a part of molecular engineering, which involves the investigation of structure–property relationships aiming at the design, synthesis and application of molecules and materials endowed with specific functions, now in demand in such areas as molecular electronics, drug design or genetic engineering Relevant properties include conductivity (normal, semi- and supra-), magnetism (ferro- or ferri-), optoelectronic effects (involving nonlinear response), photochromism and photoreactivity, radiation and thermal resistance, molecular recognition and information processing, and biological and pharmaceutical activities, as well as properties favouring self-assembling mechanisms and combination properties needed in multifunctional systems Progress in Theoretical Chemistry and Physics is made at different rates in these various research fields The aim of this book series is to provide timely and in-depth coverage of selected topics and broad-ranging yet detailed analysis of contemporary theories and their applications The series will be of primary interest to those whose research is directly concerned with the development and application of theoretical approaches in the chemical sciences It will provide up-to-date reports on theoretical methods for the chemist, thermodynamician or spectroscopist, the atomic, molecular or cluster physicist, and the biochemist or molecular biologist who wish to employ techniques developed in theoretical, mathematical or computational chemistry in their research programmes It is also intended to provide the graduate student with a readily accessible documentation on various branches of theoretical chemistry, physical chemistry and chemical physics vi Contents Preface xi Part I Density Matrices and Density Functionals Three-body correlation effects in third-order reduced density matrices C Valdemoro, L.M Tel and E Pérez-Romero Part II Electron Correlation Effects Many-particle Sturmians applied to molecules J Avery and S Sauer 19 Treatment of electron correlation in localized representation C Kozmutza, E Kapuy and L Udvardi 41 Comparing (SC)2CAS-SDCI and externally corrected CCSD methods G Peris, J.-P Malrieu and J Planelles 73 The size-consistent self-consistent SDCI method for excited states and ionization potentials J Pitarch-Ruiz, J Sánchez-Marín, I Nebot-Gil, N Ben Amor and D Maynau 87 Ab initio summation over states/SCI for static and dynamic first hyperpolarizabilities of small molecules M Spassova, V.Monev, I Kanev, B Champagne, D.H Mosley and J.-M André 101 Correlation energies for diatomic molecules: a re-evaluation of the empirical estimates for the N2, CO, BF and NO+ systems H.M Quiney, D Moncrieff and S Wilson 127 Influence of electron correlation on the electronic structure of superconducting Y-ceramics I.G Kaplan, J Hernández-Cóbos and J Soullard 143 vii Contents Part III Relativistic Formulations Energies and other properties of heavy atoms and molecules U Kaldor and E Eliav 161 Variational principle in the Dirac theory: theorems, examples and counterexamples J Karwowski, G Pestka and M Stanke 177 Perspectives in relativistic Thomas-Fermi calculations for atomic sytems I Porras and A Moya 195 Expectation values for ground-state atoms from a modified Thomas-FermiDirac approach A Moya and I Porras 215 Correlated effective single-particle theory: relativistic optimized-potential method E Engel and A Facco-Bonetti 227 Ab-initio ZORA calculations S Faas, JG Snijders and J.H van Lenthe 251 Relativistic oscillator strengths for excited-state transitions in halogen atoms Regularities C Lavín, A.M Velasco and I Martín 263 Extension of the relativistic quantum defect orbital method to the treatment of many-valence electron atoms Atomic transitions in Ar II I Martín, A.M Velasco and C Lavín 273 Part IV Valence Theory Hyperspherical harmonics as atomic and molecular orbitals in momentum space V Aquilanti, S Cavalli, C Coletti, D Di Domenico and G Grossi 291 An overview of the CASVB approach to modern valence bond calculations T Thorsteinsson and D.L Cooper 303 Modern valence-bond description of the mechanisms of six-electron pericyclic reactions P.B Karadakov, D.L Cooper, T Thorsteinsson and J Gerratt 327 viii Contents A topological study of electron transfer and three-electron bond X Krokidis and A Sevin 345 BSSE-free MCSCF method for strong hydrogen bonds: investigation of H2O-HCl and NH3-HCl complexes A Famulari, M Sironi and M Raimondi 361 Part V Nuclear Motion Non-adiabatic molecular Hamiltonian Canonical transformation coupling electronic and vibrational motions I Hubac, P Babinec, M Polásek, J Urban, P Mach, J Másik and J Leszczyn' ski 383 The effect of pseudopotential on the torsional energy levels of hydrogen peroxide and deuterium peroxide M.L Senent and Y.G Smeyers 401 Contents of Volume 415 Combined Index to Volumes and 419 ^ ix ^ ^ ^ M.L Senent and Y.G Smeyers Table 2γ Numerical and analitical derivatives of Ln g and B B' (Ln g)' (Ln g)" V' H2O2 30 60 90 120 150 180 0.0 –0.09080722 0.68824078 1.30102890 0.74943701 1.34565330 0.0 0.0 –0.00126548 –0.06799784 –0.14799801 –0.05334943 –0.07009473 0.0 –0.21210425 0.29288876 2.19835990 1.87555250 –0.27748130 –0.36889385 0.46389929 –0.5183945 0.7175492 5.4333647 4.6707902 –0.7161390 –0.9813806 1.2333458 D2O2 30 60 90 120 150 180 0.0 0.10533452 0.38020683 0.73571270 0.68221352 0.73232659 0.0 0.0 –0.00446667 –0.03300607 –0.11917699 –0.07825813 –0.05621637 0.0 –0.40099892 –0.31480621 1.35229200 1.14459144 –0.15559284 –0.35505237 0.33140294 –0.51944780 –0.40951502 1.78381630 1.93755750 –0.22768182 –0.51799593 0.48473619 (16) In the case of the deuterium peroxide is: (17) B algorithm: Numerical derivatives The derivatives of ln g and B of a single conformation which correspond to the γi torsional angle, have been calculated numerically using the double precision declaration as real *16 For this purpose, nine values of B and ln g around γ i(γ i + ∆γ, γi + 2∆γ and γi – ∆γ, γi – 2∆γ ) have been calculated The grid has been defined for ∆γ = 10–8 rad The resulting nine values have been fitted to four termed Taylor series which were derived The numerical derivatives are identical (up to 15 decimal numbers) to those obtained analytically with the C algorithm shown in Table C algorithm: analytical derivatives The vibrational levels of hydrogen peroxide can be obtained in one-dimension In this case, the B parameters is: 408 The Effect of Pseudopotential on the Torsional Energy Levels of H2O2 and D2O2 (18) where |I | is the determinant of the external rotation matrix The two determinants |I | and g are defined as: (19) and g: (20) The derivatives of these equations require one to obtain the first and second derivatives of the G –1 matrix elements This, in turn, requires to obtain the first, second and third derivatives of the d, R, α and β (equations 5) internal coordinates with respect to γ, and the first, second and third derivatives of the Cartesian coordinates with respect to the internal coordinates As an initial molecular system of reference a system centered on the O1 atom, has been selected The x axis coincides with the O1-O2 bond and the three atoms O1, O2 and Hl lie in the xy plane Appendix I shows the equations that connect Cartesian and internal coordinates and their derivatives From the initial Cartesian coordinates, the X, Y and Z center-of-mass coordinates and its X ', Y' yZ' derivatives are calculated The positions of the atoms have to be referred to the center of mass: (21) The derivatives of B and In g are easily determined: (22) and the pseudopotential is obtained with equation (9) In the case of hydrogen peroxide, the analytical pseudopotential is: 409 M.L Senent and Y.G Smeyers (23) which is shown in Figure V' for D2O2: (24) Discussion and Conclusion In a previous paper on hydrogen peroxide, the pseudopotential was determined with the A algorithm The aim of this paper was the evaluation of the basis set effect on the levels In the present paper, the old calculations have been repeated with the optimal basis set improving the optimization of the internal coordinates It has to be remarked from the results in Tables, and that the B and C algorithms lead to similar results whereas the A algorithm gives the lowest results for the pseudopotential V ' is unappreciated when is determined with the A algorithm The best method is the C algorithm where the derivatives are calculated analytically In this case, the possible error in the results only arises from the fit of the equations (5) and with the number of selected conformations for the ab initio calculations that could be insufficient The method and the derivatives are extremely accurate In addition, the same conclusion concern the B algorithm since the first 15 decimal number of derivatives are identical to the analytical ones Differences between these two last Fig The Torsional Pseudopotential of H2O2 determined with MP2/AUG-cc-p VTZ 410 The Effect of Pseudopotential on the Torsional Energy Levels of H2O2 and D2O2 methods and the first one come from the calculations of the second derivatives of In g which produces a series of errors arising form all the stages of the A method Since the B and C methods produce identical results, it may be concluded that the B numerical algorithm is the optimum It has to be taken into consideration the personal effort required by the C method for a large molecule showing more that one independent vibration In the C case, the equations shown in Appendix I have to be derived for each molecule In addition, equation 20 increases with the number of large amplitude motions On the other hand, expenditure of personal effort using the B numerical algorithm is independent of the size of the problem V ' improves slightly the levels of hydrogen peroxide (Table 1) The energies go down to the experimental values of Camy-Peiret et al [15] The n = 1, and levels decrease cm–1 The effect of the torsional staggering is very small The splitting of n = arising from the trans barrier is 12.0625 cm–1 with no V ' and 12.4941 cm–1 if V ' is added The n = level splitting is 120.4 cm–1 with no V ' and changes cm–1 when the pseudopotential is added As was expected given the size of the cis barrier, V ' has not significant effect on the cis staggering In addition, the effect of V ' on D2O2 is approximately half part of the effect on the hydrogen species Finally, the zero point vibration corrections (SET V) use to be much larger than the pseudopotential corrections In the present case, these zero point corrections seems to give rise to unrrealistic values, probably because of the harmonic approximation used in the calculations The torsion mode as well as its interactions with the remaining modes are indeed very anharmonic Appendix Coordinates xl = x2 = x3 = y2 = y3 = z3 = x2 = d x3 = d – R cos α y3 = R sin α x4 = R cos α – d y4 = R sin α cos β z4 = –R sin α sen β First derivatives x1' x2' x3' y3' x4' y4' z4 = x2' = x3' = y2' = y3' = z3' = = d' = d' – R' cos α + R sin α(α') = R' sin α + R cos α(α' ) = R' cos α – R sin α(α' ) – d' = R' sin a cos b + R cos α(α') cos β – R sin α sin β(β) = –R' sin α sin β – R cos α(α')sin β – R sin α cos β(β )' 411 M.L Senent and Y.G Smeyers Second derivatives x1" = x2''' = x3" = y2" = y3" = z3" = x2" = d" x3" = d" – R" cos α + 2R' sinα(α') + R cos α(α')2 + R sin α(α") y3" R" sin α + 2R' cos α(α') – R sinα(α' )2 + R cos α(α") x4"= R" cos α – 2R' sin α(α') – R cos α(α')2 – R sin α(α") – d" y4"= R" sin α cos β + 2R' cos α(α') cos β – 2R' sin α sin β(β') – R sin α(α')2 cos β + R cos α(α")cos β – 2R cos α(α') sinβ(β') – R sin α cosβ(β ')2 – R sin α sinβ(β") z4" = – R" sin α sin β – 2R" cos α(α') sin β – 2R' sin α cos β(β') + R sin α(α')2 sin β – R cos α(α")sin β – 2R cos α(α')cos β(β') + R sin α sinβ(β')2 – R sin α cos β(β") Third derivatives x1''' = x2''' = x3''' = y2''' = y3''' = z3''' = x2''' = d''' x3''' = d'' – R''' cos α + 3R'' sin α(α' ) + 3R' cos α(α' )2 + 3R' sin α(α'' ) – R sin α(α' )3 + 3R cos α(α' )(α'') + R sin α(α''') y3''' = R''' sin α + 3R'' cos α(α' ) – 3R' sin α(α' )2 + 3R' cos α(α '' ) – R cos α(α' )3 – 3R sin α(α' )( α'' ) + R cos α(α ''' ) x4''' = R''' cos α – R'' sin α(α' ) – 3R' cos α(α' )2 – 3R' sin α(α'' ) + R sin α(α' )3 – 3R cos α(α' )( α'' ) – R sin α(α''' ) – d''' y4''' = R''' sin α cos β + 3R'' cos α(α' )cos β – 3R'' sin α sin β(β ' ) – 3R' sin α(α' )2 cos β + 3R' cos α(α'' )cos β – 6R' cos α(α ' )sin β(β '' ) – 3R' sin α cos β(β ' )2 – 3R' sin α sin β(β '' ) – R cos α(α' )3 cos β – 3R sin α(α' )( α'')cos β + 3R sin α(α' )2 sin β(β' ) + R cos a(a ''' )cos β – 3R cos α(α'' )sin β(β ' ) – 3R cos α(α')cos β(β')2 – 3R cos α(α' )sin β(β'' ) z4''' = –R''' sin α sin β – 3R'' cos α(α' )sin β – 3R'' sin α cos β(β') + 3R' sin α(α' )2 sin β – 3R' cos α(α'' )sin β – 6R' cos α(α' )cos β(β') + 3R' sin α sin β(β ' )2 – 3R' sin α cos β(β '' ) + R cos α(α' )3 sin β + 3R sin α(α' )( α'' )sin β + R sin α(α' )2 cos β(β ' ) – R cos α(α''' )sin β – 3R cos α(α'' )cos β(β ' ) + 3R cos α(α' ) sin β(β' )2 – 3R cos α(α' )cos β(β '' ) + R sin α cos β(β' )3 + 3R sin α sin β(β' )( β '' ) – R sin α cos β(β ''' ) Acknowledgements This work has been supported by the ‘Consejería de Educación y Cultura’ de la Comunidad de Castilla y León (BU07/97) and the ‘Vicerectorado de Investigación y Relaciones Internacionales’ of the University of Burgos Y.G.S and M.L.S also acknowledge the financial assistance from the ‘ Comision Interministerial de Ciencias y Tecnologia’ of Spain through grant no PB 96-0882 412 The Effect of Pseudopotential on the Torsional Energy Levels of H2 O2 and D2 O2 References 10 11 12 13 14 J.D Lewis, T.B Malloy Jr., T.H Chao and J Laane, J Mol Struct., 12, 472 (1972) M.A Harthcock and J Laane, J Phys Chem., 89 , 4231 (1985) M.L Senent J Mol Spectrosc., 191, 265 (1998) B Podolsky, Phys Rev, 32, 812 (1928) S Fernández-Herrera and M.L Senent J Mol Struct., 470, 313 (1998) Y.G Smeyers, M.L Senent, V Botella and D.C Moule, J Chem Phys., 98 , 2754 (1993) M.L Senent, D.C Moule and Y.G Semeyers, Can J Phys., 73, 425 (1995) M.L Senent, D.C Moule and Y.G Smeyers, J Chem Phys., 102, 5952 (1995) M.L Senent and Y.G Smeyers, J Chem Phys., 105, 2789 (1996) M.L Senent, Y.G Smeyers and D.C Moule, 102, 6730 (1998) J Phys Chem M.L Senent, Y.G Smeyers and D.C Moule, 94, 949 (1998) Mol Phys Y.G Smeyers and A Hernández-Laguna, Int J Quant Chem., 22, 681 (1982) M.L Senent, Chem Phys Lett, 296, 299 (1998) R.S Grev, B.J Deleeuw, Y Yamaguchi, S.-J Kim and F Schaefer III, in ‘Structures and Conformations of Non-Rigid Molecules’, NATO SCI Series, Kluwer Academic Publishers, pag 325, 1992 15 J.M Flaud C Camy-Peyret, J.W.C Johns and B Carli, J Chem Phys., 91, 1504 (1989) 16 D.E Woon and T.H Dunning, Jr., J Chem Phys., 98, 1358 (1993); R.A.Kendall, T.H Dunning, Jr and R.J Harrison, J Chem Phys., 96, 6796 (1992); T.H Dunning, Jr, J Chem Phys., 90, 1007 (1989) 17 Gaussian 94 (Revision A.l), M.J Frisch, G.W Trucks, H.B Schlegel, P.M.W Gill, B.G Johnson, M.A Robb, J.R Cheeseman, T.A Keith, G.A Petersson, J.A Mongomery, K Raghavachari, M.A Al-Laham, V.G Zakrzewski, J.V Ortiz, J.B Foresman, J Cioslowsky, B.B Stefanov, A Nanayakkara, M Challacombe, C.Y Peng, P.Y Ayala, W Chem, M.W Wong, J.L Andres, E.S Repogle, R Gomberts, R.L Martin, D.J Fox, J.S Binkley, D.J Defrees, J Baker, J.J.P Steward M Head-Gordon, C Gonzalez and J.A Pople, Gaussian, Inc., Pittsburgh PA, 1995 413 This page intentionally left blank Contents of Volume Preface xi Part VI Response Theory Duality in two-ways interferometers: the symmetric quanton-detecton system J Martínez-Linares and D.A Harmin Atomic resonances in external fields R González-Férez and W Schweizer 17 Propagator calculations for large molecules: Determination of transition eigenvalues with a subspace bisection method in the diagonal algebraic diagrammatic construction approximation D.E Parry 27 Accurate density-functional calculation of core XPS spectra: simulating chemisorption and intermolecular effects on real systems C Bureau and S Kranias 41 SCF, CI and DFT charge transfers and XPS chemical shifts in fluorinated compounds A Khoudir, J Maruani and M Tronc 57 Part VII Condensed Matter Diffusion Monte-Carlo calculations of quasi-bound states of rare gas-halogen clusters: a diabatic approach C García-Rizo, M.I Hernández, A García-Vela, N Halberstadt, P Villarreal and G Delgado-Barrio 93 Shell-like features and charge localization in protonated helium clusters: a density functional study I Baccarelli, F.A Gianturco, B Balta, V Aviyente and C Selỗuki 103 Bond elongation and charge transfer in diatomic molecules interacting with metal clusters: H2/Ni and O2/Pt revisited A Khoudir, J Maruani and C Minot 123 Contents of Volume Reactivity at silicon surfaces Si(100) x and Si(111) x A Markovits, P Sonnet, L Stauffer and C Minot 149 DFT modeling of Stark-tuning effect: CO on polarized Pd(100) as a probe for double-layer electrostatic effects in electrochemistry C Bureau, S Kranias, X Crispin and J.-L Bredas 169 Part VIII Reactive Collisions and Chemical Reactions Electro-nuclear quantum mechanics beyond the Born-Oppenheimer approximation Towards a quantum electronic theory of chemical reaction mechanisms O Tapia 195 MCSCF study of chemical reactions in solution within the polarizable continuum model and VB analysis of the reaction mechanism C Amovilli, F.M Floris and B Mennucci 213 Modeling of the reaction of azathioprine with the hydroxide anion M Hoffmann and J Rychlewski 233 A theoretical study of the OH radical addition to the xylenes V.-H Uc, I García-Cruz and A Vivier-Bunge 241 Quantum molecular systems in astrophysics: the illustrative example of interstellar nitriles and silanitriles O Parisel and D Talbi 261 Part IX Computational Chemistry and Physics Discrete variable method for non-integrable quantum systems W Schweizer, P Faßbinder and R González-Férez 301 Systematic truncation of a distributed universal even-tempered basis set of Gaussian functions: an application to the ground state of the BF molecule D Moncrieff and S Wilson 323 N–O and P–O bond nature in hypervalent compounds: is Bader analysis basis-set and geometry independent? J.A Dobado, H Martínez-García, J Molina and M.R Sundberg 331 416 Contents of Volume Hydrogen bond between the α-hydroxycarboxyl, α-hydroxyester and α-hydroxyamide group: ab-initio gas-phase and solution study of a double linkage via the hydroxyl group A Szarecka, J Rychlewski and U Rychlewska 355 Theoretical study of the proton affinities of some substituted derivatives of histamine and homologous compounds Structure-activity relationships Z Cruz-Rodríguez, C.I Sainz-Díaz and A Hernández-Laguna 367 Contents of Volume 393 Combined Index to Volumes and 397 417 This page intentionally left blank Combined Index to Volumes and (Entries are in the form [volume number]:[page number].) 3-body correlation effects, 1:3 ab initio, 1:101, 1:251, 1:401, 2:355, 2:367 and DFT, 2:233 ADC(2), 2:27 adiabatic connection, 1:227 adsorption, 2:123 algebraic diagrammatic construction, 2:27 alkali systems, 2:17, 2:301 Ar II, 1:273 aromaticity, 1:327 arrowhead matrix, 2:27 astrochemistry, 2:261 atmospheric reactions, 2:241 atomic transition energies, 1:161 azathioprine, 2:233 Bader analysis, 2:337 BeH2, 1:3 BF, 1:127, 2:323 BO approximation, 2:195 bond elongation, 2:123 Breit interaction, 1:227 BSSE, 1:361 canonical transformation, 1:383 CASSCF, 1:303 CASVB, 1:303, 1:327 catalysis, 2:123 charge localization, 2:103 charge transfer, 2:57, 2:123 chemical shift, 2:57 chemisorption, 2:41 CI, 2:57 CI singles, 1:101 CO, 1:87, 1:127, 2:169 complex coordinate rotation, 2: 17 computational chemistry, 2:233 conformation analysis, 2:355 core excitation, 257 core XPS spectra, 2:41 corrected CCSD, 1:73 correlation energies, : 127 Coulomb potential, 1:19 Coulomb problem, 1:291 cyclic dimers, 2:355 D O2, 1:401 density functional study, 2:103 density functional theory, 1:227 density functional calculation, 2:41 DFT, 2:57 DFT modelling, 2:169 diffusion Monte Carlo calculations, 293 Dirac equation, 1:177 discrete variable technique, 2: 17, 2:301 dissociation, 1:73, 2:123 distributed universal even-tempered basis set of Gaussian functions, 2:323 double ionization, 2:27 double-layer electrostatic effects, 2: 169 duality, 2:3 eigenvalue, 2:27 electric field gradients, 1:161 electric fields, 2:301 electrochemistry, 2:169 electron correlation, 1:41, 1:143, 2:123 electron transfer, 1:345 electronegativity, 2:57 electronic and vibrational motions, :383 electro-nuclear quantum mechanics, 2: 195 embedded cluster method, 1:143 exchange-correlation energy, 1:227 finite elements, 2:17, 2:301 first hyperpolarizability, 1: 101 fluorinated compounds, 2:57 fluorobenzenes, 2:27 GAMESS-UK, 1:251 Green’s function, 2:27 ground state, 2:323 group electronegativity, 2:57 H2O2, 1:401 H2O-HCl complex, 1:361 A Hernández-Laguna et al (eds.), Quantum Systems in Chemistry and Physics, Vol 1: Basic Problems and Model Systems, 419–421 © 2000 Kluwer Academic Publishers Printed in Great Britain Combined Index to Volumes and halogen atoms, :263 Hartree-Fock energies, 2:323 Hartree-Fock results, 1:3, 1:127 heavy atoms, :161 high Tc superconductivity, 1:143 histamine and homologous compounds, 2:367 hydrogen bonds, 1:361 hydrogen molecule, 2: 123 hydrogenic orbitals, :291 hydroxyl radical, 2:241 hyperspherical harmonics, :291 hypervalent compounds, 2:337 inter- and intra-molecular hydrogen bond, 2:355 intermolecular interactions, :361 interstellar medium, 2:261 ionization potentials, 1:87 J c l coupling, :273 kinetic balance, : 177 Kohn-Sham equations, :227 Kohn-Sham perturbation theory, 1:227 Lévy-Leblond equation, : 177 localized representation, :41 LS coupling, 1:273 magnetic fields, 2:301 many-particle Sturmians, : 19 matrix dressing, :87 MCSCF, 1:361, 2:213 minimax principle, : 177 modem valence bond, 1:303, 1:327 modified Thomas-Fermi-Dirac approach, 1:215 molecular abundances, 2:261 Møller-Plesset correlation energy, :227 multi reference configuration interactions, 1:87 N2, 1:127 net charge, 2:57 NH3-HCl complex, 1:361 nickel cluster, 2: 123 NMR, 2:57 N-O and P-O bond, 2:337 NO+, 1:127 420 non-adiabatic molecular Hamiltonian, :383 non-integrable quantum systems, 2:301 OH addition reactions, 2:241 optimized potential method, :227 orbital-dependent functionals, :227 oscillator strengths, :263 oxygen molecule, 2: 123 PCM, 2:355 pericyclic reactions, 1:327 platinum cluster, 2: 123 polarizable continuum model, 2:2 13 polarized Pd(100), 2: 169 propagator, 2:27 proton affinities, 2:367 protonated helium clusters, 2: 103 pseudopotential, 1:401 quantum chemistry, 2:261 quantum electronic theory, 2: 195 quantum chaos, 2:301 quasibound states, 2:93 rare gas-halogen clusters, 2:93 reaction mechanisms, 1:327, 2:233 relativistic approximations, 1:251 relativistic coupled cluster method, : 161 relativistic many-body theory, :227 relativistic Thomas-Fermi calculations, : 195 resonances, 2: 17 RQDO method, 1:263, 1:273 Rydberg states, 2:301 (SC)2CAS-SDCI, 1:73 SCF, 2:57 SCF-MI, 1:361 shell-like features, 2: 103 Si(100), 2:149 Si(1 1), 2:149 silicon surfaces, 2: 149 size-consistency, 1:87 size-extensivity, 1:73 sparse matrix, 2:27 spin free, 1:251 spin-coupled theory, 1:303, 1:327 Stark bases, 1:291 Stark effect, 2: 17 Stark-tuning effect, 2:169 Combined Index to Volumes and structure-activity relationships, 2:367 Sturmian expansions, 1:291 subspace bisection, 2:27 summation over states, :101 symmetric quanton-detecton system, 2:3 systematic trends, :263 systematic truncation, 3 third-order reduced density matrices, :3 three-electron bond :345 torsion, 1:401 transition probabilities, :273 transition states, 2:241 variational principle, : 177 VB analysis, 1:303, 1:327, 2:213 vertical excitation energies, :87 wave-packet propagation, 2:301 White Dwarf stars, 2:301 XPS, 2:57 xylenes, 2:241 yttrium ceramics, : 143 Zeeman bases, 1:291 421 Progress in Theoretical Chemistry and Physics S Durand-Vidal, J.-P Simonin and P Turq: Electrolytes at Interfaces 2000 ISBN 0-7923-5922-4 A Hernandez-Laguna, J Maruani, R McWeeny and S Wilson (eds.): Quantum Systems in Chemistry and Physics Volume 1: Basic Problems and Model Systems, Granada, Spain, 1997 2000 ISBN 0-7923-5969-0; Set 0-7923-597 1-2 A Hernandez-Laguna, J Maruani, R McWeeny and S Wilson (eds.): Quantum Systems in Chemistry and Physics Volume 2: Advanced Problems and Complex Systems, Granada, Spain, 1998.2000 ISBN 0-7923-5970-4; Set 0-7923-597 1-2 J.S Avery: Hyperspherical Harmonics and Generalized Sturmians 1999 ISBN 0-7923-6087-7 KLUWER ACADEMIC PUBLISHERS – DORDREEHT / LONDON / BOSTON ... -0.37273 -0.330 01 -0.3 011 5 -0.28359 -0.27275 2.38649 2 .14 664 1. 86383 1. 6 013 4 1. 37573 1. 23003 1. 17063 1. 15520 0.65880 1. 517 53 2.64943 4 .11 189 5.74868 7.24846 8.56944 N (T ''11 ) p0 R 0.50000 0. 512 66 0.54763... 1. 48568 2.47989 3. 610 25 4.85930 6 .19 629 7. 619 74 Table H2 molecule with 15 a.o’s per atom s – bg1 2.00000 1. 84702 1. 64335 1. 47329 1. 3 413 1 1. 2 419 0 1. 16885 1. 111 53 33 John Avery and Stephan Sauer... - - - 0.4 419 4 0.44730 0.42026 0.37273 0.330 01 0.3 011 5 0.28359 0.27275 p0 R 2.38649 2.00744 1. 56 813 1. 32 312 1. 213 71 1 .17 023 1. 15 516 1. 1 517 8 0.70449 1. 80370 3.20655 4.66079 6.04244 7.34554 8.59497