ISSN:0300-9238    

DOI:10.1039/F298783FX033

出版商:RSC    

年代:1987

数据来源: RSC

ISSN:0300-9238    

DOI:10.1039/F298783BX035

出版商:RSC    

年代:1987

数据来源: RSC

摘要:

ISSN 0300-9238 JCFTBS 83(9) 1577-1 741 (1 987) JOURNAL OF THE CHEMICAL SOCIETY Faraday Transactions II Molecular and Chemical Physics Dr Nicholas Handy of Cambridge University was invited to contribute a Keynote Paper on the general theme of Potential-energy Surfaces and Reaction Dynamics. He was supported by a group of research workers in the United Kingdom who submitted original papers on cognate subjects. All these papers have now been refereed, and are collected in the present issue. CONTENTS 1577 Accurate Ab knitio Prediction of Molecular Geometries and Spectroscopic Con- stants, using SCF and MP2 Energy Derivatives N. C. Handy, J. F. Gaw and E. D. Simandiras 1595 Geometries, Harmonic Frequencies and Infrared and Raman Intensities for H20, NH3 and CH, R.D. Amos 1609 An A6 Initio Investigation of N2.-.CO+ J. Baker and A. D. Buckingham 1615 Ab Initio Potential-energy Surfaces for the Reactions of Ali with H2 D. M. Hirst 1629 The Diradical Nature of Ketocarbenes occurring in the Wolff Rearrangement. An MC-SCF Study J. J. Novoa, J. J. W. McDouall and M. A. Robb 1637 An A6 lnitio Molecular Orbital Study of the Structure and Vibrational Frequencies of CHIMgH G. E. Quelch and I. H. Hillier 1643 An MC-SCF Study of the X 2B2,'A2and 2 2B2States of Benzyl J. E. Rice, N. C. Handy and P. J. Knowles 1651 The Electronic Structure of CH2 and the Cycloaddition Reaction of Methylene with Ethene M. Sironi, M. Raimondi, D. L. Cooper and J. Gerratt 1663 Variational Methods. for the Calculation of Rovibrational Energy Levels of Small Molecules B. T. Sutcliffe and J. Tennyson 1675 Local Density Approximations and Momentum-space Properties in Light Molecules and Ionic Solids N. L. Allan and D. L. Cooper 1689 Atomic Anisotropy and the Structure of Liquid Chlorine P. M. Rodger, A. J. Stone and D. J. Tildesley 1703 Orientation Dependence of the F+ H2Reaction. Analysis of the Angle-dependent Line-of-centres Model J. N. L. Connor, J. C. Whitehead and W. Jakubetz 1719 A Comparison of the Vibrational Predissociation Rates in the Rare-gas- Ethylene Clusters A. C. Peet, D. C. Clary and J. M. Hutson 1733 Trajectory Studies of S +O2 and 0+ S2 Collisions W. Craven and J. N. Murrell

ISSN:0300-9238    

DOI:10.1039/F298783FP114

出版商:RSC    

年代:1987

数据来源: RSC

摘要:

JOURNAL OF THE CHEMICAL SOCIETY Faraday Transactions I, Issue 9, 1987 Physical Chemistry in Condensed Phases For the benefit of readers of Faraday Transactions /I, the contents list of Faraday Transactions I, Issue 9, is reproduced below. 2693 A New Pressure-programmed Volumetric Method of Measuring Adsorption at the Gas-Solid Interface D. I. Hall, V. A. Self and P. A. Sermon 2697 The Inclusion of Diflunisal by a-and P-Cyclodextrins S. F. Lincoln, A. M. Hounslow, J. H. Coates and B. G. Doddridge 2705 Microcalorimetric Measurement of the Enthalpies of Transfer of a Series of ortho-and para-Alkoxyphenols from Water to Octan- 1-01 and from Isotonic Solution to Escherichia coli Cells E. Beezer, M. C. P. Lima, G. G. Fox, P. Arriaga, W. H. Hunter and B.V. Smith 2709 The Vapour Pressure of Benzene. Part 1.-An Assessment of Some Vapour- pressure Equations P. D. Golding and W. D. Machin 2719 The Vapour Pressure of Benzene. Part 2.-Saturated Vapour Pressures from 279 to 300 K P. D. Golding and W. D. Machin 2727 Comparison between Heterogeneous and Homogeneous Electron Transfer in p-Phenylenediamine Systems A. Kapturkiewicz and W. Jaenicke 2735 Kinetic and Equilibrium Studies associated with the Aggregation of Non-ionic Surfactants in Non-polar Solvents P. Jones, E. Wyn-Jones and G. J. T. Tiddy 2751 The Inclusion of Tropaeolin 000 No. 2 by Permethylated P-Cyclodextrin. A Kinetic and Equilibrium Study R. P. Villani, S. F. Lincoln and J. H. Coates 2757 Chemisorption and Disproportionation of Carbon Monoxide on Palladium/ Silica Catalysts of differing Percentage Metal Exposed C.L. M. Joyal and J. B. Butt 2765 Infrared Studies on Dinitrogen and Dihydrogen adsorbed over TiOz at Low Temperatures Y. Sakata, N. Kinoshita, K. Domen and T. Onishi 2773 A Small-angle Neutron Scattering Investigation of Rod-like Micelles aligned by Shear Flow P. G. Cummins, E. Staples, J. B. Hayter and J. Penfold 2787 The Study of Aluminium Deposition from Tetrahydrofuran Solutions of AlC1,-LiAlH, using Microelectrodes. Part 1 .-1: 1 A1Cl3-LiAlH, J. N. Howarth and D. Pletcher 2795 The Study of Aluminium Deposition from Tetrahydrofuran Solutions of AlC1,-LiAlH, using Microelectrodes. Part 2.-The Influence of Solution Compo- sition J. N. Howarth and D. Pletcher 2803 Electron Spin Resonance Studies of HR(CN):- and Pt(CN)S- formed by Irradi- ation of K,Pt(CN), in Solvents J.L. Wyatt, M. C. R. Symons and A. Hasegawa 2813 Medium Effect on the Electrochemical Behaviour of the Cd"/Cd(Hg) System in Propane-l,2-diol- Water Mixtures R. M. Rodrigues, E. Brillas and J. A. Garrido 2825 Kinetic Modelling of Multiple-site Activity and the Kinetics of Inhibition Reac- tions in the Hydrogenolysis of C2H6on a Nickel Wire Catalyst S. Kristyan and R. B. Timmons 2835 Study of the Influence of the Impregnation Acidity on the Structure and Properties of Molybdena-Silica Catalysts H. M. Ismail, C. R.Theocharis and M. I. Zaki (i) Contenrs 2841 Electrochemical Properties of Cation Exchange Membranes A. D. Dimov and I.Alexandrova 2847 The Hydration of Aliphatic Aldehydes in Aqueous Micellar Solutions V. R. Hanke, W. Knoche and E. Dutkiewicz 2857 Ground-state Reduced Potential Curves (RPC) of Non-metallic First- and Second-row Hydrides F. Jeni. and B. A. Brandt 2867 Hydrogen Bonding. Part 2.-Equilibrium Constants and Enthalpies of Complexa- tion for 72 Monomeric Hydrogen-bond Acids with N-Methylpyrrolidinone in l,l,l-Trichloroethane M. H. Abraham, P. P. Duce, J. J. Morris and P. J. Taylor 2883 Catalysis by Amorphous Metal Alloys. Part 6.-Factors controlling the Activity of Skeletal Nickel Catalysts prepared from Amorphous and Crystalline Ni-Zr Powder Alloys H. Yarnashita, M. Yoshikawa, T. Funabiki and S.’Yoshida 2895 Catalysis by Amorphous Metal Alloys.Part 7.-Formation of Fine Fe Particles on the Surface of an Alloy in the Recrystallisation State prepared from an Amorphous FegoZrlo Powder Alloy H. Yamashita, K. Sakai, T. Funabiki, S. Yoshida and Y. Isozumi 2901 Chemical Equilibria and Kinetics at Constant Pressure and at Constant Volume E. Whalley 2905 Cluster Size Distribution in a Monte Carlo Simulation of the Micellar Phase of an Amphiphile and Solvent Mixture C. M. Care 2913 Transformation of But-1 -ene into Aromatic Hydrocarbons over ZSM-5 Zeolites Y. Ono, H. Kitagawa and Y. Sendoda 2925 Intermolecular Structure around Lithium Monovalent Cations in Molten LiAIC1, Y. Kameda and K. Ichikawa 2935 Excited-state Reactivity in a Series of Polymerization Photoinitiators based on the Acetophenone Nucleus J.P. Fouassier and D. J. Lougnot 2953 Kinetic Models for the Development of Density in Radiographic Film. Visible- light Exposure B. W. Darvell 2963 Formation of Hydrocarbons from CO + H2 using a Cobalt-Manganese Oxide Catalyst. A 13C Isotopic Study M. van der Riet, R. G. Copperthwaite and G. J. Hutchings 2973 Surface Reactivity and Spectroscopy of Alkaline-earth Oxide Powders. Part 3.-’H/’H and 180/160Exchange on Specpure CaO J. Cunningham and C. P. Healy 2985 The Thermodynamics of Solvation of Ions. Part 4.-Application of the Tetraphenylarsonium Tetraphenylborate (TATB) Extrathermodynamic Assump- tion to the Hydration of Ions and to Properties of Hydrated Ions Y. Marcus 2993 A Study of Proton Transfer by 2,2’-Bipyridine from Water to Nitrobenzene using Chronopotentiometry with Cyclic Linear Current-scanning and Cyclic Voltam- metry Y.Liu and E. Want 3001 Redox Reactions with Colloidal Metal Oxides. Comparison of Radiation-gener-ated and Chemically-generated RuOz -2H20 and Mn02 Colloids A. Harrirnan, M-C. Richoux, P. A. Christensen, S. Mosseri and P. Neta 3015 Non-isothermal Reduction Kinetics and Reducibilities of Nickel and Cobalt Faujasites G. Schulz-Ekloff, L. Czarnetzki and A. Zukal 3027 The Conductivity of Dilute Solutions of Mixed Electrolytes. Part 1.-The System NaCI-BaCI2-H20 at 298.2 K H. Bianchi, H. R. Corti and R. Fernandez-Prini 3039 Pairwise Gibbs Function Cosphere-Cosphere Group Interaction Parameters for Alkylammonium Salts in Aqueous Solutions at 298 K; Solubilities of Hydrocar-(ii) Contents bons in Aqueous Salt Solutions M.J. Blandamer, J. Burgess, M. R. Cottrell and A. W. Hakin 3055 Heterogeneous Decomposition of Trichlorofluoromethane on Carbonaceous Surfaces A. J. Colussi and V. T. Amorebieta 306 1 Adsorptive Properties of Semiconducting Thin NiO and TiOz Films combined with an Oppositely Polarized Ferroelectric Support Y. Inoue, K. Sat0 and 0.Hayashi 3069 Reactions of Alkenes and the Equilibration of Hydrogen and Deuterium on Zirconia R. Bird, C. Kemball and H. F. Leach 3083 Calorimetric Investigations of Association in Ternary Systems. Part 4.-The Influence of Solvation on Enthalpy of Complex Formation in Phenol-Tetrahy- drofuran and 2,6-Dimethylphenol-Tetrahydrofuran Systems P.Goralski and M. Tkaczyk The following papers were accepted for publication in Faraday Transactions IZ during June 1987 6/ 1236 Time-resolved Fluorescence of p-Dimethylamine-Benzonitrile in Mixed SoI-vents S. R. Meech and D. Phillips 6/ 1053 Excitonic Treatment and Nature of Bonding in the Aggregates of Rhodamine 6G in Ethanol M. P. R. Ojeda, I. A. K. Amashta, J. R. Ochoa and I. L. Arbeloa 6/2147 Electron Transfer Reaction of Water-solube Gold Porphyrins T. Shimidzu, H. Segwa, T. Iyoda and K. Honda 6/ 2448 The Quenching of O,( b'Zgt) at High Temperatures. Kinetics, Sensitivity Analysis and Corrections P. M. Borrell, P. Borrell and D. S. Richards 7/237 Transient Production and Decay following Laser Excitation of Opaque Materials D.Oelkrug, W. Honnen, F. Wilkinson and C. J. Willsher 7/ 246 Solvent Effects on the Theta Temperature of Polymers of Various Architec- tures M. K. Kosmas 71434 Change of the Electronic Structures of Molecular Fastener Tetrakis( alky1thio)tetrathiafulvalene(TTC-TTF)-on the Solid- Melt Transi- tion H. Yamamoto, K. Seki and H. Inokuchi 7/ 523 ZeroAield Pulsed Response and Dipolar Couplings in Systems of Spin Z = 1 Nuclei J. C. Pratt and A. Watton 7/ 606 Arrhenius Parameters for the Addition of HO' Radicals to Pent-1-ene, Hex-l- ene and cis-and trans-Hex-2-ene over the Range 400-520°C S. K. Gulati, S. Mather and R. W. Walker 7/618 Photophysical Properties of Ru-Cyanopolypyridine Complexes: Acidity and Temperature Tuning of Luminescence Properties A.Juris, F. Barigelletti, V. Balzani, P. Belser and A. V. Zelewsky 71656 A Chemical Interpretation of Vibrationally Induced Barriers to Hindered Internal Rotation T. A. Claxton and A. M. Graham 7/683 Kinetic Study of the Reactions of Ground-state Silicon Atoms, Si( 33P,), with 1,3-Butadiene and But-2-yne S. C. Basu and D. Hussain 7/ 762 Measurement of Absolute Rate Data for the Reaction of Atomic Potassium, K(4 'S,,?), with CF3CI, CFzCI, CFC13, CF,Br and SF6 as a Function of Temperature by Time-resolved Atomic Resonance Absorption Spectroscopy at A = 404 nm [K(5 'P,) -+ K(4 'S, 2)] D. Hussain and Y. H. Lee (iii) CUMULATIVE AUTHOR INDEX, Adams, N. G., 149 Clary, D. C., 139, 1719 Allan, N.L., 449, 1675 Clausen, K., 1109 Allouche, A., 871 Collette, H., 1263 Amico, A., 619 Connerade, J-P., 417 Amorim da Costa, A. M., 647 Connor, J. N. L., 1703 Amos, R. D., 1595 Cooper, D. L., 449, 1651, 1675 Anastasi, C., 277 Craven, W., 1733 Arimondo, E., 463 Curtis, M.G., 1041 Arthur, N. L., 277 Czarnowski, J, 579 Ashfold, M. N. R., 417 Davies, A. N., 707 Astheimer, H., 347 de Cogan, D., 837, 843 Atherton, N. M., 569 Delhalle, J., 503 Baig, M. A., 417 Delhalle, S., 503 Baker, J., 1609 Deremince-Mathieu, V., 1263 Baldwin, P. J., 1049 Derouane, E. G., 1263 Baldwin, R. R., 759 Devolder, P., 731 Baranyai, A., 1335 Di Biasio, A., 619 Barigelletti, F., 1567 Dixon, R. N., 417, 675 Barnett, A. J., 1453 Doggett, G., 211 Basu, S., 1325 Dowben, P.A., 403 Bateman, J. B., 355 Driscoll, D. C., 403 Bayley, J. M., 417 Dyke, J. M., 69, 1555 Beaman, R. A., 707 Edgecombe, K. E., 1307 Becerra, R., 435 Ellis, A. M., 1555 Benson, S. W., 791 Emsley, J. W., 371 Berberan-Santos, M. N., 1391 Evans, H., 1525 Berchiesi, G., 619 Evans, M. W., 463 Bernard, D. M., 29 FehCr, M., 1555 Beynon, J. H., 37 Fender, B. E. F., 1113 Billington, A. P., 1543 Fernandez, M. T., 89, 159 Blackford, D. S., 569 Ferreira Marques, M. F. R. Blaive, B., 775 M., 647 Boland, B. C., 1105 Firth, N. C., 1011, 1023, 1029 Boodaghians, R. B., 529 Fogel, N., 289 Booth, C., 917, 927 Fowles, M., 1465 Borrell, P., 1543 Frey, H. M., 435, 601, 1049 Borrell, P. M., 1543 Gabelica, Z., 1263 Boucarut, R., 1317 Gabriel, C., 355 Bowden, Z.A., i105 Gartrell-Mills, P. R., 1335 Boyd, R. J., 1307 Gaw, J. F., 1577 Boyd, R. K., 37 Gehring, S., 347 Braynis, H. S., 627, 639 Geiger, A., 1335 Brenton, A. G., 37 Gerratt, J., 1651 Brint, P., 723 Glorieux, P., 463 Brooks, M. S. S., 1189 Gray, P., 301, 539 Brydson, R. D., 747 Grice, R., 1011, 1023, 1029 Buckingham, A. D., 1609 Griffiths, T. R., 1215 Cametti, C., 619 Guo, H., 683 Campbell, C., 917, 927 Hackett, M. A., 1105 Canosa-Mas, C. E., 435, 1049, Hall, I. W., 529 1465 Handy, N.C., 1577, 1643 Carlier, M., 731 Harding, J. H., 1177 Catlow, C. R. A., 1065, 1113, Hasse, W., 347 1157, 1l.71 Hayes, W., 1105, 1109 Caudano, R., 1229 Hayhurst, A. N., 1 Chandler, G.S., 805 Heinzinger, K., 1335 Chaudron, F. Th., 1475 Henini, M., 837, 843 Chowdhury, M., 1325 Hennequin, D., 463 (iv) Herman, Z., 127 Hester, R. E., 1519 Heyes, D. M., 319 Higashi, M., 741 Hillier, 1. H., 1637 Hirst, D. M., 61, 1615 Hough, A. M., 173, 191 Houghton, P. J., 1465 Howard, B. J., 173, 191 Howard, N. W., 991 Hubbard, H. V. St. A., 1215 Huh, D. S., 971 Huizer, A. H., 1475 Hutchings, M. T., 1083, 1105, 1109 Hutson, J. M., 1719 Jackson, R. A., 1171 Jakubetz, W., 1703 Jennings, K. R., 89, 159 Jensen, J. B., 881 Johnson, C. A. F., 411, 985 Jones, R. N., 1 Jones, W. J., 693, 707 Jung, K-H., 971 Keen, A,, 759 Kelly, P. J., 1189 Kelly, S. D., 411, 985 Kime, Y.J., 403 King, T. A., 917, 927 Klenerman, D., 229, 243 Knowles, P. J., 1643 Kocot, A., 1439 Kohler, G., 513 Konijnenberg, J., 1475 Kosmas, A. M., 1001 Kosmas, M. K., 819 Koyano, I., 127 Lafage, C., 731 Lajtar, L., 473 Langley, A. J., 707 Ledwig, R., 655 Legon, A. C., 991 Leng, C. A., 1525 Lin, M. C., 905 Lips, A., 221 Litowska, M., 587 Liu, W-K., 387 Livsey, I., 1445 Luckhurst, G. R., 371 Macdonald, J. E., 1109 Macdonald, J. N., 1411 Magerl, A., 1109 Maier, J. P., 49 Malinowski, E. R., 933, 939 Mallawaarachchi, W., 707 Marciniak, B.,1475 Marston, G., 1453 Mason, R., 89 Mason, R. S., 159 Mathieson, K. J., 1041 Matthews, J. R., 1273 Matzke, H., 1121 Mayhew, C.A., 417 McAdam, K. G., 1509 McCaffery, A. J., 723 McCourt, F. R. W., 387 McCubbin, I., 1519 McDouall, J. J. W., 1629 McGreevy, R. L., 1335 Metzger, J., 775 Millican, P. G., 1041 Moore, J. N., 1487 Morris, A., 1555 Mullins, J., 301, 539 Murch, G. E., 1157 Murray, A. D., 1113, 1171 Murrell, J. N., 683, 1733 Naegele, J. R., 1229 Nagy, J. B., 1263 Nakashima, N., 1487 Nath, D., 1325 Newton, D. P., 675 Nicholas, J. E., 607 Nicholson, D., 663 Novoa, J. J., 1629 Ohse, R. W., 1235 Osborn, R., 1105, 1109 Outhwaite, C. W., 949 Palinkas, G., 1335 Parker, J. E., 411, 985 Parsonage, N. G., 663 Pasternq, K., 1439 Paszye, S., 1475 Patrykiejew, A., 473 Patterson, J. E., 255 Paul, A.J., 1555 Pauwels, J-F., 731 Peet, A. C., 1719 Pennino, D. J., 933, 939 Phillips, D., 1487, 1519 Phillips, L. F., 857 Phillips, R. A., 805 Pireaux, J-J., 1229 Plant, C., 1411 Pouzard, G., 871 Prieto, M. J. E., 1391 Prieve, D. C., 1287 Prince, J. D., 417 Quelch, G. E., 1637 Raimondi, M., 1651 Ralph, J., 1253 Raybone, D., 627, 639, 767 Rebizant, J., 1229 Reynolds, C. A.. 485, 961 Rice, J. E., 1643 Richards, D. S., 1.543 Rieley, H., 675 Riga, J., 503 Robb, M. A., 1629 Rodger, P. M., 1689 Roman, R., 1287 Roth, K., 1427 Ruff, I., 1335 Sage, I., 371 Saijo, H., 1317 Sanders, W. A., 905 Schmidt, W., 741 Schnabel, P. G., 1109 Schoenes, J., 1205 Sdranis, Y. S., 819 Sears, T.J., 111 Shilstone, G. N., 371 Siddiqui, M. A., 263 Simandiras, E. D., 1577 Sironi, M., 1651 Sloth, P., 881 Smith, D., 149 Smith, I. W. M., 229, 243 Sokolowski, S., 413 S~rensen, T. S., 881 Spencer, K., 1411 Spirlet, J-C., 1229 Stace, A. J., 29 Steiner, E., 783 Stevens, I. D. R., 601 Stevens, J. C. H., 1555 Stone, A. J., 1689 Stratton, T. G., 1143 Sutcliffe, B. T., 1663 Szczepanski, R., 319 Tanner, P. A., 553 Taylor, A. D., 1105 Tempczyk, A., 587 Tennyson, J., 1663 Thiry, P. A., 1229 Thomas, J. M., 747 Thomson, C., 485, 961 Tildesley, D. J., 1525, 1689 Tuller, H. L., 1143 Vaghjiani, G., 607 Varma, C. A. G. O., 1475 Verbist, J. J., 1263 Viras, F., 917, 927 Viras, K., 917, 927 Walker, I.C., 1041 Walker, R. W., 759, 1509 Walker, S., 263 Walsh, R., 435, 1049 Watkinson, T. M.,767 Watts, H. P., 601 Wayne, R. P., 529, 1453, 1465 Werbelow, L. G., 871, 897 Whitehead, J. C., 627, 639, 767, 1703 Williams, B. G., 747 Willis, B. T. M., 1073 Wolschann, P., 513 Wiirflinger, A., 655 Yamaguchi, H., 741 Yoshihara, K., 1487 Yun, S. J., 971 THE FARADAY DIVISION OF THE ROYAL SOCIETY OF CHEMISTRY SYMPOSIUM No. 23 Molecular Vibrations University of Reading, 15-16 December 1987 Organising Committee: Professor I.M. Mills (Chairman) Dr M. S. Child DrJ. E. Baggott Dr N. C. Handy Professor A. D. Buckingham Dr B. J. Howard The Symposium will focus on recent advances in our understanding of the vibrations of polyatomic molecules.The topics to be discussed will include force field determinations by both ab inifio and experimental methods, anharmonic effects in overtone spectroscopy, local modes and anharmonic resonances, intramolecular vibrational relaxation, and the frontier with molecular dynamics and reaction kinetics. The preliminary programme may be obtained from: Mrs. Y. A. Fish, The Royal Society of Chemistry, Burlington House, London W1V OBN ~ THE FARADAY DIVISION OF THE ROYAL SOCIETY OF CHEMISTRY GENERAL DISCUSSION No. 85 Solvation University of Durham, 28-30 March 1988 Organising Committee: Professor M. C. R. Symms (Chairman) DrJ.Yarwood Professor J. S. Rowlinson Dr A. D. Pethybridge Professor A.K. Covington Professor W. A. P. Luck Dr I. R. McDonald Dr D. A. Young The purpose of the Discussion is to compare solvation of ionic and non-ionicspecies in the gas phase and in matrices with corresponding solvation in the bulk liquid phase. The aim will be to confront theory with experiment and to consider the application of these concepts to relaxation and solvolytic processes. Topics to be covered are: (a) Gas phase non-ionic clusters, (b) Liquid phase non-ionic clusters, (c) Gas phase ionic clusters, (d) Liquid phase ionic solutions, (e) Dynamic processes including solvolysis. Speakers include: H. L. Friedman, 6.J. Howard, M.J. Henchman, S. Tomoda, 0.Kajimoto, M. H. Abraham, Yu Ya Efimov, J. L. Finney, P. Suppan, J. P.Devlin, D. W. James, G. W. Neilson, T. Clark, M. L. Klein, J. T. Hynes, G. A. Kenney-Wallace, G. R.Fleming, M. J. Blandamer and D. Chandler. The preliminary programme may be obtained from: Mr. Y. A. Fish, The Royal Society of Chemistry, Burlington House, London W1V OBN. THE FARADAY DIVISION OF THE ROYAL SOCIETY OF CHEMISTRY GENERAL DISCUSSION No. 86 Spectroscopy at Low Temperatures University of Exeter, 13-15 September 1988 Organ ising Committee : Professor A. C. Legon (Chairman) Dr P. R. R. Langridge-Smith Dr P. B.Davies Dr R. N. Perutz Dr B.J. Howard Dr M.Poliakoff The Discussion will focus on recent developments in spectroscopy of transient species (ions, radicals, clusters and complexes) in matrices or free jet expansions. The aim of the meeting is to bring together scientists interested in simi!ar problems but viewed from the perspective of different environments.Contributions for consideration by the Organising Committee are invited. Titles should be submitted as soon as possible and abstracts of about 300 words by30 September 1987 to: Professor A. C. Legon, Department of Chemistry, University of Exeter, Exeter EX4 4QD. Full papers for publication in the Discussion volume will be required by May 1988. ~~ THE FARADAY DIVISION OF THE ROYAL SOCIETY OF CHEMISTRY WITH THE ASSOCIAZIONE ITALIANA DI CHIMICA FISICA, DIVISION DE CHlMlE PHYSIQUE OF THE SOCIETE FRANCAISE DE CHlMlE AND DEUTSCHE BUNSEN GESELLSCHAFT FUR PHYSIKALISCHE CHEMIE JOINT MEETING Structure and Reactivity of Surfaces Centro Congressi, Trieste, Italy, 13-16 September 1988 Organising Committee: M.Che G. Ertl V. Ponec R. Rosei F. S. Stone A. Zecchina The conference will cover surface reactivity and characterization by physical methods: (i) Metals (both in single crystal and dispersed form) (ii) Insulators and semiconductors (oxides, sulphides, halides, both in single crystal and dispersed forms) (iii) Mixed systems (with special emphasis on metal-support interaction) The meeting aims to stimulate the comparison between the surface properties of dispersed and supported solids and the properties of single crystals, as well as the comparison and the joint use of chemical and physical methods. Further information may be obtained from: Professor C.Morterra, lnstituto di Chimica Fisica, Corso Massimo D'Azeglio 48, 10125 Torino, Italy. (vii) THE FARADAY DIVISION OF THE ROYAL SOCIETY OF CHEMISTRY SYMPOSIUM Orientation and Polarization Effects in Reactive Collisions To be held at the Physikzentrum, Bad Honnef, West Germany, 12-14 December 1988 Organ ising Committee: Dr S. Stolte Professor R. N. Dixon Professor R. A. Levine Professor J. P. Simons Dr K. Burnett Professor H. Loesch The Symposium will focus on the study of vector properties in reaction dynamics and photodissociation rather than the more traditional scalar quantities such as energy disposal, integral cross-sections and branching ratios. Experimental and theoretical advances have now reached the stage where studies of Dynamical Stereochemistry can begin to map the anisotropy of chemical interactions.The Symposium will provide an impetus to the development of 3-0 theories of reaction dynamics and assess the quality and scope of the experiments that are providing this impetus. Contributions for consideration by the Organising Committee are invited in the following areas: (A) Collisions of oriented or rotationally aligned molecular reagents (B) Collisions of orbitally aligned atomic reagents (C) Photoinitiated 'collisions' in van der Waals complexes (D) Polarisation of the products of full and half-collisional processes Abstracts of about 300 words should be sent by 31 October 1987 to: Professor J. P. Simons, Department of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD Full papers for publication in the Symposium volume will be required by 15 August 1988.(viii) FARADAY DIVISION INFORMAL AND GROUP MEETINGS ~~ Electrochemistry Group with the Society of Chemical Industry Batteries To be held at the Society of Chemical Industry, London on 13 October 1987 Further information from Or S. P. Tyfield, Central Electricity Generating Board, Berkeley Nuclear Laboratories, Berkeley, Gloucestershire GL13 9PB Polymer Physics Group with the Institute of Marine Engineers Polymers in a Marine Environment To be held in London on 14-16 October 1987 Further information from Professor G. J. Lake, MRPRA, Brickendonbury, Herts SG13 8NL Division London Symposium: Kinetics and Spectroscopy of Alkali and Ionic Species in the Laboratory in Flames and in the Upper Atmosphere To be held at the Scientific Societies Lecture Theatre, London on 3 November 1987 Further information from Mrs Y. A.Fish, The Royal Society of Chemistry, Burlington House, London W1V OBN Division with the Institute of Ph ysics and the British Society for Electro Heat Seminar in Drying and Curing To be held at Boddington Hall, University of Leeds on 17 November 1987 Further information from the Meetings Officer, Institute of Physics, 47 Belgrave Square, London SWlX 8QX Electrochemistry Group with the Electroanalytical Group Chemical Sensors To be held in London on 9-10 December 1987 Further information from Dr S.P. Tyfield, Central Electricity Generating Board, Berkeley Nuclear Laboratories, Berkeley, Gloucestershire GL13 9PB ~~~~~ ~ Electrochemistry Group with the Society of Chemical Industry Electrosynthesis To be held at the University of York on 15-17 December 1987 Further information from Dr S. P. Tyfield. Central Electricity Generating Board, Berkeley Nuclear Laboratories, Berkeley, Gloucestershire GL13 9PB Colloid and Interface Science Group with the Society of Chemical Industry The Preparation of Colloid Particulates and the Annual General Meeting To be held at the Society of Chemical Industry, Belgrave Square, London on 16 December 1987 Further information from Dr R. Buscall, ICI plc, Corporate Colloid Laboratory, PO Box 11, The Heath, Runcorn, Cheshire WA7 4QE ~~~~ ~ High Resolution Spectroscopy Group with CCF6 Spectroscopy and Dynamics of highly Excited States of Molecules To be held at the University of Reading on 16-18 December 1987 Further information from Professor 1.M. Mills, Department of Chemistry, University of Reading, Whiteknights, Reading RG6 2AD Neutron Scattering Group Scattering from Disordered Systems To be held at the University of Bristol on 16-18 December 1987 Further information from Dr G. W. Neilson. H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL Electrochemistry Group Electrochemistry/Surface Science: Must the Relationship remain Platonic? To be held at the University of Southampton on 6-7 January 1988 Further information from Dr S.P. Tyfield, Central Electricity Generating Board, Berkeley Nuclear Laboratories, Berkeley, Gloucestershire GL13 9PB (ix! Electrochemistry Group Workshop on Electrochemical Techniques and Instruments To be held at the University of Warwick on 6-7 January 1988 Further information from Dr P. N. Bartlett, Department of Chemistry, University of Warwick, Coventry CV4 7AL Surface Reactivity and Catalysis Group with the Process Technology Group and the Institute of Chemical Engineers Opportunities for Innovation in the Application of Catalysis To be held at Queen Mary College, London on 6-7 January 1988 Further information from Professor J. Pritchard, Queen Mary College, London Division with the Institute of Mathematics and its Applications Mathematical Modelling of Semiconductor Devices and Processes To be held at the University of Loughborough on 7-8 January 1988 Further information from the Institute of Mathematics, Maitland House, Warrior Square, Southend-on-SeaSS1 2JY Division London Symposium: Modern Electrochemical Systems To be held at Imperial College, London on 21 January 1988 Further information from MrsY. A.Fish, Royal Societyof Chemistry, Burlington House, London WIVOBN Polymer Physics Group with the 3Ps Group Plastics, Packaging and Printing To be held at the Institute of Physics, 47 Belgrave Square, London on 18 February 1988 Further information from Dr M. Richardson, National Physical Laboratory, Teddington, Middlesex Tw11 OLW ~~ ~~~ Theoretical Chemistry Group Postgraduate Students' Meeting To be held at University College, London on 2 March 1988 Further information from Dr G.Doggett, Department of Chemistry, University of York, York Colloid and Interface Science Group with The Society of Chemical Industry and British Radio frequency Spectroscopy Group Spectroscopy in Colloid Science To be held at the University of Bristol on 5-7 April 1988 Further information from Dr R. Buscall, ICI Corporate Colloid Science Group, PO Box 11, The Heath, Runcorn WA7 4QE Annual Congress: Division with Electrochemistry Group Solid State Materials in Electrochemistry To be held at the University of Kent, Canterbury on 12-1 5 April 1988 Further information from Dr J.F. Gibson, Royal Society of Chemistry, Burlington House, London W1V OBN Electrochemistry Group with The Society of Chemical Industry Electrolytic Bubbles To be held at Imperial College, London on 31 May 1988 Further information from Professor W. J. Albery, Department of Chemistry, Imperial College of Science and Technology, South Kensington, London SW7 2AY Electrochemistry Group with The Society of Chemical Industry Chlorine Symposium To be held at the Tara Hotel, London on 1-3 June 1988 Further information from Dr S. P. Tyfield, Central Electricity Generating Board, Berkeley Nuclear Laboratories, Berkeley, Gloucestershire GL13 9BP Gas Kinetics Group Xth International Symposium on Gas Kinetics To be held at University College, Swansea on 24-29 July 1988 Further information from Dr G. Hancock, Physical Chemistry Laboratory, South Parks Road, Oxford OX1 3QZ

ISSN:0300-9238    

DOI:10.1039/F298783BP116

出版商:RSC    

年代:1987

数据来源: RSC

摘要:

J. Chem. SOC.,Faraday Trans. 2, 1987, 83(9), 1577-1593 Accurate Ab Initio Prediction of Molecular Geometries and Spectroscopic Constants, using SCF and MP2 Energy Derivatives Nicholas C. Handy, Jeffrey F. Gaw and Emmanuel D. Simandiras University Chemical Laboratory, Lens-eld Road, Cambridge CB2 1E W The evaluation of analytic gradients and higher derivatives has had a tremen- dous impact on quantum chemistry. Although self-consistent field (SCF) first derivatives and higher derivatives are now routinely evaluated as ‘black- box’ procedures, derivatives of correlated wavefunctions are not. It is argued in the following that the least sophisticated correlated method, Mdler- Plesset second-order perturbation theory (MP2), can be treated so efficiently that first and second derivatives can be viewed as a ‘black-box’ procedure with the same limitations as the SCF first and second derivatives themselves. Discussed in this paper are the methods for MP2 geometry optimisation, evaluation of MP2 harmonic frequencies and prediction of i.r.intensities. Recent progress is reported which enables calculations with very large basis sets. Such calculations are reported for H20, NH, and CH4, where it is found that the MP2 large-basis ‘limit’ gives bond lengths within 0.003 8, and bond angles within 0.5” of experimental values. Harmonic frequencies at this MP2 ‘limit’ are typically within 2% of experimental values, and ix. intensities are much improved over SCF values. A previously suggested problem concerning the CH4 equilibrium bond length is also discussed and resolved.The evaluation of analytic third and fourth derivatives of the SCF energy is also discussed. Calculations with a DZP basis are reported for H20, NH3 and CH4, and values are given for vibration-rotation constants a!B),an-harmonic constants x,, ,vibrationally averaged corrections to bond lengths rg-re, and also ( v,-ur),the difference between fundamental and harmonic frequencies. For nearly all these values there is good agreement with the available experiment data (typically within 10%). The conclusion of this work is that ab inifio chemistry can now provide very accurate predictions of equilibrium geometries and harmonic frequen- cies using Mprller-Plesset second-order perturbation theory (MP2).Further- more, SCF cubic and quartic force constants can provide a good description of the anharmonic potential. Together these theoretical techniques yield an accurate full description of quadratic, cubic and quartic interactions, provid- ing the high-resolution spectroscopist with important data on a very wide class of molecules. In addition, as the theoretical techniques are suitably formulated for vector processing, the potential applications using supercom- puters instead of scalar mainframes moves from small to large molecules. 1. Introduction In this paper we wish to demonstrate the remarkable accuracy which it is now possible to achieve with quantum chemistry calculations, using programs which may be described primarily as ‘black-box’ in nature.We shall concentrate on the calculation of molecular properties which are of direct interest to the spectroscopist. We shall only use the simplest of ab initio methods; the self-consistent field (SCF) method, and second-order perturbation theory, commonly called M@ller-Plesset’ theory 1577 SCF and MP2 Energy Derivatives (MP2), at the correlated level. On the other hand, because we are concerned with very large calculations, we shall use the most efficient procedures known to us for the use of these two approaches. We shall be working with large basis sets and we shall use the theory of analytic derivatives wherever possible. The molecular properties we shall evaluate are (a)equilibrium geometries, (b) vibrational frequencies, (c) infrared intensities and (d) anharmonic constants.These are the principal properties of interest to the infrared and microwave spectroscopist. We shall only be concerned with closed-shell molecules well described by a single reference configuration. The molecules we have chosen to examine in detail are H20, NH3 and CH,. This choice may be criticised, but our purpose is to show that an almost complete theoretical understanding is now possible for these systems. It will be seen that we can even go so far as to question some of the ‘experimental’ data published on the ground states of these systems. Before outlining further details of the theory for these methods, we believe that it is valuable to sketch briefly recent theoretical developments in quantum-chemical methodology.In this way, these calculations can be seen as forming one specific approach among an entire set of methods to make quantum chemistry an increasingly accurate and useful field of research. 2. Resent Developments in Quantum Chemistry The successful completion of the self-consistent field energy program2 using Cartesian Gaussian basis sets3 for the representation of molecular orbitals, followed by the recognition of Pulay4 that the derivative of the SCF energy with respect to nuclear perturbations could be evaluated analytically, led to the next tremendous advance in quantum chemistry. Equilibrium geometries and transition states could now be accur- ately located. Dupuis et uL5 next provided an efficient procedure for the evaluation of Gaussian basis function integrals and their derivatives which removed difficult analytical problems.Using these ideas, coupled with the perturbation theory analysis of Gerratt and Mills,6 Pople et aL7then presented the analytic second energy derivative of the SCF energy, leading directly to (i) the characterisation of stationary points and (ii) the evaluation of harmonic frequencies. At the same time, Pople and coworkers’ were introducing correlating effects in a systematic way using perturbation theory at the second, third and fourth order (MP2, MP3 and MP4). Energy gradients were also evaluated analytically at the MP2 level.’ Pople’s work during this period culminated in the presentation of an increasingly sophisticated series of programs, GAUSSIAN (70,76,82),which were designed to be as near ‘black box’ as possible.Perhaps the greatest contribution of this work was that it made quantum chemistry an accepted tool of chemistry, available to any chemist with sufficient computing resources. As these programs have been increasingly used, the basis sets have been standardized, such as those denoted STO-3G, k -lmG‘*’, DZ, DZP. Many thousands of calculations using these programs have now been performed, a great number of which have been summarised in a recent book by Hehre et a1.’ One must of course be careful with the use of ‘black-box’ procedures and be aware of their limitations. The weakest part of the GAUSSIAN programs is the reliance on the unrestricted Hartree-Fock (UHF) wavefunction for open-shell systems.For such wavefunctions, (S’) will often differ substantially from the desired S(S + 1). Our investi- gation~,~using full configuration interaction (full CI), clearly show that UHF-MPn calculations must be viewed with the greatest suspicion when the difference between the calculated and desired (S2)exceeds 10%. This leads us to the equally important work which is continually going on to improve quantum-chemical methodology and overcome the inadequacies of SCF and MPn, especially for properties of molecules away from the equilibrium geometry. The coupled N. C. Handy, J. F. Gaw and E. D. Simandiras cluster (CC) method is finding increasing favour” because it is size-extensive and in some aspects includes all orders of perturbation theory.The coupled electron pair methods (CEPA)” may be viewed as approximations to CC. To perform reliable calculations away from equilibrium geometries on ground states, and on excited states and open-shell systems in general, there appears to be no acceptable choice other than to use variational methods, which are all based on MacDonald’s theorern.l2 Much work has thus gone into the multi-configuration SCF (MCSCF) procedure” and CI tech- nique~’~in general. Quantum chemistry has now reached the stage where MCSCF-CI calculations involving lo6 configuration state functions (CSFs) are becoming more common.15 We shall not discuss these developments further, but it is important to recognise their contribution to the long-term future of quantum chemistry.The extension of derivative theory to the correlated wavefunctions referred to in the last paragraph has demanded much effort.16 This effort, however, has been essential so that geometries and transition states can be located with a high degree of accuracy. It has paid off, as CI gradients17 are now as easily calculated as CI energies. Of equal importance has been the evaluation of derivatives beyond the second at the SCF level.’* This is a very valuable contribution of a6 initio chemistry to spectroscopy as it provides for the direct evaluation of anharmonic constants, just at the time when the experimental spectroscopist is producing an increasing number of such constants himself.” In this paper we shall discuss in some detail the present status of these calculations and report some new results.At the end of this summary of the present status of quantum-chemical methodology, it may be of interest to indicate for which procedures analytic energy derivatives are available, This is given in the Appendix. Coupled with this appendix, recognition must be given to the many quantum chemistry packages that are available, some of which have been around for a long time and predate the GAUSSIAN series. Codes which these authors have used include ATMOL,” HONDO,” GAMESS~’ and CADPAC.~~ Besides the extensive development of derivative methods and related methods for the determination of molecular properties, the other significant development of the 1980s has been the arrival of the ‘vector’ computer.In particular, the early arrival of a CRAY computer in the UK enabled quantum chemists24 to modify their codes to take advantage of the fast matrix multiply facilities. Our own quantum chemistry code, CADPAC,” now has a!l its time-consuming parts vectorised as much as possible, and is running at supercomputer centres worldwide. It should be noted that there are also supercomputer versions of GAUSSIAN and HONDO.~’ Machines with extensive main memory are becoming available. In addition to the CRAY super-computer, much work has also been done by groups using the FPS array processor (e.g. Argonne, Gainesville16 and Daresbury27). There have been several scientific meetings2’ at which quantum chemists have reported their success with CRAY, CYBER and FPS machines.Little work has been reported on the possibilities of reducing the input/output ratio by taking advantage of extensive memories. A11 of this discussion is to put into context the remaining parts of this paper. As mentioned in the introduction, we shall concentrate on large calculations using un- sophisticated methods (SCF and MP2). We underline the reason for this: we want our codes to have wide and general use and we believe our codes for these methods satisfy these criteria. We therefore use small molecules to determine the behaviour of our methods as a function of basis set and type of bonding. In greater detail we shall examine: (a)the accuracy of SCF and MP2 geometries as basis sets become complete.In particular, it will be seen that MP2 geometries are remarkably accurate at the large basis set limit; (6) the efficient evaluation of MP2 gradients; (c) the efficient evaluation of MP2 second derivatives; (d) the high accuracy of harmonic frequencies at the MP2 level evaluated with large basis sets; (e) the evaluation of i.r. intensities at the SCF and MP2 levels; (f)the evaluation of analytic SCF and MP2 Energy Derivatives third and fourth energy derivatives at the SCF level; (g) the evaluation of anharmonic spectroscopic constants. We shall show, using the results of our calculations on H20, NH3 and CH4, that (d), (e), (f) and (8) are capable of presenting extremely useful information to the spectroscopist.The scope of the remainder of the paper is as follows. In section 3 we discuss the theory and implementation for the evaluation of the first and second derivatives of the MP2 energy. In section 4 the theory for analytic third and fourth derivatives at the SCF level is discussed. In section 5 and 6 results of our calculations are reported and discussed. 3. First and Second Derivatives, and I.R. Intensities at the MP2 Level of Theory The detailed formulae for these derivatives and properties have been given el~ewhere;~'~~~ in particular we shall refer to ref. (31) and (32). We shall only outline and comment on the essential parts of our evaluation, and introduce some new aspects. Once an energy (e.g.MP2) has been expressed in terms of one- and two-electron integrals, (plhlq)and (pqlrs),over molecular orbitals &, the expression may be formally differentiated, taking into account that under a perturbation the orbitals change as X-*X+A4p -4p + wb"'= 4,+ c u;p44 i-A+;. (1) Here U$, represent the change in the molecular-orbital coefficients, and 6;denotes the evaluation of Cp, with derivatives of the basis functions. In MP2, SCF orbitals are used, and therefore the Ut,, are solutions of the coupled perturbed Hartree-Fock equations (CPHF)7 which we write HU"=b" (2) where H is a matrix derived from molecular-orbital integrals and b" is a vector derived from differentiated integrals htq and (pqlrs)". This formal differentiation of the MP2 energy expression yields (a,b, c, ... denote virtual orbitals, i, j, k, . . . denote occupied orbitals and p, q, . . . all orbitals throughout this section). L involves integrals and G" involves derivative integrals. On defining 2 as the solution HTZ=L (4) and writing c La;u:t= CZaib;, (5) it is then possible to obtain the following expression from eqn (3) Expressions for Y, W and I' are given in ref. (31). A back-transformation of Y, W, to Y, W, F gives as the working expression for the MP2 gradient in terms of A0 basis function integrals and their derivatives. Eqn (7) shows the importance of this derivation of the derivative.8 N. C. Handy, J. F. Gaw and E. D. Simandiras (i) one set of simultaneous equations, eqn (4), are solved instead of the 3 x number of nuclei (3N) sets, eqn (2), and (ii) no derivative integral is ever stored.One partial forward transformation and one partial back transformation are required, both of which can be vectorised. This is the best way for the evaluation of the MP2 gradient and is in contrast to that used in GAUSSIAN 82, where eqn (2) is solved 3N times and derivative integrals are stored. For these reasons, the GAUSSIAN 82 programs become impractical for large basis sets. The evaluation of MP2 gradients is now a routine part of CADPAC, both for the RHF (closed shell) and UHF wavefunctions. Very large cases can be run (e.g. 150 basis functions). In ref. (31) it is stated that MP2 gradients evaluated this way require less than twice as long as the corresponding SCF gradients.Since the speed of computers is increasing by a factor of two every year, quantum chemists can now use MP2 for systems that were only possible at the SCF level previously. The formula for the MP2 second derivative may be obtained in a number of ways, one of which is to evaluate the derivative of eqn (6). Another is to evaluate the second derivative of the energy directly, and then eliminate Uz in the same way that U;q was eliminated from the first derivative. This is detailed in ref. (30). It is not appropriate to reproduce the exact formula in all detail, but it may be summarised as This expression shows the complexity of the second derivative. We observe that the most difficult and time-consuming aspect is that the MO derivative integrals (rsI bj)" must be produced, but only a restricted list (ia 19)'must be stored for all x. On the other hand, second-derivative integrals are never stored or transformed. The CPHF equations, eqn (2), are solved and U" are held in memory.Most of the code is written in such a way that blocks of integrals are read into memory, and matrix operations are then performed. In spite of the considerable difficulties, an efficient code has been developed. Advantage of translational and rotational invariance has been taken to reduce by six (five for linear molecules) the total number of perturbations involved in the energy expression following the discussion by Page et aZ.34 Furthermore, in a new development, molecular symmetry has been introduced at every possible stage to reduce considerably the work for molecules with the symmetry of non-degenerate point groups.For example, only symmetry-unique A0 derivative basis function integrals are evaluated and transformed to the MO basis. In addition, only symmetry-unique elements of the second-derivative matrix are constructed. The theory for this follows directly from the work of Dupuis and King.3' The end product is that CADPAC now contains an efficient, vectorised closed-shell MP2 second-derivative code. It does, however, rely heavily on the existence of a large quantity of disc storage. We are able to perform calculations for harmonic frequencies with 120 basis functions using 1.3 GB of disc, and typical calculations are reported in section 5.To demonstrate the power of this program, we are presently calculating MP2 harmonic force constants for both benzene and pyridine36 on the CRAY-XMP; we shall need ca. 300 Mwords of disc space and 1.5 Mwords of central memory. In conclusion, we are impressed with the number of systems we can consider now that we have this program. It is hardly necessary to add that it is far more efficient to evaluate second derivatives analytically than by finite differences of gradients. A very useful by-product of this program is that it is possible to evaluate dipole- moment derivatives. In so doing, the dipole is considered as dE/dF, the derivative of SCF and MP2 Energy Derivatives the energy with respect to the external field.It is possible to write the dipole derivative as by gathering together the relevant terms in eqn (8) and eliminating U‘ by eqn (4) and (5). We repeat here the salient points of this procedure from ref. (32): ‘the overall process involves one SCF calculation, one forward 4-index transformation, seven solu-tions of first-order CPHF-like equations and three 4-index back-transformations. Our programs take two times as long as a gradient calculation, ie. it is faster than a forward-diff erence finite perturbation approach as well as being numerically more precise’. The general conclusion to this section is that we believe that we have efficient codes for the evaluation of MP2 gradients, second derivatives and i.r. intensities, which can be used with more than 100 basis functions.We make use of molecular symmetry and vector-processing capabilities. Examples of the use of these codes is given in section 5. 4. Evaluation of Third and Fourth Derivatives of the Self-consistent Field Energy According to the rules of perturbation theory, the third derivative of the energy only requires the first-order wavefunction. In other words d’E/dX d Y dZ can be expressed in terms of integrals (and their first, second and third derivatives) and U‘. The third derivative of the SCF energy was first successfully evaluated by Gaw et a/.’* The expression for the third derivative is complicated: it involves terms such as (pqI rs)”’, (pq/rs)“’U’,(pqlrs)”U”U‘and it may be found in ref. (18), (37) and (38).We have recently improved the efficiency of this program. Full molecular symmetry (including degenerate point groups) has been used in the evaluation of all the A0 derivative basis function integrals. The first-, second- and third-derivative A0 integrals are never stored, but merely evaluated, multiplied by appropriate back-transformed U” and entered into the final accumulator matrix. We find it most convenient to evaluate the first-derivative integrals twice, first to enable the solution of the CPHF equations and secondly for multiplication by U”. We believe that this is more satisfactory than storing these integrals. The most time-consuming part is the evaluation of the terms involving third-derivative integrals (apI y/3)xJ’;this has been rewritten in terms of matrix multiples and scalar products, ready for use on the vector computer. To show the scale of calculation that we can now consider, we are currently evaluating third derivatives for benzene, using a DZP basis Other examples are discussed in section 6 below.There has been a substantial improvement in our capability with the inclusion of the effects of full molecular symmetry. Our evaluation of the fourth derivatives d4E/dX 8 Y dZ d W proceeds currently by finite differences of third derivatives. We have no evidence that this procedure introduces numerical inaccuracy in our calculations. However, we are clear that it is inefficient. The evaluation of first, second and third derivatives takes ca. 2, 6 and 20 times the time for the evaluation of the SCF energy.It can be argued that these factors are determined by the increased number of Rys quadrature points. We must expect that analytical fourth derivatives will take 50 times as long, whereas, of course, finite-difference pro- cedures involve ca. 2 x 20 x 3 N times as much work! We are now in a position to begin to evaluate the fourth derivatives analytically. The expression for the fourth derivative may be obtained from a differentiation of the expression we use for the third derivative; it will involve terms such as (pqlrs)””’, rs)xJ’U”’, (pqirS)”U’”, (pqIrS)”U”U”, (pqfrs)xU”’U’’’, (pq1 rs)‘U’’U’U”, rs)U”’U’U” and (pqI rs)U‘U”U’U”’. 1583N. C. Handy, J. F. Gaw and E. D. Simandiras The algorithms for the evaluation of (cupI yS).ryzw are a straightforward extension of those3' for (ap I yS)")" and present no difficulty.The second-order CPHF equations39 HU"' = b"." (10) have to be solved; the form of b"" is known as it it has been used in the evaluation of MP2 second derivatives and CI second deri~atives.~~*~~*~~ Computationally this means that, for arguments given above, the first- and second-derivative integrals have to be evaluated twice. The U" and U"." ideally will be stored in main memory, but there will be many cases when this is not possible, and input/output facilities will have to be used. The completion of this program will substantially improve our capabilities. Of course, the reason for calculating these cubic and quartic force constants is that they give substantial information to the spectroscopist.The usual expansion formula for the vibrational levels of a polyatomic molecule (asymmetric top) is4' G(u)=CO,(U,+;)+ 1 X~~(ZI,+;)(U,+$)+* (11)* *. r rss If the potential V is expanded in dimensionless normal coordinates q then second-order perturbation theory can be used to find expressions for the anharmonic constants. Mills4* has given the formula for the anharmonic constants xr, as where Ar.Tf= (Or + 0s+ wt)(0,-~2 -mt)( -wr + + wt)(-wr -0s+ mt ) (15) and J are coriolis constants, with A, B, C the rotational constants. The cubic and quartic force constants &,( = a2V/aqrdq, dq,) and +,.sfu are obtained directly from the ab initio third and fourth derivatives by a linear transformation from Cartesian to normal coordinate space.Having evaluated the anharmonic constants, the quantum chemist can calculate the fundamentals, vr, as vr = wr+ 2xrr+ i c x,,. rfr Such calculations increase enormously the contribution that the quantum chemist can make to spectroscopy. We will merely summarise here the other spectroscopic data that we can now calculate. The cubic force constants directly give: the rotation-vibration interaction constants a z"' (the vibrational correction to the rotational constants); the sextic distortion constants HJK,HJ and HK;and the Fermi-resonance parameters yF (&,, appears in many models used in the experimental analysis of spectra). The quartic force constants give, besides the anharmonic constants, x,,, the Darling-Denni~on"~"~ constants K,,,,.Of course, other constants can be evaluated for systems with higher symmetry. Properties may also be vibrationally averaged from a knowledge of the cubic force constants. In section 6 values of some of these constants for our selected molecules will be presented. SCF and MP2 Energy Derivatives Table 1. Optimised geometries for H,O method basis set rOH/A eHOH/o ref. ~~ SCF 8s6p4d2f/6s3p 1 d 0.940 05 106.32 48 MP2 6-3 1 G" 0.969 104.0 8 MP2 DZP 0.961 58 104.48 MP2 MP2 MP2 MP2 5 s4p 2d / 8s6p3d/6s2p 8s6p4d 8s6p4d 1 f/6s3p 3s 2p 6s 3p 0.958 23 0.957 30 0.957 30 0.959 30 104.48 104.52 104.51 104.38 MP3 6-3 1 G* 0.967 104.3 8 M P4 6-31G" 0.970 103.9 8 M P4 39-§TO 0.959 6 104.4 50 CISD DZP 0.959 44 104.82 74 ClSDTQ DZP 0.963 69 104.42 51 CISD TZ2P 0.961 23 104.59 74 exptl 0.957 81 104.48 49 The theory of higher derivatives may be used to calculate properties related to external fields.For example, SCF dipole first, second and third derivatives may be calculated, to give overtone intensities and corrections to i.r. fundamental intensities. SCF polarisability derivatives may be calculated to give Raman intensities. In some of these areas the ab initio chemist has more knowledge than the experimentalist! We are currently investigating these properties for H,O and results will be published elsewhere. 5. SCF and MPS Geometries, Harmonic Frequencies and I.R.Intensities for H20, NH3 and CH4 near the Basis-set Limit The purpose of this section is to demonstrate the accuracy that can be achieved with large basis sets at the SCF and MP2 levels of calculation. All calculations were performed using CADPAC with the methods described in the earlier sections. The smaller basis sets used in our calculations were the 4s2p (2s for HI and 5s4p (3s for H) Dunning c~ntractions~~ of the Huzinaga4' 9s5p(4s) and 10s6p(5s)primitive sets. Larger basis sets are built from the 8s6p contraction of van Duijneveldt'~~~ 13s8p primitives, and for H the 6s contraction of 10s primitives. Polarisation functions were added: Id, 2d, 3d sets for C, N, 0 and lp, 2p, 3p sets for H with the following exponents: C: (0.8; 1.2,0.4; 1.8, 0.6,0.2) N: (0.8; 1.35,0.45; 2.4, 0.8,0.266) 0: (0.9; 1.35,0.45; 2.7,0.9, 0.3) H: (1.0; 1.5,0.5; 1.8, 0.6,0.2).A 4d set was made for 0 by adding a d function with exponent 0.1. For C, N, and 0 f functions with exponents 1.0 were used. For CH4 the polarisation exponents for the 2d and 2p sets were optimised for the MP2 energy. Geometries were optimised until the gradients were less than hartree bohr-I. These geometries are reported in tables 1-3 for H20, NH3 and CH4, respectively, where they are compared with other a6 initio and experimental results. N. C. Handy, J. E Gaw and E. D. Simandiras Table 2. Optimised geometries for NH3 method basis set rNH/A &NHIo ref. SCF 8s6p4d 1 f/6s3pld 0.998 108.1 48 M P2 6-31G" 1.017 106.3 8 MP2 DZP 1.013 73 106.69 MP2 MP2 MP2 5s4p2d 3 s2p 8s6p 3 d 16s 2p 8s6p3d 1 f/6s3p 1.008 96 1.007 94 1.009 26 107.22 107.07 107.14 M P2 M P3 13s8p2 d / 8s2p 1 d 6-3 1 G" 1.006 8 1.017 107.3 106.2 52 8 M P4 6-31 G* 1.021 105.8 8 CISD DZP 1.013 106.68 74 CISDTQ DZP 1.017 106.3 51 CISD TZ2P 1.014 106.4 74 exptl 1.012 106.7 75 Table 3.Optimised geometries for CH, method basis set rCH/A ref. SCF 8s6p4dl f/6s3pld 1.0815 48 MP2 DZP( d :0.8, p : 1.O) 1.088 MP2 6-3 1 G" 1.090 8 MP2 5s4p2d/ 3 s2p" 1.0826 MP2 5s4p2d 13 s2p 1.0847 MP2 Meyer's basis 1.086 11 MP2 8s6p3d 1f/6s3p 1.0829 CEPA 8s5p2d 1 f/4s2pC 1.091 11 CCI 9s5p4d 1f/4s2p 1 d 1.0880 53 CCI(Dav) 9.s5p4d1f/4s2p 1 d 1.0901 53 MP3 6-31G" 1.091 8 MP4 6-31G" 1.094 8 exptl 1.086 54 MP2 energy-optimised polarisation exponents pH:1.8, 0.6; d,: 1.2, 0.4. Diffuse pH functions pH:0.9, 0.3.'~~ :0.75, 0.3.For H20 the near Hartree-Fock limit gives a bond length 0.018A too short when compared with e~periment;~~ the MP2 near-spdlsp limit is 0.00058, too short; addition of one f function gives it to be 0.0015 8, too long. We judge from these calculations that the MP2 basis function limit is within 0.002 A of the experimental re. Note that this is a substantial improvement on MP2 with a 6-31G" basis, which is 0.011 A too long.' Optimisation at higher orders of MPn theory will bring closer agreement with experiment, but this is impractical and of doubtful value.We do, however, have the 39 Slater function MP4 H20 bond distance5' of 0.9596 A, 0.0018 8, too long. There are not many substantial CI calculations in the literature. The CISDTQ calculation5' at the DZP level has insufficient basis functions to be significant, although the CISD at TZ2P is probably more relevant. However, all of this is to indicate that the fully optimised SCF and MP2 Energy Derivatives Table 4. Harmonic frequencies (in cm-') for H20 method basis set "1 "2 w3 ref. SCF 8s6p4d2f/6s3pl d 41 30 1746 423 1 48 M P2 6-31 G" 3772 1737 3916 8 M P2 DZP 3913 1665 4059 M P2 5s4p2d13s2p 3859 1641 3985 M P2 8s6p 3 d /6s2p 3842 1628 3968 M P2 8s6p4d/6s3p 3831 1627 3959 M P2 8s6p4d 1f/6s3p 3839 1629 3966 CISD DZP 3959 1690 4082 74 CISD TZ2P 3901 1668 4006 74 CISDTQ DZP 3887 1674 4017 51 exptl 3832 1649 3942 49 MP2 geometry large-basis-set calculation gives a highly accurate prediction, both for bond length and bond angle.For NH,, the same is true. The near Hartree-Fock basis-function limit bond length is 0.014 A too short, whereas our largest MP2 calculation is only 0.003 A too short. Indications from the 6-31G* calculations8 are that an MP4 calculation would reduce this error. Our calculations are in good agreement with the large spd/spd calculations of Defrees and McClean." For CH4, there has been some discussion recently on the equilibrium bond length. In a recent paper, using large basis sets and the CCI method, Siegbahns3 concludes that his best ab initio value for the bond length is 1.090 A.This disagrees with the experimental value suggested by Gray and R~biette,~~ 1.086 A,so much that Siegbahn said 'some remaining error in the analysis of the experiments seems much more likely'. Our results, on the other hand, indicate that the experimental value is correct. We note that the near-Hartree-Fock value for re is too short by 0.005 A and that our best MP2 value is too short by 0.003 A.This MP2 limit result is consistent with the NH, value which is also 0.003 A shorter than the experimental. If the 6-31G* (MP4- MP2) correction* of 0.003 A carries over to larger basis sets, then good agreement with the value of Gray and Robiette is obtained. We believe the CEPA calculations of Meyer," used by Siegbahns3 as support for his argument, are unreliable because of a basis-set inadequacy. MP2 calculations, using Meyer's basis, yield an re of 1.086, which is 0.003 A longer than our MP2 limit.It appears that the trouble lies with the H p-exponent; calculations at the TZ2P level show that 0.75 is not a large enough exponent to span adequately the required space. To demonstrate this we optimised the polarisation exponents for the 5s4p2d/3s2p basis set; a diffuse set of 2p(H) similar to Meyer's, but obtained from our energy-optimised set by scaling by a factor of 0.5, makes re longer by 0.002 A. For Siegbahn's calculations themselves, there is no evidence of a basis-set inadequacy. We can only suggest that there may be a weakness in the CASSCF-CCI approach.Turning now to the calculations for harmonic frequencies, table 4 shows that our best MP2 (largest basis) calculations for H20 yield errors of +7 (+298), -20 (+97), +24 (+289) cm-', for the symmetric stretch, bend and asymmetric stretch modes (SCF limit values in parenthesis). As Pulay would argue," the small errors reflect the fact that the MP2 geometry is highly accurate. As can be seen from table 5, the story is similar for NH, and the corresponding values are +93 (+238), +14 (+184), -16 (+96) and +13 (+77), for the ol, 02,0,'and o4modes. It appears that the remaining error N. C. Handy, J. E Gaw and E. D. Sirnandiras 1587 Table 5. Harmonic frequencies (in cm-') for NH3 method basis set "1 "2 "3 w4 ref.SCF 8s6p4d 1 f/6s3pld 3690 1099 3815 1787 48 M P2 6-3 1 G" 3 504 1166 3659 1852 8 M P2 DZP 3574 1100 3742 1710 M P2 5 s4p 2d / 3s2p 3527 1048 3673 1692 M P2 8 s6p3 d / 6s2p 3520 1050 3669 1686 M P2 8s6p3d 1 f/6s3p 3520 1035 3670 1675 CISD DZP 3589 1120 3735 1727 74 CISD TZ2P 3526 1102 3653 1713 74 CISDTQ DZP 3528 1121 3676 1706 51 exptl 3506 1022 3577 1691 76 Table 6. Harmonic frequencies (in cm-') for CH4 method basis set "1 "2 "3 o4 ref. SCF 8s6p4d 1 f/6s3p 1 d 3150 1667 3248 1434 48 M P2 6-3 1 G" 3115 1649 3257 1418 8 M P2 DZP (d :0.75; 3104 1588 3263 1369 p :0.75) M P2 6-3 1G"" extended 3075 1594 3216 1355 M P2 5 s4p 2d / 3s2pa 3087 1605 3223 1383 M P2 8s6p3d 1 f/6s3p 308 1 1594 3218 1362 exptl 3025 1583 3157 1368 54 ~~~~~ ~ (I MP2 energy-optimised polarisation exponents. Table 7.Infrared intensities for H20 (in km mol-') method basis set "1 "2 "3 ref. SCF 8s6p4d/6s3p 15.1 97.7 91.8 SCF DZP 20.6 107.2 73.4 M P2 DZP 7.5 80.2 45.O 6-31G ext 4.5 63.9 59.8 8s6p4dl 6s3p 5.2 72.7 72.8 CISD DZP 6.3 82.6 36.5 74 CISD TZ2P 3.6 73.7 55.2 74 CISDTQ DZP 3.4 76.7 28.0 51 exptl 2.2 53.6 44.6 76 SCF and MP2 Energy Derivatives Table 8. Infrared intensities for NH3 (in km mol-') method basis set W' *2 w3 04 ref. SCF DZP 0.40 218 7.1 44 SCF 8s6p4dlf/6s3pld 1.2 179 13 38 M P2 DZP 0.0 190 4.4 39 M P2 8s6p3d 1f/6s3p 2.0 155 18 33 CISD DZP 0.10 182 0.6 36 CISD TZ2P 3.7 135 3.8 28 74 CISDTQ DZP 0.5 167 0.0 51 exptl U,+II~ 138*6 -31.7 32*0.5 77 11.4* 0.5 Table 9.Infrared intensities for CH4 (in km mol-') method basis set WI w2 w3 w4 ref. SCF DZP 0 0 130 45 SCF 8s6p3d16s2p 0 0 115 28 MP2 5 s4p2 d / 3s2pa 0 0 36 48 M P2 8s6p3d 1f/6s3p 0 0 47 35 exptl 0 0 67 33 78 a Same as in tables 3 and 4. in the o3degenerate stretch e mode is mostly due to the fact that the NH bond is 0.003 A too short. For CH, (from table 6) the errors are +11 (+84), -6 (+66), +56 (+125), +61 (+91), (for wl,02,o3and o4modes, respectively). In summary, therefore, MP2 frequencies for these three molecules are remarkably accurate when large basis sets are used, with errors reducing from typically 8% (SCF) to 2% (MP2). The results in tables 7-9 for infrared intensities at the MP2 level show a considerable improvement over SCF values.For example, our intensities for H20 have reduced from 15, 97, 92 km mol-' (modes wl, w2 and 03,respectively) at the SCF level to 5, 73, 73 km mol-' at MP2 level, compared to the 'most reliable' experimental values of 2, 54, 45 km mol-'. Our belief is, based in particular on calculations of Swanton et ~l.,~~that the outstanding errors here are failures of the MP2 approximation, and that higher orders (or higher order CI) is required to get good agreement. We do not believe that the double-harmonic approximation is responsible. There is a recent review on the calculation of i.r. intensities by Amos,57 and a collection of calculations by Hess et al.58 We would finally observe on the calculation of dipole-moment derivatives, that the recent full-CI calculations by Bauschlicher and Taylor"' indicate that it does not really matter whether the dipole moment is calculated as an expectation value or as an energy derivative, as the error in these values when calculated by a correlated method such as SDCI far exceeds this difference.6. SCF Values for the Anharmonic Constants of H20, NH3 and CH4 In this section we shall report the results of some calculations which use the third- and fourth-derivative evaluations outlined in section 4. Earlier calculations, already reported, N. C. Handy, J. E Caw and E. D. Simandiras 1589 Table 10. Some anharmonic constants and related properties for H20 (1, symmetricstretch; 2, bend; 3, asymmetric stretch; units cm-’) calcd obsd“ calcd obsd“ XI 1 x21 x22 -40.1 -15.6 -20.0 -42.6 -15.9 -16.8 QfQ2A4 0.585 -2.843 1.100 0.750 1.253 -2.941 x31 -157.2 -165.8 0.217 0.238 x3 2 -17.9 -20.3 Q2 -0.153 -0.160 x33 -45.4 -47.6 4Q2c 0.102 0.162 0.137 0.078 0.202 0.139 a: 0.132 0.145 -159.1 -155.0b 0.0158 0.0176 -167 -175 -57 -54 -178 -187 a Ref.(49). Ref. (44). indicate that it is important to perform these SCF calculations with at least a DZP basis set, but that calculations at say, TZ2P, do not differ significantly from these.60 Therefore, we report calculations at the DZP level, using the standard Huzinaga-D~nning~~?~~ double-zeta basis set [9s5p/4s2p], [4s/2s], with polarisation d exponents of 0.75, 0.80, 0.85 on C, N, 0 and polarisation p exponent of 0.75 on H.The results are given in tables 10, 11 and 12 for H20, NH, and CH4, respectively. For H20, the experimental values of Hoy et aZ.49may be regarded as reasonably reliable, because they were derived from a wealth of experimental evidence. The rotation-vibration interactions a I”’ are directly obtained from the quadratic and cubic force constants. The results in table 10 show that all calculated a!BSare within 20% of the observed values. We view this as very encouraging, especially when it is recalled that the SCF geometries and harmonic frequencies are deficient. The values for x, are also encouraging, typical agreement within 10% between calculated and observed values. The observed values cannot be completely reliable here (a quartic expansion is used), since it is known that second-order perturbation theory is unreliable for molecules containing H atoms and that Hoy et aZ.49had no information on some of the quartic force constants (which they fixed to zero).Even so, we expect the observed values for H20 to be more reliable than these calculated SCF values, based on some correlated The Darling-Dennison constant, K1133,results for x,, in the literat~re.~’ shown by Mills and Robiette to be important in the relating of normal-mode and local-mode beha~iour,~~ agrees well with their value. The table shows that the calculated anharmonic corrections vi -mi for the fundamentals are in excellent agreement with experimental values. Also, our value for vibrational correction to the bond length, rg- re, agrees within 10% with a value we obtained using data from ref.(49). For NH,, our results in table 11 for the vibration-rotation interaction constants show the same good agreement with the observed values. The greatest discrepancy here is with but mode 2 is the umbrella mode, which is certainly the most difficult to obtain theoretically, and perhaps even experimentally. The Darling-Dennison constants SCF and MP2 Energy Derivatives Table 11. Some anharmonic constants and related properties for NH3 (1, NH sym. str.; 2, umbrella mode; 3, degenerate stretch; 4, degenerate deformation; units cm-') calcd obsd" calcd obsd" x11 x12 x13 x14 -23.25 11.50 -9 1.45 8.66 -20.58 -92 -6.7 g33 g34 844 13.82 -3.98 7.98 --2.65 x22 -56.27 - x23 19.01 32.36 K1133 -89.70 -96.0b x24 -10.44 -10.73 K1333 -42.04 -45.3 x33 -40.64 -18.50 x34 -11.14 -17.25 x44 -14.39 -8.80 ffzBd 0.129 0.087 0.156 0.135 0.015 0.176 0.046 0.065 0.017 0.078 0.098 -0.009 -0.228 -0.230 0.070 0.066 -0.003 -0.026 34.703 - 0.283 0.255 0.01718 -124 -170 -98 -72 -155 -133 -47 -65 a Ref.(49). 'Reported in ref. (44). show good agreement, as do the lambda-doubling constants 4,. There is no observed value for the vibration A-doubling constant r34, There is no reliable set of observed values for the anharmonic constants x, and gttt,but we note that there is agreement in most signs and some of the orders of magnitude.However, we are confident that the calculated values are much more reliable than any presently available observed set. The anharmonic corrections for the fundamentals ( vi-mi), however, do not show the excel- lent agreement seen for H20, and indeed we do not understand this discrepancy. For CH4, the agreement between the calculated vibration-rotation constants a, b, p and 6, and the observed values is good. Gray and R~biette~~ derived a complete set of anharmonic constants, based on one quartic force constant frrrr,and a full cubic set. Our calculated values of the anharmonic constants give good agreement with ref. (54) for stretch-stretch interactions; however, degenerate stretch-deformation anharmonic constants (x, G, T, S) do not agree so well, but this is not surprising in view of the approximation used in ref, (54).The anharmonic corrections for the fundamentals show good agreement for modes 1 and 3, reasonable agreement for mode 2 and rather poor agreement for mode 4.61 We find also that our calculated value for rg-re agrees with the value 0.0208 8, derivable from ref. (54), and it also agrees with the value 0.0204 reported by Pulay et aZ.62 Thus our calculations support the reported experimental value of 1.086 A for re,s4which we discussed earlier. N. C. Handy, J. F. Gaw and E. D. Simandiras Table 12. Some anharmonic constants and related properties for CH4 (1, symmetric stretch; 2, degenerate deformation; 3, degenerate stretch; 4, degenerate deformation) Gray and Gray and calcd Robiette" calcd obsd" Robiette" XI 1 -11.2 -11.0 0.0333 -0.0388a1 x2 1 -16.1 -16.3 Q2 -0.0953 -0.0879 -0.0910 -0.4 -3.0 Q3 0.0307 0.0434 0.0363x22 x3 1 -48.3 -50.3 a4 0.0690 0.0647 0.0648 -11.2 -10.7 b2 0.0325 0.0313 0.0301x32 -26.0 -29.2 P3 -0.00 15 -0.0025 -0.0020x33 x4 1 5.0 6.1 P4 0.0036 0.0046 0.0041 -8.7 -12.1x42 -7.6 -4.0 53 0.0174 0.0637 0.0192x43 x44 -7.7 -15.6 54 0.3209 0.3028 0.3057 G22 -0.18 0.92 G33 10.96 12.13 G43 -3.22 -1.25 G44 6.04 8.95 0.96 0.46T32 T33 3.11 3.40 T42 -1.20 -0.18 T43 0.87 0.20 T44 0.47 2.00 0.98 -0.1 1 0.019 25 0.020 82 -103 -105vl-wl v2 -02 -39 -50 v3 -w3 -129 -134 v4 -a4 -36 -59 K1133 -55.2 -60.0' -222.8 -240.0'K1333 " Ref.(54). Ref. (44). Conclusion In this paper we have reported the following advances in methodology, and presented new results as follows. (i) Our MP2 gradient and second-derivative programs now work with molecular symmetry, thus allowing large calculations to be undertaken. These programs now form part of CADPAC and are thus in routine use. (ii) Our SCF third-derivative program now works with molecular symmetry. (iii) New large basis-set calculations have been reported for geometries, frequencies, intensities and anharmonic constants for CH4. Previously expressed uncertainty with the experimental value for re has been resolved. We have shown that careful optimisation of the basis sets is required. Anharmonic constants for NH, have also been reported.(iv) Our study of H20, NH3 and CH4 (and further work to be published) suggest that large basis sets MP2 geometry optimisation will yield single bonds within 0.002 A, multiple bonds within 0.01 8, and bond angles within 0.5". The authors are pleased to acknowledge valuable discussions with Drs R. D. Amos and J. E. Rice. E. D. S. thanks the E.E.C. for financial support. 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E. M. Siegbahn, Chem. Phys. Lett., 1985, 119, 515. 54 D. L. Gray and A. G. Robiette, Mol. Phys., 1979, 37, 1901. 55 G. Fogarasi and P. Pulay, Annu. Rev. Phys. Chem., 1984, 35, 191. 56 D. J. Swanton, G. B. Bacskay and N. S. Hush, J. Chem. Phys., 1986, 84, 5715. 57 R. D. Amos, Adv. Chem. Phys., 1987, 67, 99. 58 B. A. Hess, L. J. Schaad, P.Carsky and R. Zahradnik, Chem. Rev., 1986, 86, 709. 59 C.W Bauschlicher and P. R. Taylor, Theor. Chim. Acra, 1987, 71, 263. 60 J. F. Gaw and N. C. Handy, Chem. Phys. Lett., 1985, 121, 321 61 J. F. Gaw, to be published. 62 P. Pulay, W. Meyer and J. E. Boggs, J. Chem. Phys., 1978, 68, 5077. 63 H. F. King and A. Komornicki, ref. (16), p. 207. 64 P. Saxe, Y. Yamaguchi and H. F. Schaefer, J. Chem. Phys., 1982, 72, 5647. 65 Y. Osamura, Y. Yamaguchi, P. Saxe, M. A. Vincent, J. F. Gaw and H. F. Schaefer, Chem. Phys., 1982, 72, 131. 66 G. Fitzgerald, R. J. Harrison, W. D. Laidig and R. J. Bartlett, J. Chem. Phys., 1985, 82, 4379. 67 M. Page, P. Saxe, G. F. Adams and B. H. Lengsfield, J. Chem. Phys., 1984, 81, 434. 68 H-J. Werner and P. J. Knowles, J. Chem. I’hys., 1985, 82, 5053. 69 T. U. Helgaker, J. Almlof, H. J. Aa Jensen and P. Jorgensen, J. Chem. Phys., 1986, 84, 6266. 70 H. B. Schlegel and M. A. Robb, Chem. Phys. Lett., 1982, 93, 43. 71 M. Dupuis and J. J. Wendolowski, J. Chern. Phys., 1984, 80, 5696. 72 G. Fitxgerald, R. J. Harrison, W. D. Laidig and R. J. Bartlett, Chem. Phys., Lert., 1985, 117, 433. 73 A. Scheiner, G. Scuseria, J. E. Rice, T. J. Lee and H. F. Schaefer, J. Chem. Phys., 1987, in press. 74 R. B. Remington, Y. Yamaguchi, T. J. Lee and H. F. Schaefer, to be published. 75 W. S. Benedict and E. K. Plyler, Can. J. Phys., 1957, 35, 1235. 76 B. A. Ziles and W. B. Person, J. Chem. Phys., 1983, 79, 65. 77 T. Koops, T. Visser and W. M. A. Smit, J. Mol. Struct., 1983, 96, 203. 78 R. E. Hiller and J. W. Straley, J. Mol. Spectrosc., 1960, 5, 24. 79 A. Banerjee, J. 0. Jensen, J. Simons and .R. Shepard, Chem. Phys., 1984, 87, 203. Paper 71288; Received 17th February, 1987

ISSN:0300-9238    

DOI:10.1039/F29878301577

出版商:RSC    

年代:1987

数据来源: RSC

摘要:

J. Chem. SOC.,Furuduy Trans. 2, 1987, 83(9), 1595-1607 Geometries, Harmonic Frequencies and Infrared and Raman Intensities for H20,NH, and CH, Roger D. Amos University Chemical Laboratory, LensJield Road, Cambridge CB2 2E W Very large basis set calculations at the SCF level are reported for H20, NH3 and CH, ;geometries have been optimized, and frequencies, infrared and Raman intensities have been calculated. s, p, d and f basis functions are used, the largest set having 112, 133 and 154 functions, respectively. The calculations may be regarded as near the Hartree-Fock limit and will serve as benchmarks for other studies. Analytic derivative methods have had a substantial impact upon quantum chemistry in recent years. Their use in determining molecular structures and frequencies is well known and has been the subject of several re~iews.l-~ Development of the equivalent methods for molecular properties has lagged behind, but progress is being made in this area,5 and practical methods have been developed for dipole-moment derivatives at the SCF level6,' and more recently for polarizability derivative^.^.^ The equivalent develop- ments for correlated methods are underway with analytic dipole moment derivatives being available at the MP'2' lo and MCSCF" levels.Of course a great many calculations of infrared, and to a lesser extent Raman, intensities have been made using finite difference methods [an extensive bibliography is given in ref. (12), but such approaches are inevitably slow and laborious. However, the existence of an analytic technique does not overcome all problems. One of computational chemistry's perennial difficulties is the choice of basis set.The purpose of this article is to take three of the simplest and most studied molecules, H20, NH, and CH4, and use the power of the latest analytic derivative techniques to saturate the basis sets on these molecules. The hope is to approach the Hartree-Fock limit for the properties of interest. This is essentially a calibration exercise which it is hoped will enable the performance of various basis sets to be judged. Equally importantly it is only by knowing the limits of performance of the SCF model that the correlation contributions to these properties can be discussed unambiguously. Methods The first step was to fully optimize the geometry of each molecule with each basis set.At the equilibrium geometry the force constants, dipole-moment derivatives and polariza- bility derivatives were calculated analytically, and from these were obtained the harmonic frequencies and the infrared and Raman intensities. Analytic gradient, force constant and dipole derivative calculations are now standard methods, so details will not be given. The principles of the methods may be found in ref. (1)-(7). The program utilized in the present study was the CADPAC package,13 running on a CRAY 1s computer. Fully analytic methods for the calculation of polarizability derivatives are of more recent origin, but their practicality has been established by the author' and independently by Frisch et aL9 The approach used here is based on the following formula for the third 1595 1596 Geometrics, Harmonic Frequencies and I.R.1Raman Intensities derivative of the SCF energy (closed shell): occ (d3E/aaab ac) = 1 h:b'+&;bc-2&iS;bC I occ all $:) E(CC4+ -U:iUZi+ ( cab)+ (bca) i r.F occ -2 C ( E -I ~i +c(cab +(bca ) i.j where (cab), (bca) denote permutations of the superscripts. This expression would require the first, second and third derivatives of the integrals. Thus = ha+ga* D is a Fock operator constructed with first-derivative integrals. The notation g * D symbol-izes the contraction of the density matrix with the integrals which occurs in the construc- tion of a Fock ~perator,'~ i.e.g" D =1((ijl kl)-+(ikljl))Dkl The expressions and would be the equivalent operators constructed with the second derivatives of the integrals, and the third derivatives, respectively. The term is essentially the full derivative of the Fock operator, i.e. including the derivatives of the wavefunction as well as those of the integrals &(a)= ha+ ga* D+g* D" and the term &(Ob) is part of the second derivative of the Fock operator, but lacking the terms involving the second derivative of the wavefunction, E(~~)= hab+gab*D + g" * Db+ gb* D". The factor tabis Y 1JSUb= S'h + u;k + u!k u;k-SpkSibk -sfks;k where U" are the solutions of the coupled Hartree-Fock equations for the nuclear displacement^.'^ The U" coefficients are also required for the derivatives D" of the density matrices.This expression is essentially the same as that given by MocciaI6 and P~1ay.I~It should be noted that the expression does not require the second derivative of the wavefunction. It does, however, require the solution of all first-order CHF equations. If the above expression is used for polarizability derivatives then no third-derivative integrals appear and the only new terms not present in dipole derivative calculations R. D. Amos 1597 are E(~~)and tab.The latter is simply constructed from the U" and Ub matrices, and the former reduces to where a is a nuclear displacement and 6 an electric field, as there are no second derivatives of the two electron integrals (assuming the basis functions have no explicit dependence upon the field).Terms such as E~,E'"~)etc. can always be evaluated in the A0 basis and consequently derivative integrals need never be transformed or stored. As E(~~)can be constructed simultaneously with E" during the calculation of the first derivative integrals, polarizability derivative calculations require only a little more time than dipole derivatives. Each calculation was done independently and no attempt was made to use, for example, the force field from one basis set with the dipole moment and polarizability derivatives from another basis set, even though the force field generally converged to a limit more quickly that the polarizability derivatives.This is to ensure that the only variations are those due to the basis set. Basis Sets The smallest basis sets used were the standard 4-31Gand 6-31Gcontraction~'~~'~and the double-zeta (DZ) basis which was Dumming's 4s2p contraction of Huzinaga's 9s5p primitive set.'' The next level was obtained by adding a set of polarization functions on each atom to give the basis sets denoted 4-31G**,6-31G"*.The polarization functions were d-functions with exponent 0.8on carbon, nitrogen and oxygen, and a p-function with exponent 1.1 on hydrogen." Of similar size is the DZP basis obtained from the DZ basis by adding d-functions of exponent 0.8 on carbon, 0.8 on nitrogen, 0.9 on oxygen, and a p-function with exponent 1.0on hydrogen. Note that these are not the 'standard' set of polarization functions. None of these smaller basis sets can be expected to give anything except very approximate infrared and Raman intensities.The smallest realistic basis sets for calculating dipole and polarizability derivatives are probably of the triple-zeta level, with two sets of polarization functions. Two such basis sets were used in the current work. One uses the 5s4p contraction by Dunning2' of the lOs6p Huzinaga basis. To this was added d-functions with exponents 1.2and 0.4 on carbon, 1.35 and 0.45 on nitrogen and 1.35 and 0.45on oxygen. The hydrogen basis consisted of 3s (Dunning"), with a scale factor of 1.2 and p-functions of exponents 1.5 and 0.75. An alternative is the basis denoted '6-31Gextended'.This was obtained from the 6-31G basis by first adding low-exponent s and p functions, and then including two sets of polarization functions. The extra s and p functions had exponents 1/3 of the smallest values in the 6-31Gbasis. Specifically they were s and p functions with exponents 0.056, 0.5707, 0.094 and 0.054on carbon, nitrogen, oxygen and hydrogen, respectively. The polarization functions were 0.8 and 0.27on carbon, 1.0and 0.33on nitrogen, 1.2 and 0.4on oxygen and 0.75 and 0.25 for the hydrogen p-functions. Although of similar size the 5s4p2d and 6-31Gextended basis sets are of very different character, the former being much more of an energy-optimized basis set, whereas the 6-31Gextended basis is rather diffuse and more suited to property calculations, especially polarizabilities.The largest basis sets are built around an 8s6p contraction of the 13s8p primitive set given by van Duijneveldt.*l To this were added up to four d functions. The exponents were 1.8,0.6,0.2 and 0.09 on nitrogen and 2.7,0.9, 0.3and 0.07on carbon, 2.4,0.8,0.27 and 0.1on oxygen. Where three sets of d functions were used, these were the three of largest exponent from the above sets of four. The hydrogen basis was a 6s contraction of the van Duijneveldt 10s primitive set, with p functions of exponents 1.8,0.6 and 0.2. The next step was the addition off functions on the first-row atoms and d functions on hydrogen, the exponents being 1.0 in all cases. The last stage used 2 sets of f functions, with exponents 1.5 and 0.5 in all cases.Cartesian Gaussian functions were 1598 Geometries, Harmonic Frequencies and I.R./ Raman Intensities Table 1. SCF energies and optimized geometries for H20 basis set energy/ hartree r/ 8, elo 4-31G -75.908 635 0.950 46 11 1.23 6-3 1 G -75.985 359 0.949 63 111.55 DZ -76.011 002 0.951 35 112.52 4-3 1G** -75.952 442 0.942 43 105.84 6-31G** -76.023 615 0.943 06 105.97 DZP -76.047 009 0.943 74 106.62 6-3 1 G extended -76.035 004 0.943 03 106.10 5 s4p2d / 3s2p 8s6p 3 d / 6s 2p 8s6p 4d / 6s 3p 8s6p4d 1 f/6s3pld 8s6p4d2fI6s3pl d -76.061 002 -76.065 563 -76.065 920 -76.067 026 -76.067 470 0.940 28 0.940 14 0.939 86 0.940 08 0.940 05 106.31 106.32 106.25 106.33 106.32 exptl 0.957 2 104.52 Experimental data from A.R. Hoy, 1. M. Mills and G. Strey, Mol. Phys., 1972,24, 1265. Table 2. SCF energies and equilibrium geometries of NH3 basis set energy/ hartree r/ A elo 4-31G -56.106 692 0.991 18 115.84 6-31G -56.165 521 0.991 34 116.13 DZ -56.180 540 0.994 39 116.29 4-31G** -56.142 032 1.OOO 48 107.43 6-3 1G** -56.195 544 1.000 86 107.57 DZP -56.209 68 1 1.001 05 108.19 6-3 1G extended -56.203 851 1.001 52 107.70 5 s4p2d/3 s2p -56.220 759 0.998 33 107.91 8 s6p3 d 6s2p -56.223 703 0.998 48 107.66 8s6p4d16s3p -56.223 874 0.998 31 107.64 8s6p4d 1f/6s3p Id -56.224 896 0.998 06 108.09 8s6p4d2f/6s3p Id -56.224 972 0.997 99 108.11 exptl 1.011 6 106.7 Experimental data from J. L. Duncan and I. M. Mills, Spectrochirn.Acfa, 1964, 20, 523.used throughout, so the largest basis sets have 112 functions for H20, 133 for NH3 and 154 for CH,. These basis sets have been chosen in a fairly conventional manner rather than trying to bias the basis towards describing any one property well. The intention is to ensure that the Hartree-Fock limit for energy, structure and infrared and Raman intensities is approached and then to judge the various standard basis sets relative to this. Results The results, given in tables 1-14, are largely self-explanatory. Tables 1-3 contain the geometries and energies for H20, NH3 and CH,. Although the present studies have probably used larger basis sets than any other calculations in which full optimizations have been carried out, there are no surprises in the geometries.This is to be expected R. D. Amos 1599 Table 3. SCF energies and optimized bond lengths in CH4 basis set energy/ hartree r/ 8, 4-31 G -40.139 767 1.081 06 6-31G -40.180 554 1.082 10 DZ -40.185 613 1.083 40 4-3 lG** -40.163 605 1.082 88 6-31G"" -40.201 704 1.083 54 DZP -40.207 605 1.084 60 6-31G extended -40.202 562 1.085 73 5 s4p2 d / 3 s2p 8s6p3 d / 6s2p 8s6p4d/6s3p -40.213 805 -40.216 112 -40.216 099 1.081 55 1.081 37 1.081 28 8s6p4d 1f/6s3pld -40.216 783 1.081 54 8s6p4d2f/6s3p 1 d -40.216 8146 1.081 51 exptl 1.085 8 Experimental bond length from D. L. Gray and A. G. Robiette, Mol. Phys., 1979, 37, 1901. as there have been many other calculations on these systems and many [e.g.ref. (22)-(32)] have used large basis sets. Accordingly the results simply show what has been known for some time. namely that the SCF limiting geometries have bond lengths which are too short, and that the 'best' results in terms of agreement with the experimental are those determined with middle-sized basis sets. This is the case for other molecules also [see for example the extensive tabulations in ref. (4)]. There are many calculations on the geometry of HzO, NH, and CH, which have used correlated wavefunctions, and as the geometry converges quite rapidly with increasing basis set size, then these calculations must be of greater absolute accuracy than the current results. Ref. (32) contains a discussion of this subject.The SCF harmonic frequencies are given in tables 4-6. The basis sets used here are larger than earlier studies; ref. (27) probably contains the previous most detailed results. However, as with the geometries there are few surprises. This is because the frequencies converge quite rapidly with basis set size, and with one exception are essentially converged as soon as there are two sets of polarization functions on each atom. The one exception is the low-frequency bending motion in NH3 which requires the presence of an f function to approach the SCF limit; however, this too was known previously.22 As is well known, the harmonic frequencies at the SCF level are some 10% too high. This is a systematic distortion [see ref. (4) for many examples] which is the basis for the success of the various scaling techniques.It also means that harmonic frequencies are one of the properties which benefit through the inclusion of electron correlation, even in cases where the basis set is not large enough to ensure that the underlying SCF results are approaching a limit. This means that a relatively simple correlated technique (such as MP2") can be surprisingly productive. The infrared intensities (tables 7-9) are more interesting. There are fewer calculations of this property. For the present group of molecules the best is probably the study of H20 by Swanton et a1.,34although obviously other calculations exist [see ref. (5) or (12)] and recent examples include ref. (7), (lo), (35) and (36).Unlike the geometry and the force constants, the infrared intensities at the SCF level are not systematically incorrect, i.e. whereas SCF geometries have bond lengths which are nearly always a little too short, and frequencies which are ca. 10% too high, the errors in the infrared intensities are not so predictable. There is a tendency for the SCF intensities to be too 1600 Geometries, Harmonic Frequencies and I.R./ Raman Intensities Table 4. SCF harmonic frequencies (cm-') for H20 and D,O. basis set 02 01 03 H2O 4-31G 1743 3959 4111 6-3 1G 1737 3989 4146 DZ 171 1 4029 4205 4-31G** 1775 4144 4261 6-31G"" 1770 4149 4266 DZP 1752 4166 4289 6-3 1 G extended 1747 4129 4236 5 s4p 2 d / 3s2p 1757 4134 4236 8s6p3 d /6s2p 1756 4129 4229 8s6p 4d /6s3p 1759 4129 4227 8s6p4d lf16s3pld 1748 4131 4232 8s6p4d 2 f/ 6s3p 1 d 1747 4130 423 1 exptl 1649 3832 3943 D2Q 8sSp4d2f16s3p 1 d 1279 2977 3102 Experimental data from A.R. Hoy, I. M. Mills and G. Strey, Mol. Phys., 1972, 24, 1265. Table 5. SCF harmonic frequencies (cm-') for NH3 and ND3 basis set 04 w3 NH3 4-31G 62 1 1822 3760 3957 6-31G 598 1815 3781 3985 DZ 585 1800 3776 3993 4-3 1 G** 1150 1813 3700 3836 6-31G** 1142 181 1 3705 3843 DZP 1113 1903 3725 3873 6-3 1 G extended 1121 1788 3692 3821 5s4p2d/ 3 s2p 8s6p3 d ,/ 6s2p 8s6p4d/ 6s 3p 1127 1131 1129 1799 1799 1797 3696 3689 3687 3819 3809 3806 8s6p4d 1 f/6s3p 1 d 8s6p4d 2f/6s 3p 1 d 1099 1099 1787 1787 3690 369 1 3815 3815 exptl 1022 1691 3504 3577 N D3 8s6p4d 2 f /6s3p 1 d 836 1298 2634 2809 Experimental data from J.L. Duncan and I. M. Mills, Spectrochirn.Acta, 1964, 20, 523. large, but this is not a reliable feature, for these or other' molecules, and the intensity of a particular mode can be 100% too large or 100% too small, in the same molecule. This means that a scaling procedure would be very difficult to put into practice, unlike those used for frequencies. Neither is the effect of increasing the basis set size easily predictable, as some intensities are enhanced while others diminish. This means that there is little choice other than to examine the basis-set dependence for each molecule R. D. Amos 1601 Table 6.SCF harmonic frequencies (cm-') for CH4 and CD4 basis set w4 w2 w1 w3 CH4 4-31G 1522 1717 3179 3288 6-31G 1517 1709 3183 3297 DZ 1507 1699 3177 3307 4-31G** 1472 1689 3174 3285 6-31G** 1469 1686 3175 3286 DZP 1459 1671 3175 3295 6-3 1 G extended 1447 1667 3153 3261 5s4p2 d /3s2p 1456 1671 3153 3254 8s 6p3 d /6 s2p 1457 1673 3153 3250 8 s6p4d / 6s 3p 1457 1672 3150 3248 8s6p4d lf/6s3pId 1454 1667 3150 3248 8s6p4d 2 f / 6s 3p 1 d 1454 1667 3150 3248 exptl 1367 1583 3026 3157 DC4 8s6p4d 2f/6s3p 1 d 1099 1179 2228 2406 exptl 1034 1120 2140 2336 Experimental data from D. L. Gray and .4. G. Robiette, Mu). Phys., 1979, 37,1901. Table 7. Infrared intensities (kmmol-.') for H20 and D20 basis set w2 01 w3 H2O 4-3 1 G 120 2.8 50 6-31G 123 2.9 54 DZ 136 3.4 65 4-31G** 103 15 52 6-31G** 104 16 58 DZP 107 21 73 6-3 1 G extended 90 14 81 5s4p 2 d / 3s 2p 97 16 80 8s6p 3 d /6s2p 101 16 88 8s6p4d/6s3p 98 15 92 8s6p4dlf/6s3pld 97 15 92 8s6p4d2fj6~3pl d 97 15 92 exptl 53.6 2.2 44.6 D*O 8s6p4d 2f/6s3p 1 d 51 10 54 The experimental values are from B.A. Ziles and W. B. Person, J. Chem. Phys., 1983, 79, 65. 1602 Geometrics, Harmonic Frequencies and I.R./ Rarnan Intensities Table 8. Infrared intensities (km mol-') for NH3 and ND3 basis set 02 w4 01 03 NH3 4-31G 614 88 0.58 28 6-3 1G 645 94 0.55 32 DZ 660 106 0.25 37 4-3 1G** 21 1 39 0.12 0.63 6-31G** 217 41 0.14 DZP 235 49 0.43 6.7 6-31G extended 187 38 0.6 10 5s4p2d/ 3 s2p 209 42 0.0 8.8 8s6p3 d /6s 2p 187 45 0.7 1 10 8s6p4d/6s3p 176 38 1.2 11 8s6p4d lf/6s3pld 179 38 1.2 13 8s6p4d 2 f/6 s3p 1 d 179 38 1.2 13 exptl 138*6 31.7+0.5 ND3 8s6p4d2f/6s3p 1 d 104 22 0.04 11 exptl 76*5 16.6*0.25 ~1+~3 = 7.2 *0.3 Experimental values from T.Koops, T. Visser and W. M. A. Smit, J. Mol. Struct., 1983, 96, 203. Note that the experimental results give only the sum of the intensities for vl and v3. Table 9. SCF infrared intensities (km mol-') for CH, and CD4 basis set "4 02 w1 "3 CH4 4-31G 61 0 0 114 6-31G 64 0 0 113 DZ 86 0 0 180 4-3 1 G** 28 0 0 125 6-3 1G** 30 0 0 119 DZP 47 0 0 135 6-3 1G extended 26 0 0 115 5s4p2 d / 3s2p 32 0 0 97 8s6p3d/6s2p 28 0 0 115 8s6p4d/6s3p 28 0 0 114 8s6p4dlf/6s3pld 28 0 0 114 8s6p4d2f/6s3pl d 28 0 0 114 exptl 33 0 0 67 8s6p4d 2 f/6s3p 1 d 0 54 The experimental values are from R.E, Hiller and J. W. Straley, J. Moi. Spectrosc., 1960, 5, 24. R. D. Amos 1603 Table 10. Raman intensities of H20 and D20 basis set 02 01 a3 H20 4-31G 10 100 39 6-31G 10 71 25 DZ 12 91 42 4-31G"" 12 83 18 6-31G"" 4.5 87 24 DZP 6.8 75 37 6-3 1 G extended 2.0 81 27 5s4p2d /3 s2p 3.5 71 29 8s6p3 d /6s2p 8s6p4 d /6s3p 8s6p4d 1 f/6s3p 1 d 1.3 0.67 0.67 74 85 85 28 24 25 8s6p4d 2f/6s3pl d 0.68 85 24 exptl 0.9 f0.2 108f14 19.2f2.1 D20 8s6p 4d 2 f/6s3p 1d 0.38 44 13 The units are A4a.m.u.-' The experimental values are from W. F. Murphy, Mol. Phys., 1977, 33, 1701; 1978, 36, 727.Table 11. Raman depolarization ratios of H20 and D20 basis set w2 w1 w3 H20 4-3 1 G 0.403 0.720 0.75 6-3 1G 0.637 0.074 0.75 DZ 0.412 0.21 1 0.75 4-3 1G** 0.291 0.669 0.75 6-3 1 G** 0.662 0.667 0.75 DZP 0.521 0.164 0.75 6-3 1 G extended 0.558 0.080 0.75 5 s4p2d 13 s2p 0.581 0.1 19 0.75 8s6p3d/6s2p 8s6p4d /6s3p 0.670 0.750 0.102 0.069 0.75 0.75 8s6p4d 1 f/6s3pld 8s6p4d 2 f/6s3p 1 d 0.749 0.750 0.069 0.069 0.75 0.75 exptl 0.74 0.03 0.75 D2O 8s6p4d 2f /6s3p 1 d 0.730 0.068 0.75 The experimental values are from W. F. Murphy, Mol. Phys., 1977, 33, 1701; 1978, 36,727. 1604 Geornetrics, Harmonic Frequencies and I.R./ Rarnan Intensities Table 12.Raman intensities (A4a.m.u.-’) for NH3 and ND, basis set w2 04 w1 a3 NH3 4-31G 4.9 12 107 81 6-3 1 G 4.7 12 110 80 DZ 5.3 12 116 70 4-3 1 G** 8.3 119 117 111 6-3 lG** 8.7 20 118 112 DZP 8.9 22 112 99 6-3 1 G extended 1.1 3.8 139 86 5s4p2 d / 3 s2p 8 s6p3 d /6 s2p 8 s6p4d /6 s3p 3.3 1.5 0.47 13.6 4.6 1.9 112 123 148 84 91 79 8s6p4d lf/6s3pld 8 s6p4d 2 f/6s 3p 1d 0.42 0.44 1.8 1.8 147 147 78 78 ND3 8s6p4d 2f /6s3pl d 0.25 1.o 75 42 Table 13. Raman depolarization ratios for NH, and ND, basis set w2 a4 01 w3 NH3 4-31G 0.016 0.75 0.143 0.75 6-31G 0.014 0.75 0.143 0.75 DZ 0.03 1 0.75 0.136 0.75 4-31G** 0.135 0.75 0.072 0.75 6-3 1 G** 0.132 0.75 0.071 0.75 DZP 0.162 0.75 0.066 0.75 6-3 1G extended 0.726 0.75 0.030 0.75 5 s4p2 d / 3 s2p 0.059 0.75 0.039 0.75 8s6p 3 d /6s2p 0.749 0.75 0.039 0.75 8s6p4d/6s3p 0.62 1 0.75 0.026 0.75 8s6p4d 1 f/6s3pld 0.650 0.75 0.027 0.75 8s6p4d 2 f/ 6s3p 1 d 0.637 0.75 0.028 0.75 N D3 8s6p3 d 2f/ 6s3p 1 d 0.583 0.75 0.028 0.75 Raman depolarization ratios for NH3 calculated with various basis sets.individually, first at the SCF level, and then with some correlated approach. The results at the SCF level for H20, NH3 and CH4 show that at least two sets of polarization functions are required. The absolute accuracy of the SCF values is poor, with only qualitative agreement with experimental values. Most high-accuracy correlated calcula- tions thus far have been on very small molecules [see ref.(37) for a review]; however, more results are appearing for polyatomic~~~’~~’~,’~~~~-~~and the development of fully analytic approaches will aid this spread. The Raman intensities and depolarization ratios are given in tables 10-14. There have been other calculations of these properties, but with much smaller basis sets, e.g. ref. (35). As might be expected, the rate of convergence is much slower than the other properties, and at least 3 sets of polarization functions are required. The fact that the R. D. Amos 1605 Table 14. SCF Raman intensities (A4a.m.u.-’) for CH4 and CD4 basis set 04 w2 W1 03 CH4 4-31G 8.4 77 138 203 6-31G 9.0 79 146 200 DZ 9.6 81 175 191 4-31G** 6.9 59 133 193 6-31G** 7.2 61 138 186 DZP 6.8 60 157 172 6-3 1G extended 0.03 13 21 1 168 5 s4p2 d / 3s2p 8s6p 3 d / 6s 2p 8s6p 4 d / 6s 3p 8s6p4d 1f16s3pld 8s6p4d2f/6s3pl d 2.2 0.01 0.06 0.06 0.06 35 14 6.7 6.6 6.6 160 194 227 228 228 154 172 151 151 151 exptl 0.24 7.0 230 128 CD4 8s6p4d2f16s3p 1 d 1.1 3.0 99 The experimental values are from D.Bermejo, R. Escribano and J. M. Orza, J. Mol. Spectrosc., 1977, 65, 345. depolarization ratios with the smaller basis sets vary wildly in some cases indicates that details of the polarizability derivatives are poorly described. With the smaller basis sets (ie. DZP, 6-31G** or equivalent) the results are highly sensitive to the precise choice of polarization function exponents. The eventual answers are in surpsisingly good agreement with the experimental values, and it is not clear why this should be the case given the polarizability itself is not particularly well described at the SCF level.The surprisingly good Raman intensities to be obtained at the SCF level have been commented on before,35 but it was possible that the results of John et al. were artifacts of the manner in which the basis set was chosen; however, the present calculations indicate that is not the case. Conclusion The main, but not very surprising, conclusion is that with a large enough conventionally chosen basis set it is possible to approach quite closely the SCF limit for a wide range of properties. However, it is more interesting to consider the applications for various unconventionally chosen basis sets.One such basis is the ‘polarized’ basis used by La~zeretti.~~This was introduced so that the dipole moment derivatives could be evaluated from the electric-field dependence of the Hellman-Feynman force (rather than as the derivative of the full gradient expression). With a large enough basis this works; for example with the largest basis sets used here the derivative of the Hellman- Feynman force is almost exactly equal to the dipole moment derivative. However, with smaller, but conventional, basis sets there is a wide discrepancy between the two expressions. Accordingly the use of a special basis set consisting of a small basis (e.g. double zeta) plus the derivatives of the basis functions has been suggested.This does and with such a basis set the dipole derivatives from the Hellman-Feynman theorem are close to those obtained from the full analytic expression. For the present set of molecules the values are similar to those calculated with the 6-31G extended, or the 5s4p2d basis sets, which is not surprising as a ’polarized DZ’ basis would also 1606 Geometrics, Harmonic Frequencies and I.R./ Raman Intensities contain two sets of polarization functions. However, there is a price to pay, as such a basis contains sets of contracted d functions (the derivatives of the p functions in the generating basis). As a consequence evaluating the dipole derivatives from the Hellman- Feynman theorem with such a basis actually takes longer than evaluating the full analytic expression with a conventionally chosen basis of similar overall size, such as a 5s4p2d basis.This somewhat reduces the usefulness of such a basis, as the principal argument for introducing the Hellmann-Feynman approach was that it was supposed to save computing time. Another possible way of choosing a basis for the investigation of infrared and Raman intensities is to use much lower exponents for the polarization functions than in an energy-optimized basis set. This approach has been quite widely and successfully used [see ref. (35) and other papers by the same authors]. An example in the present calculation is the 6-31G extended basis, which has much lower d-function and p-function exponents than in the similarly sized 5s4p2d basis set.It is noticeable that the 6-31G extended basis actually simulates the results of some much larger basis sets quite successfully. The main danger of such an approach is that a basis set with very low exponent polarization functions is not very well suited to calculations with correlated wavefunctions and accordingly its use may obscure cases where correlation is important. An example of this comes not from the present calculations but from H2C0. If a good-quality conventional energy optimized basis is used then an SCF calculation predicts" one particular mode (the C=O stretch) to have an intensity more than twice that which is observed. With a basis including very low exponent functions this discrepancy is reduced so that the error is ca.30'/0;~~the predictions for some of the other modes are worsened. If, however, an energy optimized basis is used with a correlated approach, even one as simple as MP'2', then the predicted intensities of all the modes are greatly improved. This illustrates that although a specially adapted basis set can be used in some circumstances, it will always be safer in the long run to use one which describes a wide range of properties well, and in particular one which describes the energy well. Refetences 1 P. Pulay, in Modern Theoretical Chemistry, ed. H. F. Schaefer (Plenum Press, New York, 1977), vol. 4. 2 J. F. Gaw and N. C. Handy, Annual Reports C (Royal Society of Chemistry, London, 1984). 3 H. F. Schaefer and Y.Yamaguchi, J. Mol. Strucr. (Theochem.),1986, 135, 369. 4 W. J. Hehre, L. Radom, P. von Rague Schleyer and J. A. Pople, Ab Znitio Molecular Orbital Theory, (Wiley, New York, 1986). 5 R. D. Amos, Adv. Chem. Phys., 1987, 67, 99. 6 R. D. Amos, Chem. Phys. Lett., 1984, 108, 185. 7 Y. Yamaguchi, M. J. Frisch, J. F. Gaw, H. F. Schaefer and J. S. Binkiey, J. Chem. Phys., 1986.84,2262. 8 R. D. Amos, Chem. Phys. Lett., 1986, 124, 376. 9 M. J. Frisch, Y. Yamaguchi, J. F. Gaw, H. F. Schaefer and J. S. Binkley, J. Chem. Phys., 1986, 84, 531. 10 E. D. Simandiras, R. D. Amos and N. C. Handy, Chem. Phys., 1987, 114, 9. 11 T. U. Helgaker, J. J. Aa Jensen and P. Jorgensen, J. Chem. Phys., 1986, 84, 6280. 12 B. A. Hess, L. J. Schaad, P. Carsky and R. Zahradnik, Chem.Rev., 1986, 86, 709. 13 R. D. Amos, CADPAC: The Cambridge Analytic Derivatives Package (University of Cambridge). 14 P. Pulay, J. Chem. Phys., 1983, 78, 5043. 15 J. Gerratt and I. M. Mills, J. Chem. Phys., 1968, 49, 1719. 16 R. Moccia, Chem. Phys. Lett., 1970, 5, 260. 17 W. J. Hehre, R. Ditchfield and J. A. Pople, J. Chem. Phys., 1972, 56, 2257. 18 P. C. Hariharan and J. A. Pople, Theor. Chim. Acta, 1973, 28, 213. 19 T. H. Dunning, J. Chem. Phys., 1970, 53, 2823. 20 T. H. Dunning, J. Chem. Phys., 1971, 55, 716. 21 F. B. van Duijneveldt, ZBM Research Report RJ 945 (1971). 22 P. Pulay, J. G. Lee and J. E. Boggs, J. Chem. Phys., 1983, 79, 3382. 23 P. Botschwina, J. Chem. Phys., 1986, 84, 6523. 24 W. R. Rodwell and L. Radom, J. Chem.Phys., 1980, 72, 2205. R. D. Amos 1607 25 D. J. DeFrees and A. D. McLean, J. Chem. Phys., 1984, 81, 3353. 26 P. Pulay, W. Meyer and J. E. Boggs, J. Chem. Phys., 1978, 68,5077. 27 T. J. Lee, and H. F. Schaefer, J. Chem. Phys., 1985, 83, 1784. 28 W. Meyer, J. Chem. Phys., 58, 1973, 58, 1017. 29 P. E. M. Siegbahn, Chem. Phys. Lett., 1985, 119, 515. 30 E. D. Simandiras, R. D. Amos and N. C. Handy, Chem. Phys. Lett., 1987, 113, 324. 31 I. Shavitt, in Comparison of Ab Znitio Calculations with Experiment-The State of the Art, ed. R. Bartlett (Reidel, Dordrecht, 1986). 32 N. C. Handy, J. F. Gaw and E. D. Simandiras, J. Chem. SOC., Faraday Trans. 2, 1987, 83, 1577. 33 E. D. Simandiras, N. C. Handy and R. D. Amos, Chem. Phys. Lett., 1987, 133, 324.34 D. J. Swanton, G. B. Bacskay and N. S. Hush, J. Chem. Phys., 1986, 84, 5715. 35 I. G. John, G. B. Bacskay and N. S. Hush, Chem. Phys., 1980, 51, 49. 36 M. Dupuis and J. J. Wendoloski, J. Chem. Phys., 1984, 80, 5696. 37 H. J. Werner and P. Rosmus, in Comparison of Ab Initio Calculations with Experiment-7le State of the Art, ed. R. Bartlett (Reidel, Dordrecht, 1986). 38 P. Botschwina, Chem. Phys. Lett., 1984, 107, 535. 39 U. G. Jorgensen, J. Almlof, B. Gustafsson, M. Larsson and P. Siegbahn, J. Chem. Phys., 1985,83,3034. 40 S. M. Adler-Gordon, S. Langhoff, C. W. Bauschlicher and G. D. Carney, J. Chem. Phys., 1985,83,255. 41 P. Lazzeretti and R. Zanasi, J. Chem. Phys., 1986, 84, 3916. 42 G. B. Bacskay, S. Saebo and P. R. Taylor, Chem. Phys., 1984, 90,215. Paper 7/571; Received 31st March, 1987

ISSN:0300-9238    

DOI:10.1039/F29878301595

出版商:RSC    

年代:1987

数据来源: RSC

摘要:

J. Chem. SOC.,Faraday Trans. 2, 1987, 83(9), 1609-1614 An Ab lnitio Investigation of N2-CO+ Jon Baker and A. David Buckingham" Department of Theoretical Chemistry, University Chemical Laboratory, Lensfield Road, Cambridge CB2 1EW Recent experiments have indicated that the interaction between CO+ and N, is fairly strong; certainly stronger than would be expected from electro- static considerations alone. We present calculations using ab initio molecular orbital theory that support the experimental findings, suggesting a binding between CO+ and N, of the order of 100 kJ mol-'. However, most of this binding is the result of long-range interactions and there is little evidence for the formation of an incipient 'chemical bond'. Hamilton et al.' have reported the efficient vibrational relaxation of CO' (v = 1) by N2.Only ca. six or seven collisions are required at 300 K to convert virtually all of the CO+ into the ground state (v=O). In a related study Ferguson et a1.2 measured the.rate coefficient for three-body association of CO' and N2with He as third body; they found a large value (comparable to that for the three-body association of N2f and N2, which is known to form a strong c~mplex)~.~ and suggested that there was a 'chemical bonding' interaction between CO+ and NZ,with a well depth as large as 1eV (96 kJ mol-'). In this paper we report the results of an ab initio investigation of the [N2..CO]' complex. Computational limitations have meant that we have been unable to carry out calculations at high levels of theory, but our best results (incorporating electron correla- tion at third-order in Mprller-Plesset perturbation theory' based on structures optimized at the SCF level using the 6-31G" basis set,6 hereafter referred to as MP3/6-31G"//6- 31G* in the usual notation) support the experimental findings and predict a binding energy between CO+ and N2 of 94 kJ mol-'. Computational Details Preliminary investigations of the N2--CO' potential-energy surface were carried out at the UHF level with the 3-21G basis set7 using a modified version' of GAUSSIAN t32.9 The stationary points were located using the eigenvector following (OPT= EF) algorithm'' and were characterized by vibrational analysis.Parts of the UHF/3-21G surface were subsequently re-examined using the 6-3 1G* basis set: and single-point energy calcula- tions were then done at the MP3 level on the UHF/6-31G* structures to give our final estimates of the well depths.In view of recent work on spin contamination in UHF wavefunctions (N2. 420' is a doublet)" we reoptimized the lowest-energy structure on the UHF surface at the ROHF (restricted open-shell SCF) level using CADPAC" followed by a single-point energy calculation at the CISD (configuration interaction including all single and double excitations) level. The ROHF wavefunction is of course a pure doublet. For the CI calculation we used the GUGA CI package of Saxe et ul.l3 Results and Discussion The optimized structures at the SCF level are depicted in fig.1 and the corresponding energies in table 1. Relative energies are shown in table 2. 1609 Ab Initio Investigation of N2..1610 CO' i1.0771 t2.2511 [l.0911 [1.0771 [1.9811 1.081 2.174 1.098 1.080 2.007 (1.091) (2.080) (1.119) (1.089) (1.984) [1.0951 N-N-----C-I178.51 [127.4] 179.4 131.6 179.4 (137.1) (1b) 1.101 1.927 1.136 (1.126) (1.863) (1.158) (1.123) (1.860) 0 01 1.128 1 A94 C 1(1.232) (3) // \\ \ (1.828) // / (67.2) \ / N' N (1.416) (4) Fig. 1. Geometries of stationary points on the [N2..-CO]+potential-energy surface: ( ) UHF/3-21G; [ ] ROHF/6-31G*; other values UHF/6-31G*. Bond lengths in hgstroms, bond angles in degrees. J. Baker and A. D. Buckingham 1611 Table 1.Energies (hartree) of the various [N2..-CO]+ structures shown in fig. 1" stmc-UHF UHF M P2 M P3 ROHF CISD CISD ture + Dav' N2 -108.300 95 -108.943 95 -109.248 19 -109.245 33 -108.943 95 -109.231 65 -109.256 56 N; -107.729.01 -108.366 02 -108.698 30 -108.672 28 -108.356 46 -108.663 00 -108.695 33 CO -112.093 30 -112.737 88 -113.018 02 -113.017 32 -112.737 88 -113.007 50 -113.027 71 CO+ -111.615 77 -112.260 52 -112.509 33 -112.506 39 -112.250 73 -112.506 19 -112.528 48 (la) -219.952 30 -221.222 61 -221.790 24 -221.782 27 -221.210 89 -221.731 09 -221.800 23 (lb) -219.953 04 -221.225 94 -221.796 64 -221.787 63 -221.216 41 (2a) -219.894 42 -221.152 39 -221.699 98 -221.702 97 (2b) -219.894 42 (3) -219.828 79 -221.150 15 -221.738 01 -221.733 66 (34 -221.150 13 -221.738 01 -221.733 51 (4) -219.722 76 a The first UHF column refers to the 3-21G basis set; all other columns refer to the 6-31G" basis set.Including Davidson's ~0rrection.l~ Table 2. Relative energies (kJ moI-') of the various [N2--.CO]+structures shown in fig. 1" structure symmetry UHF UHF MP2 MP3 ROHF CISD CISD+Davb 0 0 0 0 0 0 0 2 8 17 14 14 95 56 103 94 57 -18 40 154 154 193 254 222 326 199 154 142 199 154 142 343 320 211 257 320 159 203 605 " The first UHF column refers to the 3-21G basis set; all other columns refer to the 6-31G" basis set. Including Davidson's correction. l4 Initially we considered a linear [N2.-.CO]+ complex with the carbon atom of the CO attached to nitrogen [structure (la): The most stable form of the Nz.-.Ni complex is linear4]. This structure lies 93 kJ mol-' lower in energy than the separated species at the 3-21G level and 48 kJ mol-' lower at 6-31G".However, in both cases vibrational analysis revealed two imaginary frequencies (a degenerate bending mode), and reop- timization under a C, symmetry constraint gave structure (lb), which has an NCO angle of 137"(3-21G)or 132"(6-31G*). (S') for structure (lb) is 0.897 at the 6-31G" level. This structure appears to be the global minimum on the N,CO' energy surface; the well depth is 95 kJ mol-' at UHF/3-21G, 56 kJ mol-' at UHF/6-31G* and 94 kJ mol-' at MP3/6-31G*//6-31G*. The energy difference between the linear (la) and bent (lb) structures is 2 kJ mol-.' at UHF/3-21G, 8 kJ mol-' at UHF/6.31G* and 14 kJ mol-' at MP3/6-3 1 G*/ / 6-31G*.Results at the ROHF/6-31G* level are virtually identical to the UHF results; the optimized geometry being very similar (see fig. 1) and the well depth being 57 compared to 56 kJ mol-'. However, at the CISD level (including Davidson's c~rrection)'~this value drops to 40 kJ mol-'. The CI results show the importance of a size-consistent scheme, particularly for dissociation energies; without the Davidson correction the complex is actually less stable than the separated species (by 18 kJ mol-I; table 2), which is clearly incorrect. The Davidson correction can restore size consistency to a certain Ab Initio Investigation of N2.-CO+ extent; however, it is not 'rigorous', unlike the perturbation-theory calculations.Nevertheless, the fact that the well depth of the N2-.CO+complex at the CISD level is less than half its value at the MP3 level does suggest that the MP3 results should be treated with caution. We also considered, at the UHF level, the linear complex [N2.-.OC]' with the oxygen atom of the CO attached to nitrogen [structure (2a)l. With the 3-216 basis, this is in fact a minimum although the lowest vibrational frequency (again a degenerate bending mode) is only 19cm-I. We were also able to locate a bent structure (2b), similar to (lb), which had a virtually identical energy to (2a), indicating that the energy surface in this region is extremely fiat.Population analysis indicates that structures (2a) and (2b) are best represented as complexes of NZ with CO rather than N2 with CO+; this is also suggested by the energetics. The binding with respect to Nl and CO is 189 kJ mol-'. Additional stationary points located on the UHF/3-21G surface were the two C2, T-shaped structures [(3) and (4)]. Both were saddle points; vibrational analysis indicat- ing that (3) was the transition state for COf migration from one end of the nitrogen molecule to the other [(lb) +(3)-+ (lb)] and (4) the transition state for a similar migration of CO [(2b) + (4)-+(2b)l. We did locate other stationary points on the UHFf3-21G [N2--CO]+ potential-energy surface but these were all higher in energy than either (lb) or (2b).With the 6-31G* basis, the linear [N2.-.0C]+complex (2a) has a degenerate pair of imaginary frequencies [like structure (la)]. However, we were unable to locate any bent structure equivalent to (2b); indeed all complexes with the oxygen end of the CO interacting with N2were unstable on the UHF/6-31G* surface. In contrast to the 3-21G surface, the T-shaped structure (3) was a minimum at the 6-31G" level; however, it lies in a well of almost zero depth and we were able to locate a transition state [structure (3a)l with C, symmetry linking structures (lb) and (3), which is only slightly distorted from (3) and lies only 0.05 kJ mol-' higher! Single-point MP3/6-3 lG* calculations on the 6-3 IG* optimized structures place (3) 142 kJ mol-' above (lb) (cJ 326 kJ mol-' at UHF/3-21G and 199 kJ mol-' at UHF/6- 31G*). Again, structures (3) and (3a) have almost identical energies, so there is no real evidence that (3) is a minimum on the correlated energy surface. A schematic version of the MP3/6-31G*//6-31G* [N2...CO]+ potential-energy surface is shown in fig.2. Our investigation of [N2..CO]+ indicates that there is really only one stable structure on the potential-energy surface [structure (lb)]. This can be considered as a complex between NZ and CO' and has a binding energy of 94 kJ mol-' (MP3/6-31G*//6-31G*). One question that comes to mind is how much of this binding is purely electrostatic in origin? Such a question can be answered, at least qualitatively, by considering one of the schemes available for partitioning the energy into various components {electrostatic energy, polarization energy, charge-transfer energy, exchange repulsion etc.[see ref. ( 191). However, we have chosen an alternative approach based on Stone's distributed multipole analysis (DMA)? In this approach the charge distribution derived from an a6 initio wavefunction is represented in terms of charges, dipoles, quadrupoles etc. located at a number of sites in the molecule (in our case the atomic nuclei). By considering the interactions between these multipoles for N2 and CO' at the (approxi- mate) geometry of the N2..-CO+ complex an estimate of the electrostatic energy can be obtained. A simple model based on this idea has been successfully used to predict the geometries of hydrogen-bonded cornple~es.~~ Using the program ORIENT" and consider- ing all terms up to r-' the electrostatic contribution to the N2-.C0+ binding energy is predicted to be ca.33 kJ m01-l. Although this value is based on a DMA of the ROHF/6- 31G* wavefunctions, we do not expect it to change significantly if correlation were taken into account. Thus, based on the MP3 value of 94kJ mol-l, the electrostatic contribution to the energy is ca. 35%. J. Baker and A. D. Buckingham p 1' A N-N 3 N2... CO' 1 b N,. . .CO' 1 b Fig. 2. Schematicof the MP3/6-31G*//6-31G* potential-energy surface for [ N2.-CO]'. Energies in kJ mol-' relative to structure (lb). Table 3. Atomic charges on CO+ and N2..COf [structure (lb)] calculated according to Mulliken, Lijwdin, distributed multipole (DMA) and natural population (NPA) analyses at UHF/6-31G* compound atom Mulliken Lowdin DMA NPA CO' c 0.933 0.721 1.121 1.292 0 0.067 0.279 -0.121 -0.292 Ny * co+ N 0.128 0.237 0.078 0.31 1 N 0.070 0.055 0.162 -0.092 c 0.844 0.531 0.989 1.136 0 -0.042 0.177 -0.229 -0.335 In a similar manner, provided the relevant distributed polarizabilities are known, ORIENT can give an estimate of the induction energy, which for N,.-CO+ is ca. 61 kJ mol-I.The major portion (86%) of this comes from changes in the electron distribution around N2 due to the field from CO+. The sum of the electrostatic plus induction energy is ca. 95 kJ mol-' which, although the repulsion energy has not been taken into account, indicates that most of the binding in the N,.-.CO+ complex comes from long-range interactions, and there is really no evidence for an incipient 'chemical bond' in this system.It is of interest to note that the centre of charge of CO+ (i.e. the point relative to which the dipole moment vanishes) lies 0.05 a.u. outside the C nucleus. This provides an explanation for the large magnitudes of the induction energy of N, in the field of CO' and of the electrostatic energy (the location of the principal source of the field may be thought of as being the centre of charge), and may also be significant for the stability of some transition-metal carbonyl complexes. The various schemes for 'population analysis', such as that described above, are, of course, highly dependent on just how the molecular electron density is distributed amongst the various centres, and it is instructive to note how different the results from the different schemes can be.In table 3 we present calculated atomic charges for CO' 1614 -CO+Ab Initio Investigation of NZ-and the N2. --CO+ complex obtained from four alternative analyses: M~lliken,’~ Low-din,20DMAI6 and natural population analysis (NPA).” The analyses are based on the UHF/6-3 lG* wavefunctions. Despite the range of charges predicted, all four schemes are essentially in agreement that N2--C0+ is best represented as a complex between N2 and CO+. In the spirit of the Buckingham-Fowler model1’ we have ‘optimized’ the geometry of the N2--.CO+ complex based on electrostatic considerations alone.We have assumed standard van der Waals atomic radii for oxygen and nitrogen and a van der Waals radius of 0.57 A for carbon, considering this as C+ (see table 3). This value was chosen so as to reproduce the ab initio N.-C distance of structure (lb). Gratifyingly, the optimized OCN bond angle was 128.1’, in excellent agreement with the ab initio ROHF/6-31G* angle of 127.4’. This result is encouraging for the extension of this model to charged species, although the induction energy may need to be considered and there may be problems assigning van der Waals radii to charged centres. References 1 C. E. Hamilton, V. M. Bierbaum and S. R.Leone, J. Chem. Phys., 1985, 83, 601. 2 E. E. Ferguson, N. G. Adams and D. Smith, Chem. Phvs. Lett., 1986, 128, 84. 3 P. Kebarle, Annu. Rev. Phvs. Chem., 1977, 28, 445. 4 S. C. de Castro, H. F. Schaefer 111 and R. M. Pitzer, J. Chem. Phys., 1981, 74, 550. 5 C. hlqjller and M. S. Plesset, Phys. Rev., 1934, 46, 618. 6 (a) P. C. Hariharan and J. A. Pople, Theor. Chim. Acta, 1973, 28, 213; (b) J. S. Binkley and J. A. Pople, J. Chem. Phys., 1977, 66, 879. 7 J. S. Binkley, J. A. Pople and W. J. Hehre, J. Am. Chem. Soc., 1980, 102, 939. 8 J. Baker and R. H. Nobes, unpublished work. 9 J. S. Binkley, M. J. Frisch, D. J. Defrees, K. Raghavachari, R. A. Whiteside, H. B. Schegel, E. M. Fluder and J. A. Pople, unpublished work. 10 J. Baker, J. Comput. Chem., 1986, 7, 385.11 (a) N. C. Handy, P. J. Knowles and K. Somasundram, Theor. Chim. Acra, 1985, 68, 87; (b) J. Baker, R. H. Nobes and L. Radom, J. Comput. Chem., 1986,7,349. 12 R. D. Amos, The Cambridge Analytical Derivative Package (S.E.R.C., 1984). 13 B. R. Brooks, W. D. Laidig, P. Saxe, N. C. Handy and H. F. Schaefer 111, Phys-Scr., 1980, 21, 312. 14 S. R. Langhofi and E. R. Davidson, Int. J. Quantum Chem., 1974, 8, 61. 15 K. Morokuma, J. Chem. Phys., 1971, 55, 1236. 16 A. J. Stone and M. Alderton, Mol. Phys., 1985, 56, 1047 and references therein. 17 (a) A. D. Buckingham and P. W. Fowler, J. Chem. Phys., 1983, 79, 6426; (b) A. D. Buckingham and P. W. Fowler, Can. J. Chem., 1985, 63, 2018. 18 A. J. Stone, ORIENT (Cambridge University, 1986). 19 R. S. Mulliken, J. Chem. Phys., 1955, 23, 1833. 20 P-0. Lowdin, Phys. Rev., 1955, 97, 1474. 21 A. E. Reed, R. B. Weinstock and F. Weinhold, J. Chem. Phys., 1985, 83, 735. Paper 7/385; Received 2nd March, 1987

ISSN:0300-9238    

DOI:10.1039/F29878301609

出版商:RSC    

年代:1987

数据来源: RSC

摘要:

J. Chem. SOC.,Faraday Trans. 2, 1987, 83(9), 1615-1628 Ab Initio Potential-energy Surfaces for the Reactions of Al' with H, David M. Hirst Department of Chemistry, University of Warwick, Coventry CV4 7AL Potential-energy surfaces for states of AlHt relevant to the reactions of Al+ with H, have been calculated by ab initio configuration interaction methods. Minima on the potential-energy surfaces have been located. In the case of Czvsurfaces for triplet states comparison is made with the corresponding surfaces for BH;. The reaction of Al+('S) with H2 to form A1H+(211) is interpreted in terms of an avoided intersection between the *A, and 'B2 surfaces. On the basis of the calculated potential-energy surfaces there is no simple interpretation of the apparent activation energy observed for the reaction of Al+(3P) + H2 to form AlH+(A 211).The dynamics of the reactions of Al' with H2have been investigated recently by Muller and Ottinger' who have observed chemiluminescence from the A 211 and B *I;+ states produced in the endothermic reactions: Al"('P) + H2 -+ AlH+(A 'n) + H -2.59 eV (1) Al+('S) + H2 -+ AlH+(A 'n) + H -7.25 eV (2) Al'( 'S)+ H2 -AIHS(B *C+)+ H -7.57 eV. (3) For a collision energy of 8.6 eV, they showed that the total cross-section for the formation of the B state is much larger than that for the A state and that for the formation of the A state, the cross-section for the metastable state of Al'(3P) is much larger than that for the ground-state ('S)reactant. From an investigation of the energy dependences of the B -+X and A --+ X emissions, they found that reaction (1) is dominant for energies in the range 6-10eV, but is completely inhibited at lower energies.They concluded that this reaction must have an activation energy of ca. 3.5 eV. Muller and Ottinger' discussed the dynamics of the Al'+ H? reactions in terms of potential-energy surfaces for the BH; system. There have not been any reports of a6 initio potential-energy surfaces for the AIH system, in contrast to several theoretical used the diatomics-in-molecules investigations of the BH; Schneider et al.394 method for the calculation of the lowest triplet and singlet states. The entrance and exit channels for several surfaces have been calculated by Hirst' by the a6 initio configuration interaction method.Klimo et aLS have used Mflller- Plesset second-order perturbation theory and the linearized coupled cluster method in calculations for the lowest 3A' potential-energy surface. The most extensive calculations on BH; are con- tained in a thesis by Klein6 who used the MC-SCF method to calculate grids of points for many surfaces in C,, ,Dmh, C2t,and C, symmetries. In this paper we present ab initio configuration interaction calculations for potential-energy surfaces of A1 H,' which may be important in reactions (1) and (2). Reaction (3) is much more complicated in that the products AlH+( B 'C+) + H correlate with the third state of 'C' or 'A,symmetry and we do not consider such highly excited states in this work.In fig. 1 we present a qualitative correlation,diagram for states of AIH,' correlating with Al'('S, 3P)+ H2 and with AIH'(X 'Ct,A -n).Where possible the figure includes calculated energies for minima on the various potential-energy surfaces considered here. 1615 1616 Al' +H2 Potential-energy Surfaces 14 12 10 Al ('P)+ Hi(XI 5 1 " -18 hP AIM+H>-s6 r, -2 /w0 AI'('SI+ H, Al AI-H-H H-AI-H Go" products D.,,h H' 'H C2" Fig. 1. Correlation diagram for the AIHT system. The lowest singlet state ('2+-'A'-'A1) is relatively straightforward since Al'('S) + H2('Zi) results in a single surface. Similarly from the products A1H' (X 'E+) +H('S) one can form only one singlet state. For collinear geometries Al'(3Pu) +H2('1;)results in two surfaces 3C+and 3rI.The former correlates with AlH+(X 'Z+) +H('S), whereas the 'II surface correlates with AIH'(A 'II) +H('S). In C, symmetry, the 'II state splits into 'A' and 'A" surfaces which both correlate with AlH'(A '11) +H('S). For CzL symmetries we adopt the coordinate system -H rnH H so that A, and B2 states correlate with A' in C, symmetry and B1 and A2 with A". From Al' (3Pu)+H2('Zi) one obtains surfaces of 3A1,'B1 and 3Bzsymmetry. The 'A, surface correlates through a C, surface of 'A' symmetry with one component of the 'rI surface for the C,. geometry with the arrangement AIHH+, whereas the 3Bzsurface correlates through the other 3A' surface with the 3Ec+surface. The 3B,surface correlates through the 3A"surface with the other component of the '11 surface.The correlations with states of HAlH' of D,!, symmetry on full insertion are rather more complicated because of intersections between potential curves in Dwhas rAlH increases. The 3Blstate correlates with 'Hu. One would perhaps expect the 1 3B2 state to correlate with 'EL in D,,, symmetry, but the configuration interaction calculations reported in this paper indicate that this state correlates with 'IIg for rAIH< 1.5 8, and that it is the 2 3B2 state that correlates with 'z; for these geometries. For rAlH <1.55 A, the 3n,state lies below the '1;state, but the potential curves intersect in the region of rAIH=1.55 A. For larger values of rAlH the 1 'B2surface correlates with 'E; and the 2 3B2surface with 'IIg.Both Klein' and we find that the same situation occurs for BH;. For short values of rAIH the singly occupied a, orbital (3a1in BH;, 5a, in AIH;) acquires increasing amounts of pz character as R decreases and correlates with the singly occupied T orbital in D-r!2. The 2 'Bz surface correlates asymptotically with Al('P)-t H;(X 'Xi). For short values D. M. Hirst 1617 Table 1. Details of configuration interaction for AlHt no. of reference size of configuration state configurations space 13 1846 15 2464 9 1458 16 2912 7 2266 7 2094 20 3553 6 2059 4 1281 of TAIH, the 'nustate lies below the '2; state and the two potential curves intersect in the region of rAjH = 1.8A.SO the 'A, state will correlate with '11, for values of rAlH below 1.8 A and with 'E; for larger values. Although the 3A2state cannot be formed from Ai'('Pu) + H2('Zi), avoided intersections with this surface may be important. This surface correlates with 'lIgin the Doohconfiguration and asymptotically with H2( 'cf)and an excited 'Pg state of Al+ with the configuration pxp,,. In BH;, the 'A2state also correlates with H2( 'Xi)+ B'('Pg). In this paper we present potential-energy surfaces, calculated by the ab initio configur-ation interaction method, for the triplet states 'A1,'A2,'B1,1,2 'B2,'Z+, '1I and for the singlet states 'A1,'B2 and 'E+. We hope that these data will be of use in the interpretation of the reactions of Al+ with H2 as well as providing the first reported a6 initio calculations for AIH;.Computational Details The potential-energy surfaces presented here have been calculated by the multi-reference configuration interaction method (MRDCI). The basis set for A1 consisted of the (1ls7p)[6s4p] Gaussian basis of Dunning and Hay' augmented with a set of Cartesian d functions with exponent 0.311aG2. For the hydrogen atom the (4s)[2s] basis' was augmented with a set of p functions with exponent 1.0 a;*. The SCF orbitals for the state in question were used as starting point for the CI calculations. In the CI calculations, all single and double excitations were generated from sets of reference configurations which generally included all configurations for which the coefficient in the final CI vector was larger than 0.1. The core orbitals of A1 were kept doubly occupied in all configurations, and excitations to the corresponding high-energy virtual orbitals were excluded. Table 1 contains details of numbers of reference configurations and of the sizes of the configuration spaces used.For CZupotential surfaces having wells, the geometries of the minima were calculated by the SCF gradient technique. Energies were calculated for these geometries by the CI method. Geometries for minima in Dooh symmetry were optimized at the CI level. In order to provide a comparison of the potential-energy surfaces of AlHz with those of BH:, we have extended our previous calculations' and present here contour diagrams for the triplet surfaces of CZusymmetry.Results and Discussion In table 2 we present the calculated energies for reactant and product asymptotes and the energies at optimized geometries. There are no other calculations in the literature with which we can compare our energies. From calculations at the reactant asymptote 1618 Al'+ H2 Potential-energy Surfaces Table 2. Energetics of AIH; system CI energy/Eh relative energy/eV -242.85913 0.0 -242.68852 4.643 -242.71240 3.992 -242.58394 7.488 -242.82 177 1.017 -242.5 523 4 8.348 -242.69236 4.538 -242.609 18 6.802 -242.545 53 8.534 -242.68568 4.720 -242.60234 6.988 -242.70215 4.272 -242.7 1907 3.811 5 .O 4 .O 5 3.0 2 .o 1 .o 1 .o 1.5 2.0 2.5 30 THHIA Fig.2. Potential-energy surface for the 'A, state of AlH;. Contour 1 = -242.84 Eh, contours drawn at intervals of 0.02 Eh. we obtain an energy of 4.643 eV for the separation of the 'S and 3Pustates of Al'. This compares favourably with the experimental value of 4.56 eV. The separation between the product asymptotes leading to the X and A states of AlH'+ H is 3.496 eV, which can be compared with the experimental T, value of 3.428eV. Thus our calculations appear to be giving a satisfactory description of the asymptotic regions. The ground state of AlH,' is 'Ci and in our CI calculations we obtain an optimum bond length of 1.5395 A. The potential-energy surface for the 'Xi-'A,state is shown in fig. 2, from D. M.Hint 1619 2.5 2 .o 1.5 1.0 0.75 1.0 1.5 2 .o 2.5 %HIA Fig. 3. Potential-energy surface for the 'Xc+state of AlHH+. Contour 1= -242.84 Eh, contours drawn at intervals of 0.02 E,. which it can be seen that the ion in this state is metastable relative to Al+('S) +H2('X,'), lying ca. 1 eV higher in energy. This is in contrast to the BH; ion for which the 'Z+ state is ca. 2.5 eV lower than B+('S)+H2('Z;). The potential minimum on the 'Al-Zg surface can only be reached in Czvsymmetry by surmounting a barrier of ca. 4.35 eV. This barrier arises from an avoided intersection between the 1 'Al and 2 'A,surfaces. In the vicinity of the potential minimum, the dominant configuration is, for Dcohsymmetry la;2a;la~17r43a;2a; (4) which correlates in CZ0symmetry with the 'A,configuration la:2a:3ail btl b;4a:2b: whereas in the asymptotic region corresponding to Al+(IS)+ H2, the wavefunction is predominantly lai2a:3a:1 b:l b:4a:5a:.(6) The reaction Al+('S)+H2('Xi)+ AlH+(X 'Z')+H(*S) (7) is endothermic by 3.82 eV, and from our calculations it is apparent that for collinear geometries (fig. 3) there is no barrier other than the endothermicity of the reaction. Reaction (2) cannot occur adiabatically because the reactants correlate with 'C+in collinear C,, geometries and with 'Alin C2,symmetry, whereas the products correlate with 'I3 and 'B2surfaces, respectively. However, in C,, symmetry both the 'A,and 'B2 surfaces transform to 'A'and an intersection between these two surfaces in C2,symmetry will become an avoided intersection in C, symmetry.The reaction could then occur by Al' +H2 Potential-energy Surfaces 5 .O 4 .O 3.O 5 Q 2 .o 1 .o 0.75 1 .o 1.5 2.0 rHH/A Fig. 4. Potential-energy surface for the 'B, state of AlHt. Contour 1= -242.68 E,, contours drawn at intervals of 0.02 E,. Dashed line indicates intersection with 'Al surface. a non-adiabatic transition between the two surfaces. The 'B2surface is shown in fig. 4 and has a very flat minimum covering the range of geometries from LHAlH=41", rAlH = 1.6 A to LHAlH =67", RAIH= 1.8 A. In this region it actually intersects the 'A, surface and the seam of intersection is indicated by a broken line in fig. 4. Thus on distortion to C, in this region the intersection will become avoided, but one expects the separation between the two surfaces to be very small and non-adiabatic transitions are expected to occur readily for trajectories reaching this region of the potential surface. The reaction of B'('S)+ H2 to form BH+(A 'n) has been interpreted in a similar manner.276 In the case of Al'+H,, the intersection of the 'A, and 'B, surfaces lies ca.4.8 eV above the energy of the reactants AI'('S)+ E2, whereas in the case of B+('S)+ H2, the corresponding energy is ca. 3.24 eV. Muller and Ottinger' observed that the ratio of the cross-sections for the formation of the B and A states from the ground-state ions was larger in the case of Al'. Thus for Al'('S), the formation of the A state may be less favourable because of the IA,-'B, intersection lies at higher energy.The reactions of Al'(3P,) will now be considered. In addition to reaction (1) resulting in the A state of AlH+, formation of ground-state AIH+ (X ?Z') is also possible in the exothermic reaction Al+(3Pu)+H2('C;) +AlH+(X 'Z+) +H('S) +0.84 eV. (8) For collinear AlHH+ geometries, this can occur on the C,, surface 3C' (fig. 5) which is attractive and has no activation barrier. Reactants can evolve directly downhill into products. In Doohgeometries it is the 'X: state that correlates with the X state, but as discussed above, because the 'Z: and 'Jig states intersect in the region of rAlH = 1.55 A, it is only in the regions of large rHH(>3.0A) that the 1 3B2 state correlates with 'X:.For Dinhsymmetries the %, state has a minimum for rAiH = 1.69 A, whereas the minimum D. M. Hirst 1621 2.5 2.0 ? z k.? 1.5 10 0.75 1 1.5 2 .o 2.5 THHIA Fig. 5. Potential-energy surface for the 3C+ state of AlHH+. Contour 1= -242.70 Eh, contours drawn at intervals of 0.02 E,. 2in the 'E: curve is for rAlH =3.24 A. The entrance channel of the 1 3~ surface [fig. 6(a)] is very slightly attractive and leads to a very flat region extending from PHH =0.75 to 3.0 A in which R decreases from 1.75 to 1.25 A. This region widens as THH increases. Thus motion on this surface can quite easily lead to the region which correlates with the 'Z: surface in Dmh symmetry. The 1 'B2surface for BHT [fig. 6(b)]is similar in appearance to that for AlH,' but the 2 3B2surface [fig.7( b)]is in closer proximity over a larger region (from R = 5 to 3 A for THH = 1.25 A). Also the well in the AlH,' surface extends over a larger range of geometries than in the case for BH;. The other collinear triplet surface for the C,, geometry AlHH+ is the 311 surface (fig. 8) and motion on this collinear surface leads smoothly upwards from Al+('P,) +Hz to the products AlH' (A'rI) +H. Again there is no activation barrier. The corresponding surfaces in CZt sjmmetry are 3A, [fig. 9(a)] and 'B, [fig. lO(a)]. The 3B, surface ucorrelates with 'II,, in Dmh symmetry and the 3A,with 3~ for rAlH < 1.8 A and with 3+Zg for larger values. The 'A, surface is initially repulsive with a barrier of ca.3.8 eV with respect to insertion. The 3B, surface has a very flat entrance channel with a minimum at R =2.079 A, rHH =0.749 A, but is otherwise repulsive. Muller and Ottinger' have discussed motion on these surfaces in terms of intersections of the 3A1surface with the 2 'B2 surface and between the 'I?, and 'A2surfaces. In C, symmetry these pairs of surfaces transform to 'A'and 3A",respectively, and the intersections will become avoided. The 3A2surface correlates with 'ZI, in Dochand fig. ll(a) indicates that the ,energy steadily decreases as the minimum in the 3~ state (for rAIH= 1.69A) is approached. Thus motion on the appropriate 3A"surface would give a route from the 'B, surface to the 'IIg surface. Similarly a 3A'surface connects the 'A, surface with the 2 'B2 surface which, for large values of rHH,also correlates with 'IIg.Removal of Al' +Hz Potential-energy Surfaces 5 .O 4.0 3.O ? Q 2.0 1 .o L0.75 1.o 1.5 rHHlA 2.0 -1 .o 0.75 1 .o 1.5 2 .o IHHIA Fig. 6. Potential-energy surfaces for the 1 3B2 states of (a) AlHt, contour 1 = -242.70 E,; (b)BHT, contour 1 = -25.38 E,. Contours drawn at intervals of 0.02 Eh. D. M. Hint 1623 2.o 1.0 I I I 0.75 1.o 1.5 2.0 5.0 4.0 3.0 2.o -3' I 1 .o I I 0.75 1 .o 1.5 c 3 THHIA Fig. 7. Potential-energy surfaces for the 2 'B2 states of (a) AIH;, contour 1 = -242.62 E,; (b) BHf , contour 1= -25.22 Eh.Contours drawn at intervals of 0.02 Eh.Dashed line indicates intersection with 3A,surface. Al' +H2 Potential-energy Surfaces 2.5 2 .o 1 .o 1.5 1 .o 1.5 2.0 2.5 THHIA Fig. 8. Potential-energy surface for the 311 state of AlHH+. Contour 1= -242.68 Eh, contours drawn at intervals of 0.02 E,. a hydrogen atom from HAlH+('II,) results in AlH+(A 'n) +H. Muller and Ottinger' interpret the activation barrier for reaction (1) in terms of the energies of these intersec- tions. On the basis of the calculations of Klein6 for BH; they argue that for BH; these intersections lie at about the same energy as the exit channel to BH++H, whereas for AlH;, the intersections would be expected to occur at higher energy. The reason given for this is that the 'A2 surface is expected to correlate with AI(*P)+Hf('Z;) or A1(4P)+ Ht(X 'Xi) and the 2 'B, surface with Al('P) +Hl(X 'Xi).These energies are 2.31 eV higher than the corresponding energies for BH;. The intersections of 3A1 and 2 'B2surfaces and of the 'B, and 3Az surfaces for AiHi are indicated in fig. 7(a), 9(a), 10(a) and ll(a). In the case of the 3A1 and 2'B2 surfaces, the intersection occurs over quite a wide range of geometries and the energy on the seam of intersection ranges from -242.62 to -242.50 Eh. A trajectory reaching the 23B2 surface would find itself on an attractive surface with a well in the region of rHH = 1.25 A,R =4-5 8, with an energy of ca. -242.62 Eh. In order to reach the portion of the surface correlating with the 311g state, it would have to surmount a barrier having an energy of ca.-242.56 Eh. This is only ca. 0.7 eV higher than the calculated energy of the products AIH+ (A'II) +H(-242.5894 Eh). There is a further seam of intersection between the 3A2 and 2 'Bzsurfaces for the range of geometries R = 1.25 A, THH = 1.4 8, to R = 1.5 A, THH =2.0 A covering the energy range -242.50 to -242.56 &. The intersec- tion of the 3Bland 'A20surfaces occurs over the region from R = 1.0 A,THH =0.75 8, to R = 1.75 A,RHH=2.0 A. The energy on the seam of intersection ranges from -242.57 Eh to -242.46 Eh. In this region the 'A2surface is attractive and the system can evolve downhill to the 311gstate. Since the energies at some sections of the seams of intersection are comparable with the energies of AlH'(A), one cannot give a simple explanation of the deduced activation energy in terms of energetics.D. M. Hint 1625 5 .O 4 .O 2 .o 1 .o 1 .o 1.5 2.0 rHHIA 5.0 4 .O ? 3 .O !x 2.0 1.0 I .O 1.5 THHIA Fig. 9. Potential-energy surfaces for the 3A, states of (a) AIH;, contour 1= -242.68 E,; (b)BH;, contour 1 = -25.28 Eh. Contours drawn at intervals of 0.02 Eh. Dashed line indicates intersection with 2 3B2surface. 1626 Al' +H2 Potential-energy Surfaces 5 .O 4.0 ? 3.0 Q 2 .o 1 .o 1.0 15 2.0 THHIA 5 .O 4 .O ? 3.0 Q 2 .o 1 .o 1 .o 1.5 2 .o THH /A Fig. 10. Potential-energy surfaces for the 3B, states of (a) AlHt ,contour 1 = -242.70 E,; (b) BH;, contour 1 =-25.34 E,.Contours drawn at intervals of 0.02 Eh. Dashed line indicates intersection with 3A2surface. D. M. Hirst 1627 5.0 4 .O 3 .O ? & 2.0 1 .o 5.0 4.O 3.0 "b,& 2.0 1 .o 1 .o 1.5 2 .o THHIA Fig. 11. Potential-energy surfaces for the 'A2states of (a) AIH;, contour 1 = -242.58 E,; (b) BH;, contour 1 = -25.30 E,. Contours drawn at intervals of 0.02 E,. Dashed line indicates intersection with 'B, surface. Al' + H2 Potential-energy Surfaces In the case of BH,', the seam of intersection of the 3B, and 3A2surfaces covers the region R = 0.75 A, rHH =0.75 A to R = 1.5 A,rHH = 2.0 A and over this seam the energy ranges from -24.99 to -25.26 Eh. For a considerable part of the seam the energy is comparable with that of the products BHf( A 'II) +H of -25.2405 Eh. The 'B, and 3A2 surfaces for BH; [fig.lO(6) and 11( 6)] and AlHl [fig. 10(a) and ll(a)] are qualitatively similar. The 3B1 surface for BH; has a deeper minimum (1.45 eV) in the entrance channel (for R = 1.5 A, rHH = 0.75 A) than is the case in the AlHi surface. The location of the seam of intersection with the 'A2surface is similar for the two systems. The first seam of intersection of the 3A1and 2 'B2surfaces for BH; covers the range of geometries R =0.75 A, YHH=0.75 A to R = 2.0 A, rHH = 1.3 A with the energy varying from -24.60 to -25.22 Eh. These energies are higher than the energy of the product BH+ (A). As in the case of AlH;, there is a second seam of intersection which extends from R = 1.2 A, YHH= 1.25 A to R == 1.5 A, rHH =2.0 A, with energies ranging from -25.10 to -25.18 &.There is a qualitative similarity between the 3A2surfaces for the two species. It does not seem possible to understand the difference between the reactions of Al+(3P) and B'(3P) to form the A 211 state of the hydride ion simply on the basis of the potential-energy surfaces presented here. There does not seem to a noticeable difference between the energies at which the 'A,, 2 3B2and 3B1,3A2surfaces intersect relative to the energies of the products. To gain a fuller understanding of these reactions it will be necessary to extend the calculations to include the relevant surfaces of C, symmetry and to perform dynamical calculations.In view of the complexity of the system, this will be quite a formidable task. The author is grateful to Prof. Ch. Ottinger for drawing attention to this problem and for communicating his experimental results prior to publication. He thanks Prof. P. Rosmus for providing the relevant material from the thesis of Klein6 and Prof. J. N. Murrell for useful discussions. The provision of computing facilities by the S.E.R.C. is gratefully acknowledged. References 1 B. Muller and Ch. Ottinger, J. Chem. Phys., 1986, 85, 232. 2 D. M. Hirst, Chem. Phys. Lett., 1983, 95, 591. 3 F. Schneider, L. Zulicke, R. P6lak and J. Vojtik, Chem. Phys., 1984, 84, 217. 4 F. Schneider, L. Zulicke, R. P6lak and J. Vojtik, Chem. Phys. Lett., 1984, 105, 608. 5 V. Klimo, J. Tiiio and J. Urban, Chem. Phys., 1986, 104, 207. 6 R. Klein, Thesis (University of Frankfurt, 1984). 7 T. H. Dunning and P. J. Hay, in Methods of Electronic Structure Theory, ed. H. F. Schaefer (Plenum Press, New York, 1977), p. 1. Paper 7/289; Received 17th February, 1987

ISSN:0300-9238    

DOI:10.1039/F29878301615

出版商:RSC    

年代:1987

数据来源: RSC

摘要:

J. Chem. SOC.,Furuduy Trans. 2, 1987, 83(9), 1629-1636 The Diradical Nature of Ketocarbenes occurring in the Wolff Rearrangement An MC-SCF Study Juan J. Novoa,? Joseph J. W. McDouall and Michael A. Robb Department of Chemistry, King's College London, Strand, London WC2R 2LS Using MC-SCF gradient optimisation techniques (at the 6-3 1 G" basis-set level) the minima and transition structures occurring in the rearrangements of formylmethylene to oxirene have been characterised. The triplet-state and singlet-state surfaces and the crossing region have been studied. The results show that the lowest-energy singlet state of formylmethylene is a pure diradical. The related triplet state has a very similar geometrical structure and lies only slightly lower in energy.Further, both states have the two unpaired electrons in sigma orbitals and the minimum-energy singlet- triplet crossing point occurs very near singlet-triplet diradical minimum of formylmethylene. Ketocarbenes (11) are postulated to be intermediates in the Wolff rearrangement (WR)' of diazoketones (I) to form ketenes (111): 0 Nz 0 R' II IIhuR~-c-c-R* ---+ R'-C-C--R~+N~ -+ \C=C=O+N,heat R2/ (IV) Since the original work of Wolff' a large number of theoretical and experimental papers have been devoted to this topic.'-'8 However, the mechanism has still not been established unequivocally. The relevant experimental facts that must be explained by any proposed mechanism are as follows. (a) Experiments with isotope-labelled diazoketones seem to indicate the participa- tion of oxirenes (IV) as short-lived intermediate^,^ although they have never been isolated.(b) There is experimental4 and theoreticals evidence for the formation of planar triplet ketocarbenes, isolated in low-temperature matrices. This fact seems to contradict the hypothesis made by some authors that the WR involves predominantly singlet intermediates6 This fact has suggested to some authors? the existence of more than one iPermanent address: Department of Physical Chemistry, lJniversity of Barcelona, Avenue Diagonal 647, 08028-Barcelona. Spain. 1629 MC-SCF Study of the Wolfl Rearrangement mechanism: one which passes through intermediates and a second which is concerted. However, Torres et a1.8 ruled out the concerted mechanism in their work on the basis of experimental data as well as on the basis of previous theoretical work.' (c) The experimental results of Torres et aL8 also clearly indicate the existence of conformational control with preference for the s-z (cis) conformation.Thus the available data seem to indicate that the conformational control originates in the ketocar- bene, i.e. the conformational identity of the diazoketone must be preserved in the ketocarbene, something which only is possible if such a compound is ~lanar.~ E.s.r. studies have shown in some cases that the conformation of the most abundant triplet ketocarbene is the same as that of the precursor diazoketone." (d) Chemically induced dynamic nuclear polarization studies have shown that for the diazoacetone the intersystem crossing occurs from triplet ketocarbene to singlet ketocarbene" and that the singlet ketocarbene is not an intermediate in the WR.This crossing has been also postulated by Tomioka et al.'* and is frequently observed in analogous carbene systems.13 In order to clarify the mechanism of WR, there have been several ab initi~~,'~-'~and semiempirical computation^^"^ on the structure of the C2H20 isomers, some of including electron correlation. However, all except one5 of these computations has been for the singlet state. These computations have shown that one must include d polarization functions and electron correlation for a reliable determination of the relative barriers and activation barriers for the interconversion of the C2H20isomers.The results of Tanaka and Yoshimine are the most comprehensive and were obtained using the configuration interaction method with a wavefunction which includes all single and double excitations from the reference (Hartree-Fock) configuration (using geometries for the isomers optimized at the SCF level with a double-zeta plus polarisation basis set). Their results indicate (i) that ketene is the most stable isomer (36 kcall- mol-' more stable than hydroxyacetylene and 82 kcal mol-' more stable than oxirene), (ii) that formylmethylene is unstable with respect to rearrangement to ketene, (ii) the rearrange- ment from oxirene to formylmethylene has a small barrier of 2 kcal mol-' and (iv) that there is a barrier of 73 kcal mol-' for the conversion of hydroxyacetylene to ketene.They also find that the formylmethylene is non-planar, with the hydrogen associated with the methylene group lying above the plane formed by all the other atoms in the molecule. Thus, in the light of the new experimental work developed after the theoretical study of Tanaka and Yoshimine, it would appear that one cannot ignore the role of the triplet surface of the formylmethylene and the singlet-triplet crossing for such species in the mechanism of the WR. Further, the experimental evidence suggests that the photo- decomposition of the diazocompound gives a triplet ketocarbene. Accordingly, as a first step in a better understanding of the mechanism of the WR, it is important to re-examine the various possible molecular structures (minima and associated transition structures) of the simplest ketocarbene-oxirene rearrangement in both singlet and triplet states and to investigate the geometry and the energy at which the singlet-triplet crossing occurs.Methylene is the prototypical carbene. MC-SCF computation^'^ show the existence of a diradical triplet ground state having two unpaired electrons, one in the CT (in-the-plane) orbital and the other in the T (perpendicular-to-the-plane) orbital. The electronic structure of the most stable singlet has the two electrons paired in the (7 orbital. A singlet u-7diradical would correspond to an excited state and would lie much higher in energy.If ketocarbenes behaved like methylene one would expect an analogous electronic structure illustrated schematically in fig. l(a)-(c). Thus one might expect that the singlet ? 1 cal=4184J. J. J. Novoa, J. J. W. McDouall and M. A. Robb 163 1 on4 HJj H Fig. 1. Possible electronic structures for ketocarbenes: (a)-(c) carbene-like structures, (d) cr-u diradical, (e)T-T diradical. would correspond to fig 1(a) or (b) and the triplet to fig 1(c). However, the existence of a carbonyl group in the molecule must modify, to some extent, the electronic structure of ketocarbenes in view of the new type of rearrangements that these molecules can undergo, particularly intramolecular cyclizations. Further, the experimental data can only be rationalised if an accessible singlet-triplet crossing exists.In order to explain the possibility of such reactions one must consider the possibility that there are two unpaired electrons in the singlet state [i.e.a diradical, fig. 1(c)]and/or that these two unpaired electrons are localized on different centres [the C and 0 atoms, viz. fig. l(d)] rather than on the carbene-like carbon [fig. l~c)].Further, assuming that ketocarbenes are planar, we recognise that we have four n electrons in three T orbitals (similar to the open form of ozone). Thus we are led to expect the possibility of an important contribution from a diradical-like 7r long bond between C and 0 in the singlet state [fig. l(e)]. In general, similar considerations should also apply to the triplet state of the ketocarbene.While the singlet carbene of fig. 1 (d)can close to the cyclic oxirene without changing the spin coupling, the triplet carbene [fig. l(d)] cannot. Thus the structure of fig. l(e) (with triplet coupling) must correlate with the cyclic triplet oxirene. In order to describe properly such rearrangements of ketocarbenes theoretically, one must include the various possible orbital occupancies in one’s wavefunction in an unbiased way. Thus an SCF treatment (both RHF and UHF) will be inadequate and MC-SCF must be used. Computational Details All computations in this work have been carried out using an MC-SCF” gradient2* program that has been implemented as a link of the GAUSSIAN 80” suite of programs. MC-SCF Study of the WoljJRearrangement The computations have been performed at the STO-3G 23 and 6-3 1G* 24 levels.In each case the critical points have been characterized by computing the hessian by finite difference. The geometry of the singlet-triplet crossing has been investigated using the Lagrange- Newton method2’ introduced into quantum chemistry by Morokuma26 [see ref. (27) for a description of the implementation used in this work]. Here one is searching for the minimum of the ‘seam of intersection’ of the singlet and triplet surfaces rather than the usual transition structure. Thus we find the lowest-energy point common to both surfaces. Of course the probability of crossing is determined by that matrix element with the spin-orbit coupling operator, but this has not been investigated in the present work. In the MC-SCF we have included in the active space the orbitals discussed previously. Thus the active space for the planar species consists of all configurations built from two u orbitals and two 77 orbitals with four electrons. In a chemical sense these can be described as follows: (a) for the u orbitals, the carbon p orbitals of the carbene group and also the oxygen pu orbital which will be used to form a new C-0 u bond in an intramolecular cyclization in the singlet state: (b)for the T orbitals, the bonding/anti-bonding orbitals. There remains one T orbital that is restricted to be doubly occupied ( i.e.inactive). However, some exploratory computations were also performed a reference space that included three active orbitals.Results and Discussion The geometries of the various critical points and the singlet-triplet crossing are collected in fig. 2-4, while the corresponding energetics are given in table 1. We begin drawing the reader’s attention to the salient points. (i) Both the singlet and triplet ketocarbenes [fig. 2(a) and 3(a)] have very similar geometries, and both can be described unambiguously as u-udiradicals. The occupation numbers of the u orbitals for the singlet (in the 6-31G” basis) are 1.084 and 0.915. On the other hand, the singlet oxirene has a closed-shell structure, where the occupation numbers of the strongly occupied u and T orbitals are 1.96 and 1.90, respectively. The transition structure that connects the ketocarbene minimum and the oxirene minimum has an electronic structure that is only partly diradicaloid.(ii) In the STO-3G basis the singlet oxirene has a higher energy than the singlet ketocarbene, while in the 6-31G* basis the opposite is true. This result is merely a manifestation of the fact that the STO-3G basis is notorious in the overestimation of the stability of diradicals. (iii) The triplet oxirene is a 7r-T diradical and does not connect in a simple way with the singlet-triplet ketocarbenes (which are u-u diradical). There will be only a surface crossing and this region of the surface has not been explored. (iv) The geometry (fig. 4) of the lowest-energy crossing point between the singlet and triplet surfaces is very similar to that of the corresponding minima.It can be seen that the energy of this crossing point is just slightly above the energy of the singlet. (v) There is of course the possibility that the diradicals (singlet and/or triplet) are u-7~type. Using a reference space with only two active T orbitals and two active u orbitals this state lies much higher in energy than the (T-ustructures reported here. However, there are two quasi-degenerate a-77-type diradical states that differ in the permutation of singly (ie. active) and doubly (i.e. inactive) occupied T orbitals. For this reason some exploratory calculations were performed with five active orbitals (three T).The u-udiradical states (both singlet and triplet) were unaffected by this extension.However, the triplet u-7~state turns out to have a lower energy than the 0-0 triplet state with this choice of reference space, Thus the lowest-energy triplet state will have one 7r and one u orbital with single occupancy. In contrast, the singlet Q-T diradical remains at a higher energy than the u-udiradical in this extended basis. The mechanism J. J. Novoa, J. J. W. McDouall and M. A. Robb H H H Fig. 2. Geometries in (A and ") for singlet O=CH-CH isomers: (a)G-G diradical formylmethyl- ene, (b)closed-shell oxirene, (c)transition structure. The atoms are identified in the upper corner of (a). For each figure the upper geometrical parameters refer to the STO-3G geometries while the lower parameters are those obtained in the 6-31G* basis.MC-SCF Study of the Wolf Rearrangement 0 (a> 1.413 1.349 123.0 1.089 124.G H 1.340 9 1.082 \ H 1.068 Fig. 3. Geometries for triplet O=CH-CH isomers: (a) u-u triplet diradical minimum, (b) oxirene T-Tdiradical. The atoms and geometrical parameters are identified following the same convention as in fig. 2. H Fig. 4. Geometry of the minimum of the ‘seam of intersection’ of the single and triplet O=CH-CH u-udiradical surfaces. The atoms and geometrical parameters are identified following the same convention as in fig. 2. The calculations have been carried out only at the STO-3G level. of the intersystem crossing of the possible triplet diradical states among themselves has not yet been investigated.Thus in contrast to previous theoretical studies, the singlet ketocarbene is found to be a planar diradical with an easily accessible crossing point to a nearly degenerate triplet state of slightly lower energy. Of course closed-shell (RHF) SCF studies (which predict” the singlet closed-shell ketocarbene to be non-planar) explicitly preclude any diradical character. Conclusions The possibility that both triplet and singlet ketocarbenes might exist as planar u-u diradicals with an energetically accessible crossing point does not seem to have been J. J. Novoa, J. J. W. McDouall and M. A. Robb Table 1. Absolute and relative energies of O=CH-CH isomers absolute energy relative energy structure state (in Ell) STO-3G/6-31G* (kcal mol-') STO-3G/6-31G* ~~ fory m yl met hylene CT-(T triplet (T-usinglet -149.7077/-151.6387 -149.7062/ -15 1.6366 o.o/o.o0.9,' 1.3 formylmethylene to oxirene singlet -149.691 8/ -151.6341 10.0/2.9 transition state oxirene singlet triplet T-T -149.7025/-151.6454 -149.6147/-151S632 3.3/ -4.2 58.3/47.3 singlet-crossing minimum of seam of intersection -149.7055/- 1.4/- considered explicitly in attempts to rationalise the experimental data associated with such species. The present results shed new light on this field.Thus, our results show the importance of the triplet state in this reaction, and are consistent with the hypothesis of Strausz et a1.l' that the WR can take place through 'excited' states. The results obtained in this work demonstrate that the singlet oxirene can be formed either from the singlet or triplet ketocarbene with almost no activation for the singlet or the triplet.The short life of the oxirene can be explained becuase of the negligible computed barrier of formation from the singlet carbene and because (from the results Yoshimine et al.") this compound apparently undergoes a facile 1-3 shift reaction on order to form the final ketene compound. Our results are also consistent with the existence of two signals (cis-trans isomerism) in the e.s.r. spectrum of the triplet ketocarbenes. We have only studied one of the aspects of the WR. The elucidation of the complete mechanism must involve a study of (i) the photochemical formation of ketocarbenes, (ii) the triplet-triplet intersystem crossing, (iii) the 1-3 shift final reaction and (iv) the concerted mechanism of the WR. This work is in progress.The MC-SCF gradient codes were developed under NATO grant RG 096.81 and have been interfaced with the GAUSSIAN 80 suite of programs. The development of surface- crossing programs has been supported by grant GR/ D/233005 from the S.E.R.C. J.J.N. is grateful to the Generalitat de Catalunya for a CTRIT grant which has made his stay at King's College possible, and to the British Council for support in the initial stages of this work. References 1 L. Wolff, Justus Liebigs Ann. Chem., 1902, 325; 1912, 394, 24. 2 H. Meir and K. P. Zeller, Agnew. Chem., Int. Ed. Engl., 1975 14, 32; M. Torres, E.M. Lown, H. E. Gunning and 0. P. Strausz, Pure Appl. Chem., 1980, 52, 1623. 3 I. G. Csizmadia, J. Font and 0. P. Strausz, J. Am. Chem. SOC.,1968, 90, 7360; S. A. Matlin and P. G. Samrnes, J. Chem. SOC.,Chem. Commun., 1972,ll; J. Chem. SOC.,Perkin Trans. I, 1972,2623; 1973,2851. 4 A. M. Trozzolo, Acc. Chem. Res., 1968, 1, 329; R. S. Hutton, M. L. Manion, H. D. Roth and E. Wasserman, J. Am. Chem. SOC.,1974, 96, 4680; R. S. Hutton and H.D. Roth, J. Am. Chem. SOC., 1978, 100, 4324. 5 N. C. Baird and K. F. Taylor, J. Am. Chem. SOC., 1978, 100, 1333. 6 D. 0. Cowen, M. M. Couch, K. R. Kopecky and G. S. Harnmond, J. Org. Chem., 1964, 29, 1922; A Padwa and R. Layton, Tetrahedron Lett., 1965, 2167; M. Jones and W. Ando, J. Am. Chem. SOC., 1968,90, 2200; D.E. Thornton, R. K. Gosavi and 0. P. Strausz, J. Am. Chem. SOC., 1970,92, 1766. 7 F. Kaplan and M. L. Mitchell, Tetrahedron Lett., 1979, 759. 8 M. Torres, J. Ribo, A. Clement and 0.P. Strausz, Can. J. Chem., 1983, 61, 996. MC-SCF Study of the Wolf Rearrangement 9 I. G. Csizmadia, H. E. Gunning, R. K. Gosavi and 0. P. Strausz, J. Am. Chem. SOC.,1973,95, 133. 10 0. P. Strausz, H. Murai and M. Torres, J. Photochem., 1981, 17, 207. 11 H. D. Roth and M. L. Manion, J. Am. Chem. SOC.,1976, 98, 3392. 12 H. Tomioka, H. Okuno and Y. Izawa, J. Org. Chem., 1980,45, 5278. 13 H. Tomioka, H. Kitagawa and Y. Izawa, J. Org. Chem., 1979,44,3072; H. D. Roth and M. L. Manion, 3. Am. Chem. SOC.,1976, 98, 3392; H. D. Roth, Acc. Chem. Res., 1977, 10, 85. 14 0.P. Strausz, R. K. Gosavi, A. S. Denes and I. G. Csizmadia, J. Am. Chem. SOC.,1976, 98, 4784; 0. P. Strausz, R. K. Gosavi and H. E. Gunning, J. Chem. Phys., 1977,67,3057; 0.P. Strausz, R. K. Gosavi and H. E. Gunning, Chem. Phys. Lett., 1978, 54, 510; A. C. Hopkinson, J. Chem. SOC.,Perkin Truns. 2, 1973, 749. 15 C. E. Dykstra and H. F. Schaeffer 111, J. Am. Chem. SOC.,1976,98, 2689. 16 C. E. Dykstra, J. Chem. Phys., 1978,68, 4244. 17 K. Tanaka and M. Yoshimine, J. Am. Chem. SOC.,1980, 102, 7655 18 M. J. S. Dewar and C. A. Ramsden, J. Chem. SOC.,Chem. Commun., 1973, 688. 19 S V. O'Neil, H. F. Schaefer and C. F. Bender, J. Chem. Phys., 1971, 55, 162. 20 R. H. A. Eade and M. A. Robb, Chem. Phys. Lett., 1981,83, 362. 21 H. B. Schlegel and M. A. Robb, Chem. Phys. Lett., 1982, 93, 43. 22 J. S. Binkley, R. A. Whiteside, R. Krishnan, R. Seeger, D. J. De Frees, B. Schlegel, S. Topiol, L. R. Kahn and J. A. Pople, QCPE, 1981, 13, 406. 23 W. J. Hehre, R. F. Stewart and J. A. Pople, J. Chem. Phys., 1969, 5, 2657. 24 P. C. Hariharan and J. A. Pople, Theor. Chim. Acta, 1973, 28, 213. 25 R. Fletcher, in Practical Methods of Optimization (Wiley, New York, 1981), vol. 2. 26 K. Morokuma and N. Koga, Chem. Phys. Lett., 1986, 123, 331. 27 J. J. W. Mcdouall, M. A. Robb and F. Bernardi, Chem. Phys. Lett., 1986, 129, 595. Paper 71265; Received 11th February, 1987

ISSN:0300-9238    

DOI:10.1039/F29878301629

出版商:RSC    

年代:1987

数据来源: RSC

摘要:

J. Chern. SOC.,Furuduy Trans. 2, 1987, 83(9), 1637-1642 An Ab Initio Molecular Orbital Study of the Structure and Vibrational Frequencies of CH,MgH Geoffrey E. Quelch and Ian H. Hillier* Chemistry Department, University of Manchester, Manchester M13 9PL The fully optimized geometry and harmonic frequencies of CH,MgH have been calculated at the ab initio Hartree-Fock level using a close to triple-zeta valence basis. A scaled quantum-mechanical force field has been derived for this molecule using the experimentally observed vibrational frequencies, which is then used to predict the frequencies of the isotopically substituted species. There is considerable interest in the photochemical reaction of metal atoms with hydrogen and small hydrogen-containing molecules, particularly alkanes, since the activation of the latter has obvious catalytic relevance.'-3 The photoexcitation of matrix-isolated metal atoms in neat methane matrices at 12 K has resulted in the spectroscopic study of a series of insertion However, the interpretation of such data may be unclear owing to the number of species present and uncertainty as to their exact nature.Theoretical calculations, which permit accurate calculations of both the geometric structure of the possible species, and their associated spectroscopic properties have a valuable role to play when coupled with such experimental data. Photoexcitation of matrix-isolated magnesium atoms at the 3p 'P+3s 'S resonance transition in neat methane matrices results in the formation of methyl magnesium hydride (CH3MgH): Mg( 'P)+CH, + CH3MgH.McCaff rey et al.' have studied this molecule by infrared isotopic substitution experiments and measured its electronic absorption spectrum. In this paper we describe a theoretical study of the geometric structure and bonding in this molecule and predictions of its vibrational frequencies, the latter being designed to aid an assignment of its reported infrared absorption spectrum. Computational Details A triple-zeta, or better, valence basis of contracted Gaussian functions was used in the calculations. A hydrogen (5s) basis was contracted to (3s),' a magnesium (12.~9~)basis was contracted to (6~5~)~and a carbon (10s6p) basis was contracted to (5s3p).' All calculations were carried out at the restricted Hartree-Fock (RHF) level.The equilibrium geometry of the singlet ground state of CH3MgH was determined by use of the analytic gradients of the energy as implemented in the program GAMESS." A full geometry optimization was carried out, the only constraint being that of C, symmetry. For purposes of comparison, geometry optimisation of the doublet ground states of both MgCH3 and MgH were carried out in the same basis. Harmonic frequencies were calculated using analytic second derivatives implemented in the program CADPAC." Owing to the well known error in such frequencies when calculated at the RHF level, we adopted the scaling procedure developed by Pulay et all2 Here, the force constants ( Fg),calculated 1637 Ab Initio Study of CH3MgH Table 1.Calculated atomic populations for MgCH3, MgH and CH3MgH S Mg4.95 5.03 4.57 P 6.44 6.56 6.54 total 11.39 11.59 11.11 atomic charge/ e +0.61 +0.41 +0.89 C S 3.46 3.45 P 3.63 3.64 total 7.09 7.09 atomic charge/ e -1.09 -1.09 H (hydride) s 1.40 1.30 atomic charge/ e -0.40 -0.30 H (CH3) s atomic charge/ e 0.84 +0.16 0.83 +O. 17 in internal coordinate^'^ are scaled by empirical factors (x), so that the scaled force constant (F;) is given as F:,= (x;xj)”2F,i. (1) Vibrational frequencies may then be calculated by the GF matrix method. Optimal values of x were obtained by a least-squares fit to the observed frequencies for CH3MgH and were then used to predict the frequencies of CD3MgD and I3CH3MgH, which have also been reported.’ Such a procedure using a scaled quantum-mechanical (SQM) force field has been found to be successful in the prediction of the vibrational spectra of many organic molecules.14 Computational Results The Bonding and Structure of CH3MgH The electronic structure of the doublet ground state of MgCH3 and MgH can be described in terms of the interaction of the hybridized magnesium configuration (3.~~3~’)with a methyl radical (with the unpaired electron in a C 2p77 orbital) or with a hydrogen atom, leading to a single a-bond involving mainly the 3pu orbital of magnesium.Such a picture is borne out by Mulliken bond overlap populations and by the formal Mulliken atomic populations shown in table 1.Here it can be seen that the magnesium s population is essentially five electrons, the polarity of the Mg-X bond being reflected in the magnesium p populations. In the closed-shell species CH3MgH, the magnesium 3s orbital now participates in the two a-bonds, its population being reduced to ca. 0.6 electrons, the polarity of the Mg-I-I and Mg-C bonds being close to the values in MgH and MgCH3, respectively. In the species MgH and MgCH3 ,interactions involving the magnesium 3s orbital are weakly bonding or antibonding in nature, whilst in CH3MgH they are more strongly bonding. Such changes in the nature of these interac- tions are reflected in the optimized bond lengths shown in table 2, where there is a significant reduction in both the Mg-H and Mg-C bond lengths when the magnesium atom is involved in the two a-bonds. Note also that the geometry optimization procedure G.E. Quelch and I. H. Hillier 1639 Table 2. Predicted molecular geometries of MgCH3(2Al), MgH('Z+) and CH3MgH(1A1) -MgCH3 (C3J MgH (G") CH,MgH W3J Mg-C/A 2.1 13 2.093 Mg-H/A 1.735 1.719 C-H/A 1.089 1.088 LMgCH/" 111.4 111.7 RH F energy/ hartree -239.1 827 -200.1433 -239.76 19 Table 3. Calculated and measured vibrational wavenumbers (cm-') of CH3MgH calc measured assignment 3155 3088 1624 1600 1326 658 561 335 a Average of the two experimental wavenumbers at 353 and 340 cm-I given in ref. (7). predicts a C3vstructure for CH3MgH, as expected from the 3s13p1 hybridization at the magnesium atom.The two highest-filled orbitals (7a1, 6a1) contain essentially all the contributions to the Mg-H and Mg-CH3 a-bonds. Vibrational Frequencies of CH3MgH The harmonic frequencies for CH3MgH, calculated at the predicted equilibrium geometry are shown in table 3, together with the values measured by McCaffrey et al.' In all calculations we have assumed the dominant isotope, 24Mg. In spite of the calculated values being of the order of 10% greater than the experimental values as expected for a RHF wavefunction, an assignment of the experimental frequencies is possible. This is in agreement with that suggested by McCaffrey et al.' To obtain an SQM force-field which allows the prediction of the vibrational frequencies of the isotopically substituted species and related molecules, the scale factors for the internal coordinates [eqn (l)] were obtained which reproduced the experimental frequencies to better than 1 cm-'.These are shown in table 4. The scale factors are similar to those found for organic molecules, being generally less than unity, except for the linear bend and torsional motions. The internal coordinates for CH3MgH are shown in table 5 and fig. 1, and the SQM force constants in table 6. In table 7 we show the vibrational frequencies predicted using these derived scale factors for the species 13CH3MgH, CD,MgD, MgH, MgD, CH3Mg, '"CH3Mg and CD3Mg, together with the experimental values for the first two molecules. For ',CH,MgH there is excellent agreement between theory and experiment, with a maximum deviation of 3 cm-', although the effect of this isotopic substitution on the vibrational frequencies is, of course, small.For the CD3MgD species, the correlatim between theory and experiment is generally satisfactory and lends further support for the majority of the assignments. However, we predict an inversion in the Ab Initio Study of CH3MgH Table 4. Optimized scale factors for SQM force field of CH3MgH scale factor" mode 0.8630 0.8794 0.8800 0.8566 0.7167 0.6414 0.92 12 1.1605 From eqn (1). Table 5. Internal coordinates for CH3MgH no. internal coordinates description CH, sym. stretch d R H-Mg C-Mg stretch stretch CH2 sym.def. H-Mg-C bend CH3 asym. stretch CH3 asym. stretch' CH2 asym. def. CH2 asym. def.' s11 MgCH3 rock s12 MgCH3 rock' Fig. 1. Definition of the internal coordinates of CH3MgH. G. E. Quelch and I. H. Hillier 1641 Table 6. SQM force constants for CH3MgH" 1 CH, str. 4.8392 2 H-Mg str. 0.0158 1.3218 3 C-Mg str. 0.0408 0.0378 1.6062 4 CH2 def. 0.191 1 -0.01 13 -0.1319 0.3553 5 H-Mg-C bend 0.2278 6 H-Mg-C bend' 0 0.2278 7 CH3 str. -0.0094 0 4.6488 8 CH3 str.' 0 0.0094 0 4.6488 9 CH2 def. -0.0032 0 -0.1840 0 0.5871 -10 CH2 def.' 0 .0.0032 0 0.1840 0 0.5871 11 MgCH3 rock -0.05 19 0 0.1090 0 0.0046 0 0.1770 12 MgCH, rock' 0 0.05 19 0 0.1090 0 .0.0046 0 0.1770 The units of the force constants are consistent with the energy measured in aJ, bond length in 8, and bond angles in radians.Table 7. Wavenumbers (cm-') calculated using optimized CH,MgH scale factors cal cd exptl cald exptl assignment 13CH,MgH CD3MgD 2922 2924 2165 2190 2893 2896 2075 2036 1523 1524 1102 1115 1474 - 1074 - 1114 - 867 872 547 546 425 424 528 528 500 441 346 345" 252 294" CH,Mgh I3CH3Mgb CD3Mgh 2927 2917 2162 2887 2884 2069 1474 1479 1072 1101 1093 850 470 468 352 5 19 509 487 MgHb MgDh 1466 1058 " Average of the two experimental wavenumbers assigned to 6(C-Mg-H) given in ref. (7). Calculated wavenumbers. order of the p(MgCD,) and v(C-Mg) modes when compared to CH3MgH. This suggests a modification of the assignment given by McCaffrey et aZ.,' with the frequencies observed at 424 and 441 cm-' being assigned to p(MgCD3) and v(C-Mg), respectively.However, we note a rather disturbing discrepancy between the mode observed at 441 cm-' and the calculated value of 500 cm-I. The calculated frequencies for CH,Mg and MgH are in line with the weaker Mg-X bond in these molecules compared to CH3MgH. Conclusions In this paper we have shown how a series of a6 initio m.0. calculations can characterize the structure and vibrational modes of CH3MgH. The force-field scaling parameters 1642 Ab Initio Study of CH3MgH have been obtained by the use of the experimental frequencies observed for the species in a low-temperature matrix so that they contain environmental effects which may affect their possible transferability to other systems.We thank the S.E.R.C. for support of this research. References 1 W. E. Billups, M. M. Konarski, R. H. Hauge and J. L. Margrave, J. Am. Chem. SOC.,1980, 102, 7393. 2 G. A. Ozin, S. A. Mitchell and J. Garcia-Prieto, Angew. Chem., 1982, 94, 218. 3 Z. H. Kafafi, R. H. Hauge and J. L. Margrave, J. Am. Chem. SOC., 1985, 107, 6134. 4 K. J. Klabunde and Y. Tanaka, J. Am. Chem. SOC., 1983, 105, 3544. 5 J. M. Parnis and G. A. Ozin, J. Am. Chem. SOC.,1986, 108, 1699. 6 J. M. Parnis, S. A. Mitchell, J. Garcia-Prieto and G. A. Ozin, J. Am. Chem. SOC., 1985, 107, 8169. 7 J. G. McCaffrey, J. M. Parnis, G. A. Ozin and W. H. Breckenridge, J. Phys. Chem., 1985, 89, 4945. 8 T. H. Dunning, J. Chem. Phys., 1971, 55, 716. 9 A. D. McLean and G. S. Chandler, J. Chem. Phys., 1980, 72, 5639. 10 M. F. Guest and J. Kendrick, GAMESS User Manual, CCP1/86/1, Daresbury Laboratory. 11 R. D. Amos, CADPAC, Publication CCP1/84/ 1, Daresbury Laboratory. 12 P. Pulay, G. Fogarasi, G. Pongor, J. E. Boggs and A. Vargha, J. Am. Chem. Soc., 1983, 105, 7037. 13 P. Pulay, G. Fogarasi, F. Pang and J. E. Boggs, J. Am. Chem. SOC., 1979, 101, 2550. 14 Z. Niu, K. M. Dunn and J. E. Boggs, Mol. Phys., 1985, 55, 421. Paper 71451; Received 11th March, 1987

ISSN:0300-9238    

DOI:10.1039/F29878301637

出版商:RSC    

年代:1987

数据来源: RSC