Beyond the MNDO model: Methodical considerations and numerical results

It is suggested to improve the MNDO model by the explicit inclusion of valence‐shell orthogonalization corrections, penetration integrals, and effective core potentials (ECPs) in the one‐center part of the core Hamiltonian matrix. Guided by analytic formulas and numerical ab initio results, the orthogonalization corrections are expressed in terms of the resonance integrals that are represented by a new empirical parametric function. All two‐center Coulomb interactions and ECP integrals are evaluated analytically in a Gaussian basis followed by a uniform Klopman–Ohno scaling. One particular implementation of the proposed NDDO SCF approach is described and parameterized for the elements H, C, N, O, and F. In a statistical evaluation of ground‐state properties, this implementation shows slight but consistent improvements over MNDO, AM1, and PM3. Significant improvements are found for excited states, transition states, and strong hydrogen bonds. Possible further enhancements of the current implementation are discussed. © 1993 John Wiley & Sons, Inc.

[1]  W. Doering,et al.  Kinetics of the cope rearrangement of 1,1-dideuteriohexa-1,5-diene☆☆☆ , 1971 .

[2]  M. Meot-Ner,et al.  The ionic hydrogen bond. 1. Sterically hindered bonds. Solvation and clustering of protonated amines and pyridines , 1983 .

[3]  Shinichi Yamabe,et al.  Gas-phase stabilities of symmetric proton-held dimer cations , 1986 .

[4]  W. R. Wadt,et al.  Ab initio effective core potentials for molecular calculations. Potentials for main group elements Na to Bi , 1985 .

[5]  Karl F. Freed,et al.  Ab initio calculation of the effective valence shell hamiltonian of carbon: Simultaneous treatment of neutral and ion states , 1978 .

[6]  Andrey A. Bliznyuk,et al.  MNDO/M Calculations on hydrogen bonded systems , 1988 .

[7]  Steef de Bruijn,et al.  Analysis of the inadequacies of some semi-empirical MO methods as theories of structure and reactivity , 1984 .

[8]  Michael Mautner,et al.  The ionic hydrogen bond and ion solvation. 1. NH+.cntdot..cntdot..cntdot.O, NH+.cntdot..cntdot..cntdot.N, and OH+.cntdot..cntdot..cntdot.O bonds. Correlations with proton affinity. Deviations due to structural effects , 1984 .

[9]  Miguel A. Ríos,et al.  Semiempirical study of compounds with O‐HO intramolecular hydrogen bond , 1992 .

[10]  Michael J. S. Dewar,et al.  Evaluation of AM1 calculated proton affinities and deprotonation enthalpies , 1986 .

[11]  Walter Thiel.  The MNDOC method, a correlated version of the MNDO model , 1981 .

[12]  Walter Thiel,et al.  MNDOC Study of Excited States , 1981 .

[13]  Karl Jug,et al.  Development and parametrization of sindo1 for second‐row elements , 1987 .

[14]  J. Stewart,et al.  Mechanism of the Diels-Alder reaction: reactions of butadiene with ethylene and cyanoethylenes. , 1986, Journal of the American Chemical Society.

[15]  J. Pople,et al.  Self‐Consistent Molecular‐Orbital Methods. I. Use of Gaussian Expansions of Slater‐Type Atomic Orbitals , 1969 .

[16]  L. W. Sieck,et al.  The ionic hydrogen bond and ion solvation. 5- OH.cntdot..cntdot..cntdot.O- bonds. Gas-phase solvation and clustering of alkoxide and carboxylate anions. , 1986, Journal of the American Chemical Society.

[17]  Trevor J. Sears,et al.  Far infrared laser magnetic resonance of singlet methylene: Singlet–triplet perturbations, singlet–triplet transitions, and the singlet–triplet splittinga) , 1983 .

[18]  R. Stewart.  Small Gaussian Expansions of Atomic Orbitals , 1969 .

[19]  Harold Basch,et al.  Compact effective potentials and efficient shared‐exponent basis sets for the first‐ and second‐row atoms , 1984 .

[20]  Larry A. Curtiss,et al.  Studies of molecular association in H2O and D2O vapors by measurement of thermal conductivity , 1979 .

[21]  Richard W. Duerst,et al.  Microwave spectroscopic study of malonaldehyde. 3. Vibration-rotation interaction and one-dimensional model for proton tunneling , 1984 .

[22]  Frederic W. Schuler,et al.  The Kinetics of the Rearrangement of Vinyl Allyl Ether1 , 1950 .

[23]  Amiram Goldblum,et al.  Improvement of the hydrogen bonding correction to MNDO for calculations of biochemical interest , 1987 .

[24]  J. Stewart.  Optimization of parameters for semiempirical methods I. Method , 1989 .

[25]  Kendall N. Houk,et al.  Transition structures of pericyclic reactions. Electron correlation and basis set effects on the transition structure and activation energy of the electrocyclization of cyclobutene to butadiene , 1988 .

[26]  J. Pople,et al.  Approximate Self‐Consistent Molecular Orbital Theory. III. CNDO Results for AB2 and AB3 Systems , 1966 .

[27]  M. J. Goldstein,et al.  Boat and chair transition states of 1,5-hexadiene , 1972 .

[28]  Paul Baybutt,et al.  Ab initio effective core potentials: Reduction of all-electron molecular structure calculations to calculations involving only valence electrons , 1976 .

[29]  Henry S. Rzepa,et al.  Calculations of electron affinities using the MNDO semiempirical SCF-MO method , 1978 .

[30]  Michael Meot-Ner,et al.  The ionic hydrogen bond and ion solvation. 7. Interaction energies of carbanions with solvent molecules , 1988 .

[31]  Th. Zeegers-Huyskens,et al.  Enthalpies of hydrogen bonds and proton affinities , 1986 .

[32]  Robert W. Carr,et al.  The Thermal Isomerization of Cyclobutene1a , 1965 .

[33]  L. Oleari,et al.  The evaluation of the one-centre integrals in the semi-empirical molecular orbital theory , 1966 .

[34]  K. R. Roby,et al.  On the justifiability of neglect of differential overlap molecular orbital methods , 1971 .

[35]  Walter Thiel,et al.  Comparison of semiempirical MO methods for open‐shell systems , 1988 .

[36]  Caoxian Jie,et al.  Mechanism of the Cope rearrangement , 1987 .

[37]  Kendall N. Houk,et al.  Transition structures of ene reactions of ethylene and formaldehyde with propene , 1987 .

[38]  A. Sklar,et al.  Calculations of the Lower Excited Levels of Benzene , 1938 .

[39]  Aron Kuppermann,et al.  Singlet→triplet transitions in C≡N containing molecules by electron impact , 1984 .

[40]  Colin Thomson,et al.  Comparison of semiempirical MO methods applied to large molecules , 1991 .

[41]  Martin J. Field,et al.  MC−SCF study of the Diels-Alder reaction between ethylene and butadiene , 1988 .

[42]  Michael C. Zerner,et al.  Removal of core orbitals in ‘valence orbital only’ calculations , 1972 .

[43]  Karl Jug,et al.  Semiempirical Molecular Orbital Calculations and Molecular Energies. A New Formula for the β Parameter , 1973 .

[44]  J. Sunner,et al.  Hydrogen bonding of water to onium ions. Hydration of substituted pyridinium ions and related systems , 1979 .

[45]  Aron Kuppermann,et al.  Electron-impact spectroscopy of acetaldehyde , 1987 .

[46]  K. R. Roby,et al.  Fundamentals of an orthonormal basis set molecular orbital theory , 1972 .

[47]  Walter Thiel,et al.  Extension of MNDO to d Orbitals: Parameters and Results for the Halogens , 1992 .

[48]  W. J. Stevens,et al.  Effective Potentials in Molecular Quantum Chemistry , 1984 .

[49]  Walter Thiel,et al.  Analytical Second Derivatives for Effective Core Potentials , 1988 .

[50]  Walter Thiel,et al.  Correlation Effects on Semiempirical Transition States , 1986 .

[51]  Walter Thiel,et al.  Semiempirical methods: current status and perspectives , 1988 .

[52]  Henry F. Schaefer,et al.  The malonaldehyde equilibrium geometry: A major structural shift due to the effects of electron correlation , 1985 .

[53]  P. Löwdin.  On the Non‐Orthogonality Problem Connected with the Use of Atomic Wave Functions in the Theory of Molecules and Crystals , 1950 .

[54]  Michael Meot-Ner,et al.  The ionic hydrogen bond and ion solvation. 3. Bonds involving cyanides. Correlations with proton affinities , 1985 .

[55]  D. Rowley,et al.  Kinetics of diene reactions at high temperatures , 1951 .

[56]  Andrew Komornicki,et al.  Transition structures for the Claisen rearrangement , 1988 .

[57]  Karl F. Freed,et al.  Ab Initio Calculation of One‐Center Integrals of Semiempirical Theories of Valence , 1980 .

[58]  Walter Thiel,et al.  Comparison of semiempirical and ab initio transition states for organic reactions , 1985 .

[59]  D. B. Cook,et al.  Approximate ab initio calculations on polyatomic molecules , 1967 .

[60]  Eamonn F. Healy,et al.  Development and use of quantum mechanical molecular models. 76. AM1: a new general purpose quantum mechanical molecular model , 1985 .

[61]  Fernando Bernardi,et al.  An MC-SCF study of the mechanisms for 1,3-dipolar cycloadditions , 1987 .

[62]  M. Dewar,et al.  Ground States of Molecules. 38. The MNDO Method. Approximations and Parameters , 1977 .

[63]  Michael J. S. Dewar.  Applications of quantum mechanical molecular models to chemical problems. Part 70. Quantum mechanical molecular models , 1985 .

[64]  G. Klopman,et al.  A semiempirical treatment of molecular structures. II. Molecular terms and application to diatomic molecules , 1964 .

[65]  M L McKee,et al.  Concerted dihydrogen exchange between methanol and formaldehyde: a theoretical study. , 1986, Journal of the American Chemical Society.

[66]  Inga Fischer-Hjalmars,et al.  Deduction of the Zero Differential Overlap Approximation from an Orthogonal Atomic Orbital Basis , 1965 .

[67]  H. J. Bernstein,et al.  The heat of dimerization of some carboxylic acids in the vapour phase determined by a spectroscopic method , 1969 .