AB Initio Molecular Orbital Calculations of Bond Index and Valency

Publisher Summary This chapter reviews the applications of the quantitative definitions of bond index and valency for single determinant self-consistent-field (SCF) wavefunctions. A statistical interpretation of bond index is also presented. The chapter discusses the definitions of bond index and valency for correlated wavefunctions. Later, the results corresponding to SCF and correlated wavefunctions are discussed. The results of the calculations reviewed indicate that at the ground state equilibrium geometry of a molecule the SCF wavefunction is adequate for the study of its nature of bonding on the basis of bond indices and valencies. The latter quantities are sensitive to basis sets and the population analysis schemes. Generally basis sets of double-zeta quality augmented with a set of polarization and a set of diffuse functions (only in the case of highly ionic and/or negatively charged species) on highly electronegative centers should be employed in these calculations. Of the two schemes of population analysis—Mulliken's population analysis (MPA) and Lowdin population analysis (LPA) that are currently in use, the MPA generally gives a more consistent picture of bonding.

[1]  S. Bhattacharyya,et al.  The behavior of quantum chemical bond order in the vicinity of a saddle point on the reaction path , 1990 .

[2]  J. Yadav,et al.  Bond orders, valence indices and oxidation numbers of some isomeric chlorobenzenes , 1987 .

[3]  P. Pitanga,et al.  Direct consequences of the bond index statistical interpretation , 1986 .

[4]  Ralph E. Christoffersen,et al.  Electron population analysis. Gross atomic charges in molecules , 1971 .

[5]  M. Natiello,et al.  On the quantum theory of valence and bonding from the ab intio standpoint , 1984 .

[6]  H. Freund,et al.  Analysis of Bonding Properties in Molecular Ground and Excited States by a Cohen-Type Bond Order , 1983 .

[7]  P. Siddarth,et al.  Molecular strain from valency , 1986 .

[8]  P. Pitanga,et al.  Reply to “comment on direct consequences of the bond index statistical interpretation” , 1987 .

[9]  István Mayer,et al.  Charge, bond order and valence in the AB initio SCF theory , 1983 .

[10]  Robert G. Parr,et al.  A Semi‐Empirical Theory of the Electronic Spectra and Electronic Structure of Complex Unsaturated Molecules. II , 1953 .

[11]  W. Lipscomb,et al.  Self‐consistent‐field wavefunctions for complex molecules. The approximation of partial retention of diatomic differential overlap , 1973 .

[12]  M. Gopinathan,et al.  A concept of charge and valence for ab initio wave functions , 1989 .

[13]  C. Trindle.  Bond index description of delocalization , 1969 .

[14]  M. Gopinathan.  Determination of atomic hybridization in molecular orbital theory: A valency method , 1988 .

[15]  J. Williams,et al.  Preparation of m-Divinylbenzene1 , 1947 .

[16]  F. Hund.  Zur Deutung der Molekelspektren. IV , 1927 .

[17]  I. Mayer,et al.  Bond orders and valences in some simple sulphur compounds , 1983 .

[18]  Karl Jug,et al.  SINDO1. A semiempirical SCF MO method for molecular binding energy and geometry I. Approximations and parametrization , 1980 .

[19]  P Pieter Ros,et al.  Molecular Orbital Calculations on Copper Chloride Complexes , 1966 .

[20]  K. Jug.  A maximum bond order principle , 1977 .

[21]  I. Mayer.  On bond orders and valences in the Ab initio quantum chemical theory , 1986 .

[22]  Jacopo Tomasi,et al.  Electronic Molecular Structure, Reactivity and Intermolecular Forces: An Euristic Interpretation by Means of Electrostatic Molecular Potentials , 1978 .

[23]  P. Schleyer,et al.  Chemical bonding in hypervalent molecules. The dominance of ionic bonding and negative hyperconjugation over d-orbital participation , 1990 .

[24]  R. Bader,et al.  Spatial localization of the electronic pair and number distributions in molecules , 1975 .

[25]  Keith R. Roby,et al.  Quantum theory of chemical valence concepts , 1974 .

[26]  P. Siddarth,et al.  Dependence of valency on geometry for configuration interaction wave functions , 1990 .

[27]  R. Lavery,et al.  The calculation of molecular electrostatic potential from a multipole expansion based on localized orbitals and developed at their centroids: Accuracy and applicability for macromolecular computations , 1982 .

[28]  Á. Somogyi,et al.  Does a bond exist between the two silicons in cyclodisiloxane , 1990 .

[29]  J. B. Collins,et al.  Integrated spatial electron populations in molecules: Application to simple molecules , 1980 .

[30]  P. Politzer,et al.  An investigation of definitions of the charge on an atom in a molecule , 1968 .

[31]  Robert S. Mulliken,et al.  The Assignment of Quantum Numbers for Electrons in Molecules. I , 1928 .

[32]  T. Kar,et al.  Molecular orbital calculations of valency within the framework of a general non-singular transformation of the atomic orbital basis sets , 1990 .

[33]  H. Villar,et al.  On the density matrix definition of valency , 1986 .

[34]  V. Fock,et al.  Näherungsmethode zur Lösung des quantenmechanischen Mehrkörperproblems , 1930 .

[35]  J. Pires,et al.  Mollesse d'un atome dans une molecule et definition de la mollesse d'un groupement fonctionnel: Une echelle LCAO , 1988 .

[36]  Michel Dupuis,et al.  Bond orders and valencies from ab initio wavefunctions: application to prototypical molecules and to the characterization of solitons in polyenes , 1987 .

[37]  Jon Baker,et al.  Classical chemical concepts from ab initio SCF calculations , 1985 .

[38]  J. Yadav,et al.  MNDO Evaluation of bond orders in some fluorobenzenes , 1987 .

[39]  R. Maclagan,et al.  A new approach to the definition of the effective atomic-charge calculated from molecular wavefunctions , 1971 .

[40]  Peter A. Kollman,et al.  A method of describing the charge distribution in simple molecules , 1978 .

[41]  K. Jug.  A valence criterion for diradicals and zwitterions , 1985 .

[42]  N. D. Epiotis,et al.  Valence and molecular structure , 1986 .

[43]  I. Cohen.  Bond Order in LCAO Molecular Orbital Theory , 1972 .

[44]  J. Ángyán,et al.  The use of theoretical indices for the characterization of SO linkage multiplicity , 1988 .

[45]  R. S. Mulliken.  Electronic Population Analysis on LCAO–MO Molecular Wave Functions. I , 1955 .

[46]  T. Kar,et al.  Ab initio investigation of the nature of bonding in LiX dimers with first row substituents , 1988 .

[47]  I. Mayer.  Bond orders and valences in the SCF theory: a comment , 1985 .

[48]  Clemens C. J. Roothaan,et al.  New Developments in Molecular Orbital Theory , 1951 .

[49]  K. Roby.  Quantum theory of chemical valence concepts: II. Hybrid atomic orbitals and localized molecular orbitals studied by projection operator techniques , 1974 .

[50]  M. Gopinathan,et al.  Valency changes in chemical reactions , 1985 .

[51]  T. Kar,et al.  Comparison of atomic charges, valencies and bond orders in some hydrogen-bonded complexes calculated from Mulliken and Löwdin SCF density matrices , 1987 .

[52]  Harold S. Johnston,et al.  Activation Energies from Bond Energies. I. Hydrogen Transfer Reactions , 1963 .

[53]  N. Kestner.  He–He Interaction in the SCF–MO Approximation , 1968 .

[54]  J. Lennard-jones,et al.  The electronic structure of some diatomic molecules , 1929 .

[55]  K. Jug.  Bond order orbitals and eigenvalues , 1978 .

[56]  R. K. Nesbet,et al.  Self‐Consistent Orbitals for Radicals , 1954 .

[57]  Bond order and valence: Analogy between the mayer and the eigenvalue treatments , 1988 .

[58]  P. Mishra,et al.  Bond order-bond length relationship in all-valence-electron molecular orbital theory , 1972 .

[59]  Robert Rein,et al.  On Physical Properties and Interactions of Polyatomic Molecules: With Application to Molecular Recognition in Biology , 1973 .

[60]  K. Jug.  Continuity of bond order , 1979 .

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

[62]  Erich Hckel,et al.  Quanstentheoretische Beitrge zum Benzolproblem: II. Quantentheorie der induzierten Polaritten , 1931 .

[63]  István Mayer,et al.  Comments on the quantum theory of valence and bonding: Choosing between alternative definitions , 1984 .

[64]  W. Lipscomb,et al.  Approximations to self-consistent field molecular wavefunctions. , 1972, Proceedings of the National Academy of Sciences of the United States of America.

[65]  J. Ángyán,et al.  Bonding between nonbonded sulfur and oxygen atoms in selected organic molecules (a quantum chemical study) , 1987 .

[66]  K. Jug,et al.  Valence partitioning for diradicals and zwitterions , 1990 .

[67]  Similarity transformation of the ab initio density matrix , 1986 .

[68]  E. Hückel,et al.  Quantentheoretische Beiträge zum Problem der aromatischen und ungesättigten Verbindungen. III , 1932 .

[69]  R. Bader,et al.  Theoretical development of a virial relationship for spatially defined fragments of molecular systems , 1973 .

[70]  F. E. Jorge,et al.  Bond index: relation to second-order density matrix and charge fluctuations , 1985 .

[71]  J. Yadav,et al.  Acetaldehyde photochemistry: Testing the additivity assumption and polarized basis set effects , 1986 .

[72]  P. Siddarth,et al.  Valency and molecular structure , 1986 .

[73]  S. F. Boys,et al.  The calculation of small molecular interactions by the differences of separate total energies. Some procedures with reduced errors , 1970 .

[74]  K. Jug,et al.  Comparative studies on the reactivity of molecules by atomic valences , 1985 .

[75]  J. J. Esperilla,et al.  About the overestimation of the basis set superposition error on interaction energy calculations for van der Waals systems , 1986 .

[76]  R. S. Mulliken.  Electronic Structures of Molecules XI. Electroaffinity, Molecular Orbitals and Dipole Moments , 1935 .

[77]  P. Mishra,et al.  CNDO-CI study of electronic structure and molecular geometry in ground and excited states , 1973 .

[78]  I. Mayer.  Bond orders in three-centre bonds: an analytical investigation into the electronic structure of diborane and the three-centre four-electron bonds of hypervalent sulphur , 1989 .

[79]  István Mayer,et al.  Bond orders and valences from ab initio wave functions , 1986 .

[80]  C. C. J. Roothaan,et al.  Self-Consistent Field Theory for Open Shells of Electronic Systems , 1960 .

[81]  T. Kar,et al.  Effect of a general nonsingular transformation of the AO basis set on MO calculations of valency , 1989 .

[82]  P. Pitanga,et al.  Remarks about the definition of a bond index , 1986 .

[83]  George S. Hammond,et al.  A Correlation of Reaction Rates , 1955 .

[84]  L. Raff,et al.  Semiclassical wave packet studies of elastic and inelastic atom–surface scattering from a 3D model surface , 1985 .

[85]  I. Mayer.  Bond orders and valences: Role of d-orbitals for hypervalent sulphur , 1987 .

[86]  P. Surján,et al.  Energy, geometry and valence: The influence of sulfur d-orbital exponent , 1988 .

[87]  D. Hartree.  The Wave Mechanics of an Atom with a Non-Coulomb Central Field. Part I. Theory and Methods , 1928, Mathematical Proceedings of the Cambridge Philosophical Society.

[88]  Tapas Kar,et al.  Three-center bond index , 1990 .

[89]  István Mayer,et al.  Towards a “Chemical” Hamiltonian , 1983 .

[90]  Robert S. Mulliken,et al.  Electronic Structures and Spectra of Triatomic Oxide Molecules , 1942 .

[91]  J. Polanyi,et al.  Distribution of reaction products (theory). VIII. Cl+HI, Cl+DI , 1973 .

[92]  O. Sǐnanoğlu,et al.  Local orbital and bond index characterization of hybridization , 1969 .

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

[94]  J. Pople,et al.  Electron interaction in unsaturated hydrocarbons , 1953 .

[95]  G. Lendvay.  Bond orders from ab initio calculations and a test of the principle of bond order conservation , 1989 .

[96]  G. G. Hall,et al.  Optimal population analysis , 1987 .

[97]  R. S. Mulliken.  Electronic States and Band Spectrum Structure in Diatomic Molecules. VII. 2 P--> 2 S and 2 S--> 2 P Transitions , 1928 .

[98]  Robert S. Mulliken,et al.  Electronic Population Analysis on LCAO–MO Molecular Wave Functions. II. Overlap Populations, Bond Orders, and Covalent Bond Energies , 1955 .

[99]  Kenneth B. Wiberg,et al.  Application of the pople-santry-segal CNDO method to the cyclopropylcarbinyl and cyclobutyl cation and to bicyclobutane , 1968 .

[100]  F. Weinhold,et al.  Natural population analysis , 1985 .

[101]  T. Kar,et al.  Effect of basis set on Mulliken and Löwdin atomic charges, bond orders and valencies of some polar molecules , 1988 .

[102]  R. Bader,et al.  Partitioning and characterization of molecular charge distributions , 1971 .

[103]  R. Parr,et al.  Absolute hardness: companion parameter to absolute electronegativity , 1983 .

[104]  M. Gopinathan,et al.  Valency. II. Applications to molecules with first-row atoms , 1983 .

[105]  István Mayer,et al.  Bond order and valence: Relations to Mulliken's population analysis , 1984 .

[106]  K. Jug.  A unified treatment of valence and bond order from density operators , 1984 .

[107]  R. Bochicchio,et al.  On the theory of valence and bonding: a further generalization , 1986 .

[108]  J. Pople.  The Electronic Structure and Polarity of the Water Molecule , 1953 .

[109]  Frank Weinhold,et al.  Natural hybrid orbitals , 1980 .

[110]  A. Balaban,et al.  Ab initio study of neutral O2, SO, S2, C2H2 and their mono- and dications , 1989 .

[111]  T. Kar,et al.  Ab initio SCF study of the ground state electronic structure of SN2+2, SN2, SN2−2, S2N+ and S2N− , 1990 .

[112]  I. H. Hillier,et al.  On partitioning the overlap charge density in self-consistent charge molecular-orbital calculations , 1969 .

[113]  M. Gopinathan,et al.  Valency. I. A quantum chemical definition and properties , 1983 .

[114]  H. F. King,et al.  Fitting atomic scattering factors to molecular charge distributions , 1976 .

[115]  Joseph G. Hoffman,et al.  Quantum Theory of Atoms, Molecules and the Solid State: A Tribute to John C. Slater , 1967 .

[116]  Donald G. Truhlar,et al.  Systematic study of basis set superposition errors in the calculated interaction energy of two HF molecules , 1985 .

[117]  F. E. Jorge,et al.  Comment on“direct consequences of the bond index statistical interpretation” , 1987 .

[118]  Karl Jug,et al.  Theoretical basis and design of the PPP model Hamiltonian , 1990 .

[119]  R. Bader,et al.  Virial Field Relationship for Molecular Charge Distributions and the Spatial Partitioning of Molecular Properties , 1972 .

[120]  M. Natiello,et al.  A generalized formalism of the quantum theory of valence and bonding , 1985 .

[121]  G. G. Hall.  Atomic Charges Within Molecules , 1985 .

[122]  T. Kar,et al.  Effect of basis-set superposition on the atomic charges and valencies in hydrogen- and lithium-bonded complexes , 1990 .

[123]  F. A. Rushworth.  NUCLEAR MAGNETIC RESONANCE ABSORPTION IN ANTHRACENE , 1952 .

[124]  Linus Pauling,et al.  Atomic Radii and Interatomic Distances in Metals , 1947 .

[125]  Per-Olov Löwdin,et al.  Approximate Formulas for Many‐Center Integrals in the Theory of Molecules and Crystals , 1953 .

[126]  R. Bochicchio,et al.  The UHF extension of the quantum theory of valence and bonding , 1989 .