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Basic concepts: Molecules

Chapter 2. Basic concepts: Molecules. 2.1 Bonding models: an introduction. In a covalent species, electrons are shared between atoms. In an ionic species, one or more electrons are transferred between atoms to form ions.

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Basic concepts: Molecules

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  1. Chapter2 Basic concepts: Molecules Dr. Said M. El-Kurdi

  2. 2.1 Bonding models: an introduction In a covalent species, electrons are shared between atoms. In an ionic species, one or more electrons are transferred between atoms to form ions. Modern views of molecular structure are based on applying wave mechanics to molecules; such studies provide answers as to how and why atoms combine. The Schrödinger equation can be written to describe the behavior of electrons in molecules, but it can be solved only approximately. Dr. Said M. El-Kurdi

  3. Valence bond (VB) theory Molecular orbital (MO) theory Dr. Said M. El-Kurdi

  4. Lewis structures Localized Bonding Models Localized implies that electrons are confined to a particular bond or atom • Pairs of electrons are localized in bonds or as non-bonding “lone pairs” on atoms. Each bond is formed by a pair of electrons shared by two atoms. • Lewis structures give the connectivity of an atom in a molecule, the bond order and the number of lone pairs Dr. Said M. El-Kurdi

  5. I expect you to be able to: • Draw Lewis structures (including resonance structures when necessary). • Determine bond orders. • Determine and place formal charges. Dr. Said M. El-Kurdi

  6. 2.2 Homonuclear diatomic molecules: valence bond (VB) theory A homonuclear covalent bond is one formed between two atoms of the same element, e.g. the H  H bond in H2, the O  O bond in O2 and the O  O bond in H2O2 A homonuclear molecule contains one type of element. Homonuclear diatomic molecules include H2, N2 and F2, homonuclear triatomics include O3 (ozone) and larger homonuclear molecules are P4, S8 and C60. Dr. Said M. El-Kurdi

  7. Covalent bond distance, covalent radius and van der Waals radius The length of a covalent bond (bond distance), d, is the internuclear separation and may be determined experimentally by microwave spectroscopy or diffraction methods For an atom X, the value of the single bond covalent radius, rcov, is half of the internuclear separation in a homonuclear XX single bond. The van der Waals radius, rv, of an atom X is half of the distance of closest approach of two non-bonded atoms of X. Dr. Said M. El-Kurdi

  8. The valence bond (VB) model of bonding in H2 Dr. Said M. El-Kurdi

  9. The valence bond (VB) model of bonding in H2 Valence bond theory considers the interactions between separate atoms as they are brought together to form molecules. overall description of the covalently bonded H2 molecule; covalent is a linear combination of wavefunctions 1 and 2. The equation contains a normalization factor, N (see Box 1.4). In the general case where: Dr. Said M. El-Kurdi

  10. Another linear combination of 1 and 2 can be written as In terms of the spins of electrons 1 and 2, +corresponds to spin-pairing, and  corresponds to parallel spins (nonspin-paired). Calculations of the energies associated with these states as a function of the internuclear separation of HA and HB show that Dr. Said M. El-Kurdi

  11.  represents a repulsive state (high energy), • the energy curve for + reaches a minimum value when the internuclear separation, d, is 87 pm and this corresponds to an HH bond dissociation energy, U, of 303 kJ/mol. the experimental values of d = 74 pm and U = 458 kJ/mol Dr. Said M. El-Kurdi

  12. Improvements • allowing for the fact that each electron screens the other from the nuclei to some extent • taking into account the possibility that both electrons 1 and 2 may be associated with either HA or HB, i.e. allowing for the transfer of one electron from one nuclear centre to the other to form a pair of ions. • HA+ HB or HA  HB+ by writing two additional wavefunctions, 3 and  4 (one for each ionic form), Dr. Said M. El-Kurdi

  13. The coefficient c indicates the relative contributions made by the two sets of wavefunctions Since the wavefunctions 1 and 2 arise from an internuclear interaction involving the sharing of electrons among nuclei, and 3 and 4 arise from electron transfer. Dr. Said M. El-Kurdi

  14. Based on this model of H2, calculations with c = 0.25 give values of 75 pm for d(H–H) and 398 kJ/mol for the bond dissociation energy. resonance structure and the double-headed arrows indicate the resonance between them. resonance structures is that they do not exist as separate species. Rather, they indicate extreme bonding pictures, the combination of which gives a description of the molecule overall Dr. Said M. El-Kurdi

  15. Valence bond theory (VBT) is a localized quantum mechanical approach to describe the bonding in molecules. • VBT provides a mathematical justification for the Lewis interpretation of electron pairs making bonds between atoms. • VBT asserts that electron pairs occupy directed orbitals localized on a particular atom. • The directionality of the orbitals is determined by the geometry around the atom which is obtained from the predictions of VSEPR theory. In VBT, a bond will be formed if there is overlap of appropriate orbitals on two atoms and these orbitals are populated by a maximum of two electrons. Dr. Said M. El-Kurdi

  16.  bonds: symmetric about the internuclear axis  bonds: have a node on the inter-nuclear axis and the sign of the lobes changes across the axis.

  17. The valence bond (VB) model applied to F2, O2 and N2 F 2s 2p F 2s 2p Z axis 2pz 2pz This gives a 2p-2p  bond between the two F atoms.

  18. O 2s 2p O 2s 2p Lewis structure Valence bond theory treatment of bonding in O2 Z axis 2pz 2pz This gives a 2p-2p  bond between the two O atoms. Z axis 2py (the choice of 2py is arbitrary) 2py This gives a 2p-2p  bond between the two O atoms. In VBT,  bonds are predicted to be weaker than  bonds because there is less overlap. 8/21/2014

  19. Double bond:  bond +  bond Triple bond:  bond + 2  bond In a diamagnetic species, all electrons are spin-paired; a diamagnetic substance is repelled by a magnetic field. A paramagnetic species contains one or more unpaired electrons; a paramagnetic substance is attracted by a magnetic field. The Lewis approach and VBT predict that O2 is diamagnetic – this is wrong! 8/21/2014

  20. 2.3 Homonuclear diatomic molecules: molecular orbital (MO) theory In molecular orbital (MO) theory, we begin by placing the nuclei of a given molecule in their equilibrium positions and then calculate the molecular orbitals such interactions are: • allowed if the symmetries of the atomic orbitals are compatible with one another. • efficient if the region of overlap between the two atomic orbitals is significant. • efficient if the atomic orbitals are relatively close in energy. 8/21/2014

  21. the number of MOs that can be formed must equal the number of atomic orbitals of the constituent atoms. Molecular orbital theory applied to the bonding in H2 An approximate description of the MOs in H2 can be obtained by considering them as linear combinations of atomic orbitals (LCAOs). Mathematically, we represent the possible combinations of the two 1s atomic orbitals by equations 8/21/2014

  22. Where N and N* are the normalization factors. MO is an in-phase (bonding) interaction *MO is an out-of-phase (antibonding) interaction. S is the overlap integral. 8/21/2014

  23. overlap integral, S, is a measure of the extent to which the regions of space described by the two wavefunctions 1 and 2 coincide. we construct the orbital interaction diagram first and then put in the electrons according to the aufbau principle. 8/21/2014

  24. The ground state electronic configuration of H2 may be written using the notation g(1s)2 We cannot measure the bond order experimentally but we can make some useful correlations between bond order and the experimentally measurable bonddistances and bond dissociation energies or enthalpies. 8/21/2014

  25. Experimentally, the bond dissociation energy, U, for H2 is 458 kJ/mol and for [H2]+ is 269 kJ mol1. experimentally determined bond lengths of H2 and [H2]+ are 74 and 105 pm. 8/21/2014

  26. Schematic representations of (a) the bonding and (b) the antibonding molecular orbitals in the H2 molecule 8/21/2014

  27. The bonding in He2, Li2 and Be2 The ground state electronic configuration of He2 g(1s)2u*(1s)2 MO picture of He2 is consistent with its non-existence. The bond order is zero Orbital interaction diagrams for the formation of (a) He2 from two He atoms 8/21/2014

  28. The bonding in He2, Li2 and Be2 The ground state electronic configuration of Li2 g(1s)2u*(1s)2g(2s)2 b.o. = 1 Orbital interaction diagrams for the formation of (a) Li2 from two Li atoms 8/21/2014

  29. A basis set of orbitals is composed of those which are available for orbital interactions. extremely unstable Be2 species with bond length 245 pm and bond energy 10 kJ/mol !!! 8/21/2014

  30. The bonding in F2 and O2 8/21/2014

  31. 8/21/2014

  32. 8/21/2014

  33. ground state electronic configuration of F2 g(2s)2 u*(2s)2 g(2pz)2 u(2px)2 u(2py)2 g*(2px)2 g*(2py)2 The MO picture for F2 is consistent with its observed diamagnetism. The predicted bond order is 1 8/21/2014

  34. What happens if the sp separation is small? In crossing the period from Li to F, the energies of the 2s and 2p atomic orbitals decrease owing to the increased effective nuclear charge. 8/21/2014

  35. Orbital mixing may occur between orbitals of similar symmetry and energy, with the result that the ordering of the MOs in B2, C2 and N2 differs from that in F2 and O2. 8/21/2014

  36. – crossover that occurs between N2 and O2. 8/21/2014

  37. photoelectron spectroscopy, a technique in which electrons in different orbitals are distinguished by their ionization energies. 8/21/2014

  38. 2.4 The octet rule and isoelectronic species The octet rule: first row p-block elements An atom obeys the octet rule when it gains, loses or shares electrons to give an outer shell containing eight electrons (an octet) with a configuration ns2np6. ions such as Na+ (2s22p6), Mg2+ (2s22p6), F (2s22p6), Cl (3s23p6) and O2 (2s22p6) do in fact obey the octet rule, they typically exist in environments in which electrostatic interaction energies compensate for the energies needed to form the ions from atoms 8/21/2014

  39. In general, the octet rule is most usefully applied in covalently bonded compounds involving p-block elements. Isoelectronic species Two species are isoelectronic if they possess the same total number of electrons. 8/21/2014

  40. If two species are isostructural, they possess the same structure. 8/21/2014

  41. The octet rule: heavier p-block elements As one descends a given group in the p-block, there is a tendency towards increased coordination numbers. 8/21/2014

  42. 2.5 Electronegativity values In a homonuclear diatomic molecule X2, the electron density in the region between the nuclei is symmetrical; each X nucleus has the same effective nuclear charge. On the other hand, the disposition of electron density in the region between the two nuclei of a heteronuclear diatomic molecule XY may be asymmetrical. Pauling electronegativity values, P electronegativity ‘the power of an atom in a molecule to attract electrons to itself ’ (the electron withdrawing power of an atom) 8/21/2014

  43. Electronegativity and bond enthalpy Linus Pauling’s original formulation of electronegativity drew on concepts relating to the energetics of bond formation. For example, in the formation of AB from the diatomic A2 and B2 molecules, He argued that the excess energy, ΔD, of the A-B bond over the average energy of A-A and B-B bonds can be attributed to the presence of ionic contributions to the covalent bonding. The greater the difference in electron attracting powers (the electronegativities) of atoms X and Y, the greater the contribution made by XY (or XY), and the greater the value of D. 8/21/2014

  44. He defined the difference in electronegativity as 8/21/2014

  45. Mulliken electronegativity values, M IE1 is the first ionization energy, and EA1 the first electron affinity, Allred-Rochow electronegativity values,AR measure of electronegativity of an atom by means of the electrostatic force exerted by the effective nuclear charge Zeff (estimated from Slater’s rules) on the valence electrons. 8/21/2014

  46. 2.6 Dipole moments Polar diatomic molecules The symmetrical electron distribution in the bond of a homonuclear diatomic renders the bond non-polar In heteronuclear diatomic, the electron withdrawing powers of the two atoms may be different, and the bonding electrons are drawn closer towards the more electronegative atom. The bond is polar and possesses an electric dipole moment (). 8/21/2014

  47. The dipole moment of a diatomic XY  =q × e × d where d is the distance between the point electronic charges (i.e. the internuclear separation), e is the charge on the electron (1.602 × 1019 C) and q is point charge. SI unit of is the coulomb metre (Cm) but for convenience,  tends to be given in units of debyes (D) where 1D = 3.336×1030Cm. 8/21/2014

  48. 8/21/2014

  49. By SI convention, the arrow points from the  end of the bond to the + end, which is contrary to long-established chemical practice. Molecular dipole moments Polarity is a molecular property. For polyatomic species, the net molecular dipole moment depends upon the magnitudes and relative directions of all the bond dipole moments in the molecule. In addition, lone pairs of electrons may contribute significantly to the overall value of . 8/21/2014

  50. polar CF4 is non-polar The molecules NH3 and NF3 have trigonal pyramidal structures , and have dipole moments of 1.47 and 0.24D respectively. 8/21/2014

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