《有机化学》课程教学资源（参考书籍）The Vocabulary and Concepts of Organic Chemistry, 2nd Ed 2005, Milton Orchin, Roger S. Macomber, Allan R. Pinhas, R. Marshall Wilson

Atomic Orbital Theory 1.1 Photon (Quantum) 、 1.2 Bohr or Planck-Einstein Equation Planck's Constant h 4 Heisenberg Uncertainty Principle Wave(Quantum)Mechanics 16 Standing (or Stationary)Waves Nodal Points(Planes) Wavelength入 11 en 66 (or s 115 p 7 1.15 Orbital (Atomic Orbital) 116 Wave Function 1.17 Wave Equation in One Dimension 1.18 Wave Equation in Three Dimensions 9 1.19 Laplacian Operator 9 1.20 Probability Interpretation of the wave Function 9 12 Schrodinger Equation 22 Eigenfunction dinger Equation for the Hydrogen Atom 12 entum)Quantum NumberI 135 Number m 1 111222 120 antum Number m 120 131 1s Orhital 1212 1.32 2s Orbital 133 n Orhitals 134 Nodal Plane or Surface 1.35 2p Orbitals 1.36 d Orbitals 1.37 fOrbitals 1.38 Atomic Orbitals for Many-Electron Atoms and Co Second Edirion.by Milton Orchin Roger S.Mac r.A and R.Marshall Wilson iley&Sons,Inc

1 Atomic Orbital Theory 1.1 Photon (Quantum) 3 1.2 Bohr or Planck–Einstein Equation 3 1.3 Planck’s Constant h 3 1.4 Heisenberg Uncertainty Principle 3 1.5 Wave (Quantum) Mechanics 4 1.6 Standing (or Stationary) Waves 4 1.7 Nodal Points (Planes) 5 1.8 Wavelength λ 5 1.9 Frequency ν 5 1.10 Fundamental Wave (or First Harmonic) 6 1.11 First Overtone (or Second Harmonic) 6 1.12 Momentum (P) 6 1.13 Duality of Electron Behavior 7 1.14 de Broglie Relationship 7 1.15 Orbital (Atomic Orbital) 7 1.16 Wave Function 8 1.17 Wave Equation in One Dimension 9 1.18 Wave Equation in Three Dimensions 9 1.19 Laplacian Operator 9 1.20 Probability Interpretation of the Wave Function 9 1.21 Schrödinger Equation 10 1.22 Eigenfunction 10 1.23 Eigenvalues 11 1.24 The Schrödinger Equation for the Hydrogen Atom 11 1.25 Principal Quantum Number n 11 1.26 Azimuthal (Angular Momentum) Quantum Number l 11 1.27 Magnetic Quantum Number ml 12 1.28 Degenerate Orbitals 12 1.29 Electron Spin Quantum Number ms 12 1.30 s Orbitals 12 1.31 1s Orbital 12 1.32 2s Orbital 13 1.33 p Orbitals 14 1.34 Nodal Plane or Surface 14 1.35 2p Orbitals 15 1.36 d Orbitals 16 1.37 f Orbitals 16 1.38 Atomic Orbitals for Many-Electron Atoms 17 The Vocabulary and Concepts of Organic Chemistry, Second Edition, by Milton Orchin, Roger S. Macomber, Allan Pinhas, and R. Marshall Wilson Copyright © 2005 John Wiley & Sons, Inc. 1 c01.qxd 5/17/2005 5:12 PM Page 1

2 ATOMIC ORBITAL THEORY 1.39 Pauli Exclusion Principle Hund's Rule Building Up)Principle 143 145 146 Atomic Co re(or Kemel) 1.47 Hybridization of Atomic Orbitals 778891223 1 48 Hybridization Index 1.49 Equivalent Hybrid Atomic Orbitals 1.50 Nonequivalent Hybrid Atomic Orbitals 23 The detailed study of the structure of atoms (as distinguished from molecules)is largely the domain of the physicist.With respect to atomic structure,the interest of the chemist is usually confined to the behavior and properties of the three funda- mental particles of atoms,namely the electron,the proton,and the neutron.In the model of the atom postulated by Niels Bohr(1885-1962),electrons surrounding the et The clectrons move in these orbits much mic emission that the ng ato spectra of the hydrog en atom ectron in different as quann d tha is,the ene d not I eas in a instead had nner as th v larg r,bu describe the behavior of small particles such as electrons proved unsatisfactory,par- ticularly because this model did not take into account the uncertainty principle. When it was demonstrated that the motion of electrons had properties of waves as well as of particles,the so-called dual nature of electronic behavior,the classical mechanical approach was replaced by the newer theory of quantum mechanics According t quantum mechanical theory the behavior of elect ons is described by denoted by k le er .The phys Ψr es in ct that its square multiplied by the siz a volume element,d gives the probability of finding the electron in a partic lar elemen or space surounc ing the nucleus of the atom.Thus.the Bohr model of the atom.which placed the eled tron in a fixed orbit around the nucleus,was replaced by the quantum mechanical model that defines a region in space surrounding the nucleus(an atomic orbital rather than an orbit)where the probability of finding the electron is high.It is,of course,the electrons in these orbitals that usually determine the chemical behavior of the atoms and so knowledge of the positions ande ies of the electrons is of great imp rtance Thec relation of the sof atoms ato ic structure expre ed in the aw and the e was a milestone in the c velopment of che enc Although most of organic chemistry deals with molecular orbitals rather than with isolated atomic orbitals,it is prudent to understand the concepts involved in atomic orbital theory and the electronic structure of atoms before moving on to

1.39 Pauli Exclusion Principle 17 1.40 Hund’s Rule 17 1.41 Aufbau (Ger. Building Up) Principle 17 1.42 Electronic Configuration 18 1.43 Shell Designation 18 1.44 The Periodic Table 19 1.45 Valence Orbitals 21 1.46 Atomic Core (or Kernel) 22 1.47 Hybridization of Atomic Orbitals 22 1.48 Hybridization Index 23 1.49 Equivalent Hybrid Atomic Orbitals 23 1.50 Nonequivalent Hybrid Atomic Orbitals 23 The detailed study of the structure of atoms (as distinguished from molecules) is largely the domain of the physicist. With respect to atomic structure, the interest of the chemist is usually confined to the behavior and properties of the three funda￾mental particles of atoms, namely the electron, the proton, and the neutron. In the model of the atom postulated by Niels Bohr (1885–1962), electrons surrounding the nucleus are placed in circular orbits. The electrons move in these orbits much as planets orbit the sun. In rationalizing atomic emission spectra of the hydrogen atom, Bohr assumed that the energy of the electron in different orbits was quantized, that is, the energy did not increase in a continuous manner as the orbits grew larger, but instead had discrete values for each orbit. Bohr’s use of classical mechanics to describe the behavior of small particles such as electrons proved unsatisfactory, par￾ticularly because this model did not take into account the uncertainty principle. When it was demonstrated that the motion of electrons had properties of waves as well as of particles, the so-called dual nature of electronic behavior, the classical mechanical approach was replaced by the newer theory of quantum mechanics. According to quantum mechanical theory the behavior of electrons is described by wave functions, commonly denoted by the Greek letter ψ. The physical significance of ψ resides in the fact that its square multiplied by the size of a volume element, ψ2 dτ, gives the probability of finding the electron in a particular element of space surround￾ing the nucleus of the atom. Thus, the Bohr model of the atom, which placed the elec￾tron in a fixed orbit around the nucleus, was replaced by the quantum mechanical model that defines a region in space surrounding the nucleus (an atomic orbital rather than an orbit) where the probability of finding the electron is high. It is, of course, the electrons in these orbitals that usually determine the chemical behavior of the atoms and so knowledge of the positions and energies of the electrons is of great importance. The cor￾relation of the properties of atoms with their atomic structure expressed in the periodic law and the Periodic Table was a milestone in the development of chemical science. Although most of organic chemistry deals with molecular orbitals rather than with isolated atomic orbitals, it is prudent to understand the concepts involved in atomic orbital theory and the electronic structure of atoms before moving on to 2 ATOMIC ORBITAL THEORY c01.qxd 5/17/2005 5:12 PM Page 2

HEISENBERG UNCERTAINTY PRINCIPLE 3 consider the behavior of shared between atoms and the conepts of molecular orbital theory. 1.1 PHOTON (QUANTUM) The most elemental unit or particle of electromagnetic radiation.Associated with each photon is a discrete quantity or quantum of energy. 1.2 BOHR OR PLANCK-EINSTEIN EQUATION E=hv=hch. (1.2) This fundamental equation relates the energy of a photon E to its frequency v(see Sect.1.9)or wavelength(see Sect.1.8).Bohr's model of the atom postulated that the electrons of an atom moved about its nucleus in circular orbits or as later sug gested by Amold Su merfeld (1868-1951).in elliptical orbits each with a certair allowed" energy.When subjected to appropriate electr gnetic radiation the electron may absorb energy,resulting in its promotion (excitation)from one orbit to a higher (energy)orbit.The frequency of the photon absorbed must correspond to the energy difference between the orbits,that is,AE=hv.Because Bohr's postulates were based in part on the work of Max Planck(1858-1947)and Albert Einstein (1879-1955),the Bohr equation is alternately called the Planck-Einstein equation. 1.3 PLANCK'S CONSTANT The proportionality constant h=6.6256x 10-27erg seconds (6.6256 10-Js). which relates the energy of a photon E to its frequency v(see Sect.1.9)in the Bohr or Planck-Einstein equation.In order to simplify some equations involving Planck's constant h,a modified constant called h,where h=h/2,is frequently used. 1.4 HEISENBERG UNCERTAINTY PRINCIPLE This principle as formu ted by Werer Heisenberg (1901-1976),states that the properties of small particles(electrons,protons,etc.)cannot be known precisely at any particular instant of time.Thus,for example,both the exact momentum p and the exact position x of an electron cannot both be measured simultaneously.The product of the uncertainties of these two properties of a particle must be on the order of Planck's constant:Ap-Ar=h/2r,where Ap is the uncertainty in the momentum Ax the uncertainty in the position,and h Planck's constant. to the ur rt periods of m&,,A上ay生hwhe定the ein the eery of the ee

consider the behavior of electrons shared between atoms and the concepts of molecular orbital theory. 1.1 PHOTON (QUANTUM) The most elemental unit or particle of electromagnetic radiation. Associated with each photon is a discrete quantity or quantum of energy. 1.2 BOHR OR PLANCK–EINSTEIN EQUATION E
hν
hc/λ (1.2) This fundamental equation relates the energy of a photon E to its frequency ν (see Sect. 1.9) or wavelength λ (see Sect. 1.8). Bohr’s model of the atom postulated that the electrons of an atom moved about its nucleus in circular orbits, or as later sug￾gested by Arnold Summerfeld (1868–1951), in elliptical orbits, each with a certain “allowed” energy. When subjected to appropriate electromagnetic radiation, the electron may absorb energy, resulting in its promotion (excitation) from one orbit to a higher (energy) orbit. The frequency of the photon absorbed must correspond to the energy difference between the orbits, that is, ∆E
hν. Because Bohr’s postulates were based in part on the work of Max Planck (1858–1947) and Albert Einstein (1879–1955), the Bohr equation is alternately called the Planck–Einstein equation. 1.3 PLANCK’S CONSTANT h The proportionality constant h
6.6256 1027 erg seconds (6.6256 1034 J s), which relates the energy of a photon E to its frequency ν (see Sect. 1.9) in the Bohr or Planck–Einstein equation. In order to simplify some equations involving Planck’s constant h, a modified constant called h – , where h –
h/2π, is frequently used. 1.4 HEISENBERG UNCERTAINTY PRINCIPLE This principle as formulated by Werner Heisenberg (1901–1976), states that the properties of small particles (electrons, protons, etc.) cannot be known precisely at any particular instant of time. Thus, for example, both the exact momentum p and the exact position x of an electron cannot both be measured simultaneously. The product of the uncertainties of these two properties of a particle must be on the order of Planck’s constant: ∆p.∆x
h/2π, where ∆p is the uncertainty in the momentum, ∆x the uncertainty in the position, and h Planck’s constant. A corollary to the uncertainty principle is its application to very short periods of time. Thus, ∆E.∆t
h/2π, where ∆E is the uncertainty in the energy of the electron HEISENBERG UNCERTAINTY PRINCIPLE 3 c01.qxd 5/17/2005 5:12 PM Page 3

4 ATOMIC ORBITAL THEORY and At the uncertainty in the time that the electron spends in a particular energy state. Accordingly,if At is very small,the electron may have a wide range of energies.The uncertainty principle addresses the fact that the very act of performing a measurement of the properties of small particles perturbs the system.The uncertainty principle is at the heart of quantum mechanics;it tells us that the position of an electron is best essed in t ms of the probabiliry of finding it in a particular space,and .eliminates conceptfe-defmed trajectory or orbit forecle the 1.5 WAVE (QUANTUM)MECHANICS The mathematical description of very small particles such as electrons in terms of their wave functions(see Sect.1.15).The use of wave mechanics for the description of electrons follows from the experimental observation that electrons have both character results in a probability interpreta 1.6 STANDING (OR STATIONARY)WAVES The type of wave generated,for example,by plucking a string or wire stretched between two fixed points.If the string is oriented horizontally,say,along the x-axis,the waves moving toward the right fixed point will encounter the reflected waves moving in the opposite ion.If the forw d wave d the reflected w e have the ame amp at each point along the string.there will be a number of points along the string that wil have no motion.These points,in addition to the fixed anchors at the ends,correspond to nodes where the amplitude is zero.Half-way between the nodes there will be points where the amplitude of the wave will be maximum.The variations of amplitude are thus a function of the distance along x.After the plucking.the resultant vibrating string will e the m or e ne。neo Example.See Fig.1.6 amplitude nodal points Figure 1.6.A standing wave;the two curves represent the time-dependent motion of a string vibrating in the third harmonic or second overtone with four nodes

and ∆t the uncertainty in the time that the electron spends in a particular energy state. Accordingly, if ∆t is very small, the electron may have a wide range of energies. The uncertainty principle addresses the fact that the very act of performing a measurement of the properties of small particles perturbs the system. The uncertainty principle is at the heart of quantum mechanics; it tells us that the position of an electron is best expressed in terms of the probability of finding it in a particular region in space, and thus, eliminates the concept of a well-defined trajectory or orbit for the electron. 1.5 WAVE (QUANTUM) MECHANICS The mathematical description of very small particles such as electrons in terms of their wave functions (see Sect. 1.15). The use of wave mechanics for the description of electrons follows from the experimental observation that electrons have both wave as well as particle properties. The wave character results in a probability interpreta￾tion of electronic behavior (see Sect. 1.20). 1.6 STANDING (OR STATIONARY) WAVES The type of wave generated, for example, by plucking a string or wire stretched between two fixed points. If the string is oriented horizontally, say, along the x-axis, the waves moving toward the right fixed point will encounter the reflected waves moving in the opposite direction. If the forward wave and the reflected wave have the same amplitude at each point along the string, there will be a number of points along the string that will have no motion. These points, in addition to the fixed anchors at the ends, correspond to nodes where the amplitude is zero. Half-way between the nodes there will be points where the amplitude of the wave will be maximum. The variations of amplitude are thus a function of the distance along x. After the plucking, the resultant vibrating string will appear to be oscillating up and down between the fixed nodes, but there will be no motion along the length of the string—hence, the name standing or stationary wave. Example. See Fig. 1.6. 4 ATOMIC ORBITAL THEORY nodal points + − + − amplitude Figure 1.6. A standing wave; the two curves represent the time-dependent motion of a string vibrating in the third harmonic or second overtone with four nodes. c01.qxd 5/17/2005 5:12 PM Page 4

FREQUENCY 5 1.7 NODAL POINTS (PLANES) The positions or points on a standing wave where the amplitude of the wave is zero (Fig.1.6).In the description of orbitals,the node represent a point or plane where a change of sign occurs. 1.8 WAVELENGTH The minimum distance between nearest-neighbor peaks,troughs,nodes or equiva- lent points of the wave. Example..The values of入，as shown in Fig.l.8. 321 : 12 Figure 1.8.Determination of the wavelength of a wave. 1.9 FREQUENCYV The number of wavelengths(or cycles)in a light wave that pass a particular point pe unit time.Time is usually sured in seconds;hence,the fre s-1.The uni 、of fre al to uency,eq cycles pe ond.is called the He z(HZ) to wavelength:the proportionality factor is the

1.7 NODAL POINTS (PLANES) The positions or points on a standing wave where the amplitude of the wave is zero (Fig. 1.6). In the description of orbitals, the node represent a point or plane where a change of sign occurs. 1.8 WAVELENGTH λ The minimum distance between nearest-neighbor peaks, troughs, nodes or equiva￾lent points of the wave. Example. The values of λ, as shown in Fig. 1.8. 1.9 FREQUENCY ν The number of wavelengths (or cycles) in a light wave that pass a particular point per unit time. Time is usually measured in seconds; hence, the frequency is expressed in s1 . The unit of frequency, equal to cycles per second, is called the Hertz (Hz). Frequency is inversely proportional to wavelength; the proportionality factor is the speed of light c (3 1010 cm s1 ). Hence, ν
c/λ. Example. For light with λ equal to 300 nm (300 107 cm), the frequency ν
(3 1010 cm s1 )/(300 107 cm)
1 1015 s1 . FREQUENCY ν 5 λ λ 3/2 λ 1/2 λ Figure 1.8. Determination of the wavelength λ of a wave. c01.qxd 5/17/2005 5:12 PM Page 5