This is a new undergraduate textbook on physical chemistry by Horia Metiu published as four separate paperback volumes. These four volumes on physical chemistry combine a clear and thorough presentation of the theoretical and mathematical aspects of the subject with examples and applications drawn from current industrial and academic research. By using the computer to solve problems that include actual experimental data, the author is able to cover the subject matter at a practical level. The books closely integrate the theoretical chemistry being taught with industrial and laboratory practice. This approach enables the student to compare theoretical projections with experimental results, thereby providing a realistic grounding for future practicing chemists and engineers. Each volume of Physical Chemistry includes Mathematica(R) and Mathcad(R) Workbooks on CD-ROM.
Metiu's four separate volumes-Thermodynamics, Statistical Mechanics, Kinetics, and Quantum Mechanics-offer built-in flexibility by allowing the subject to be covered in any order.
These textbooks can be used to teach physical chemistry without a computer, but the experience is enriched substantially for those students who do learn how to read and write Mathematica(R) or Mathcad(R) programs. A TI-89 scientific calculator can be used to solve most of the exercises and problems.
(R) Mathematica is a registered trademark of Wolfram Research, Inc.
(R) Mathcad is a registered trademark of Mathsoft Engineering & Education, Inc.
Horia Metiu has created a significant set of volumes on undergraduate physical chemistry. The integration of Mathematica and Mathcad workbooks into the four texts provides instructors with an attractive new option in teaching. Metiua's writing style is folksy and the graphics minimal, a refreshing approach|.Taken as a whole, the four volumes on physical chemistry by Metiu are impressive, particularly Thermodynamics and Quantum Mechanics|.Without a doubt, the four textbooks provide essential materials of great utility to physical chemistry instructors. The bottom line is that the set of four volumes is a must have-a keeper- as a novel resource or invaluable classroom tool.
Journal of Chemical Education
February 2008, Vol. 85, No. 2, p. 206
Preface | p. xxi |
How to use the workbooks, exercises, and problems | p. xxvii |
Why quantum mechanics? | p. 1 |
Molecular vibrations | p. 1 |
Radiation by a hot body | p. 2 |
The stability of atoms | p. 3 |
Dynamic variables and operators | p. 5 |
Operators: the definition | p. 5 |
Examples of operators | p. 6 |
Operations with operators | p. 7 |
Operator addition | p. 7 |
Operator multiplication | p. 8 |
Powers of operators | p. 9 |
The commutator of two operators | p. 9 |
Linear operators | p. 11 |
Dynamical variables as operators | p. 11 |
Position and potential energy operators | p. 12 |
Potential energy operator | p. 13 |
The momentum operator | p. 14 |
The kinetic energy operator | p. 14 |
The total energy (the Hamiltonian) | p. 16 |
Angular momentum | p. 17 |
Review of complex numbers | p. 21 |
Complex functions of real variables | p. 24 |
The eigenvalue problem | p. 25 |
The eigenvalue problem: definition and examples | p. 25 |
The eigenvalue problem for p[subscript x] | p. 26 |
p[subscript x] has an infinite number of eigenvalues | p. 26 |
The eigenvalue problem for angular momentum | p. 27 |
If two operators commute, they have the same eigenfunctions | p. 29 |
Degenerate eigenvalues | p. 30 |
Which eigenfunctions have a meaning in physics? | p. 32 |
Not all eigenfunctions are physically meaningful | p. 32 |
Normalization | p. 32 |
A relaxed condition | p. 33 |
An example: the eigenfunctions of kinetic energy | p. 34 |
One-dimensional motion in the force-free, unbounded space | p. 34 |
The eigenfunctions of the kinetic energy operator | p. 35 |
Which of these eigenfunctions can be normalized? | p. 37 |
Boundary conditions: the particle in a box | p. 38 |
Forcing the eigenfunctions to satisfy the boundary conditions | p. 38 |
Quantization | p. 40 |
The particle cannot have zero kinetic energy | p. 40 |
Imposing the boundary conditions removes the trouble with normalization | p. 42 |
Some properties of eigenvalues and eigenfunctions | p. 42 |
What do we measure when we study quantum systems? | p. 45 |
Introduction | p. 45 |
The preparation of the initial state | p. 46 |
Not all quantum systems have "well-defined" energy | p. 46 |
Three examples of energy eigenstates | p. 48 |
A particle in a one-dimensional box | p. 49 |
The vibrational energy of a diatomic molecule | p. 50 |
The energy eigenstates of the hydrogen atom | p. 51 |
Energy measurements by electron scattering | p. 52 |
Electron scattering from a gas of diatomic molecules | p. 53 |
Energy measurements by photon emission | p. 57 |
Photon emission | p. 57 |
Applications | p. 58 |
Some results are certain, most are just probable | p. 61 |
Introduction | p. 61 |
What is the outcome of an electron-scattering experiment? | p. 62 |
Classical interpretation of the experiment | p. 63 |
The quantum description of the experiment | p. 64 |
Probabilities | p. 65 |
A discussion of photon absorption measurements | p. 68 |
Why the outcome of most absorption experiments is certain | p. 69 |
A discussion of photon emission measurements | p. 69 |
A one-photon, one-molecule experiment | p. 70 |
The probabilities of different events | p. 72 |
The physical interpretation of the wave function | p. 73 |
Application to a vibrating diatomic molecule | p. 75 |
Data for HCl | p. 76 |
Interpretation | p. 79 |
Average values | p. 79 |
The effect of position uncertainty on a diffraction experiment | p. 80 |
The effect of position uncertainty in an ESDAID experiment | p. 81 |
Tunneling | p. 85 |
Classically forbidden region | p. 85 |
How large is the accessible region? | p. 85 |
The classically allowed region for an oscillator | p. 86 |
Tunneling depends on mass and energy | p. 89 |
Tunneling junctions | p. 90 |
Scanning tunneling microscopy | p. 91 |
Particle in a box | p. 95 |
Define the system | p. 95 |
The classical Hamiltonian | p. 96 |
Quantizing the system | p. 97 |
The boundary conditions | p. 98 |
Solving the eigenvalue problem (the Schrodinger equation) for the particle in a box | p. 100 |
Separation of variables | p. 100 |
Boundary conditions | p. 101 |
The behavior of a particle in a box | p. 104 |
The ground state energy is not zero | p. 105 |
Degeneracy | p. 107 |
Degeneracy is related to the symmetry of the system | p. 109 |
The eigenfunctions are normalized | p. 111 |
Orthogonality | p. 112 |
The position of a particle in a given state | p. 113 |
Light emission and absorption: the phenomena | p. 117 |
Introduction | p. 117 |
Light absorption and emission: the phenomena | p. 118 |
An absorption experiment | p. 118 |
Characterization of an absorption spectrum | p. 119 |
Why the transmitted intensity is low at certain frequencies | p. 120 |
Emission spectroscopy | p. 122 |
Units | p. 126 |
How to convert from one unit to another | p. 128 |
Why we need to know the laws of light absorption and emission | p. 130 |
Light emission and absorption: Einstein's phenomenological theory | p. 135 |
Introduction | p. 135 |
Photon absorption and emission: the model | p. 136 |
Photon energy and energy conservation | p. 136 |
How to reconcile this energy conservation with the existence of a line-width | p. 137 |
The model | p. 137 |
Photon absorption and emission: the rate equations | p. 138 |
The rate of photon absorption | p. 138 |
The rate of spontaneous photon emission | p. 139 |
The rate of stimulated emission | p. 140 |
The total rate of change of N[subscript 0] (or N[subscript 1]) | p. 140 |
Photon absorption and emission: the detailed balance | p. 141 |
Molecules in thermal equilibrium with radiation | p. 141 |
The detailed balance | p. 143 |
The solution of the rate equations | p. 144 |
Using the detailed balance results to simplify the rate equation | p. 145 |
The initial conditions | p. 146 |
The ground state population when the molecules are continuously exposed to light | p. 146 |
Analysis of the result: saturation | p. 147 |
Why Einstein introduced stimulated emission | p. 149 |
Simulated emission and the laser | p. 150 |
The rate of population relaxation | p. 151 |
Light absorption: the quantum theory | p. 153 |
Introduction | p. 153 |
Quantum theory of light emission and absorption | p. 154 |
The absorption probability | p. 154 |
Electrodynamic quantities: light pulses | p. 154 |
Electromagnetic quantities: the polarization of light | p. 156 |
Electromagnetic properties: the direction of propagation | p. 157 |
Electromagnetic quantities: the energy and the intensity of the pulse | p. 157 |
The properties of the molecule: the transition dipole moment <[psi subscript f vertical bar]m[vertical bar psi subscript i]> | p. 158 |
The properties of the molecule: the line shape | p. 159 |
How the transition probability formula is used | p. 162 |
The probability of stimulated emission | p. 163 |
Validity conditions | p. 163 |
The connection to Einstein's B coefficient | p. 163 |
Single molecule spectroscopy and the spectroscopy of an ensemble of molecules | p. 165 |
Light emission and absorption by a particle in a box and a harmonic oscillator | p. 169 |
Introduction | p. 169 |
Light absorption by a particle in a box | p. 170 |
Quantum dots | p. 170 |
Photon absorption probability | p. 172 |
The amount of light and its frequency | p. 173 |
The energies and absorption frequencies | p. 173 |
The transition dipole | p. 174 |
The energy eigenfunctions for a particle in a box | p. 174 |
The dipole operator m | p. 175 |
The role of light polarization | p. 176 |
The evaluation of the transition moment for a particle in a box | p. 176 |
The first selection rule | p. 178 |
Physical interpretation | p. 178 |
The second selection rule | p. 178 |
A calculation of the spectrum in arbitrary units | p. 180 |
Light absorption by a harmonic oscillator | p. 181 |
The eigenstates and eigenvalues of a harmonic oscillator | p. 183 |
The transition dipole | p. 183 |
The molecular orientation and polarization | p. 184 |
Two-particle systems | p. 187 |
Introduction | p. 187 |
The Schrodinger equation for the internal motion | p. 189 |
The laboratory coordinate system | p. 189 |
The energy | p. 190 |
Because there is no external force, the system moves with constant velocity | p. 191 |
A coordinate system with the origin in the center of mass | p. 194 |
The total energy in terms of momentum | p. 195 |
The Hamiltonian operator | p. 196 |
The concept of quasi-particle | p. 197 |
The Hamiltonian of the quasi-particle in spherical coordinates | p. 199 |
The role of angular momentum in the motion of the two-particle system | p. 201 |
Angular momentum in classical mechanics | p. 201 |
The properties of angular momentum | p. 201 |
The Schrodinger equation of the quasi-particle and the square of the angular momentum | p. 205 |
The role of angular momentum in the motion of the two-particle system | p. 207 |
The evolution of the angular momentum | p. 207 |
A polar coordinate system | p. 208 |
The angular momentum in polar coordinates | p. 210 |
The energy in polar coordinates | p. 210 |
Angular momentum in quantum mechanics | p. 213 |
Introduction | p. 213 |
The operators representing the angular momentum in quantum mechanics | p. 215 |
Angular momentum in classical mechanics | p. 215 |
The angular momentum operator in quantum mechanics | p. 216 |
Angular momentum in spherical coordinates | p. 217 |
The operator L[superscript 2] | p. 218 |
The commutation relations between L[superscript 2] and L[subscript x], L[subscript y], L[subscript z] | p. 218 |
The eigenvalue equations for L[superscript 2] and L[subscript z] | p. 220 |
The eigenvalue problem for L[superscript 2] | p. 221 |
The eigenvalue problem for L[subscript z] | p. 222 |
Spherical harmonics | p. 222 |
The physical interpretation of these eigenstates | p. 225 |
A brief explanation of the procedure for changing coordinates | p. 226 |
Two particle systems: the radial and angular Schrodinger equations | p. 231 |
Introduction | p. 231 |
The Schrodinger equation in terms of L[superscript 2] | p. 232 |
The Hamiltonian of a two-particle system in terms of L[superscript 2] | p. 232 |
The radial and the angular Schrodinger equations | p. 233 |
The separation of variables in the Schrodinger equation | p. 233 |
Additional physical conditions | p. 234 |
The integral over the angles | p. 235 |
The radial normalization | p. 235 |
The energy eigenstates of a diatomic molecule | p. 239 |
Introduction | p. 239 |
The harmonic approximation | p. 240 |
The form of the function V(r) | p. 240 |
The physics described by V(r) | p. 241 |
When the approximation is correct | p. 244 |
The harmonic approximation to V(r) | p. 245 |
The rigid-rotor approximation | p. 247 |
Physical interpretation | p. 247 |
The rigid-rotor approximation decouples vibrational and rotational motion | p. 248 |
The eigenstates and eigenvalues of the radial Schrodinger equation in the harmonic and rigid-rotor approximation | p. 249 |
The eigenvalues | p. 249 |
An improved formula for the energy | p. 250 |
The radial eigenfunctions | p. 252 |
The physical interpretation of the eigenfunctions | p. 254 |
The probability of having a given interatomic distance and orientation | p. 255 |
The probability of having a given bond length | p. 256 |
Turning point and tunneling | p. 258 |
The average values of r - r[subscript 0] and (r - r[subscript 0])[superscript 2] | p. 260 |
The energy eigenstates and eigenvalues of a diatomic molecule | p. 262 |
Diatomic molecule: its spectroscopy | p. 265 |
Introduction | p. 265 |
Collect the necessary equations | p. 269 |
The frequencies of the absorbed photons | p. 269 |
Photon absorption and emission probabilities | p. 271 |
The wave function for the nuclear motion | p. 272 |
The electronic wave function | p. 273 |
The dipole moment of the molecule | p. 274 |
The separation of the transition dipole matrix element into a rotational and vibrational contribution | p. 275 |
The harmonic approximation for the dipole moment | p. 277 |
Physical interpretation | p. 279 |
The integral <l[subscript f], m[subscript f vertical bar]cos([theta])[vertical bar]l[subscript i], m[subscript i]> | p. 280 |
Vibrational and rotational excitation by absorption of an infrared photon | p. 281 |
The molecules in a gas have a variety of states | p. 285 |
The infrared absorption spectrum of a gas at a fixed temperature | p. 286 |
The probability of [characters not reproducible] (v, l, m; T) | p. 288 |
The probability of various states in a gas: a numerical study | p. 289 |
Back to the spectrum: the relative intensity of the absorption peaks | p. 291 |
Numerical analysis | p. 291 |
The hydrogen atom | p. 295 |
Introduction | p. 295 |
The Schrodinger equation for a one-electron atom | p. 296 |
Why the properties of a one-electron atom are so different from those of a diatomic molecule | p. 297 |
The solution of the Schrodinger equation for a one-electron atom | p. 299 |
The eigenvalues | p. 300 |
The eigenfunctions | p. 301 |
The energy | p. 302 |
The magnitude of the energies | p. 302 |
The energy scale [epsilon] and the length scale a | p. 304 |
The radial wave functions R[subscript n,l] (r) and the mean values of various physical quantities | p. 306 |
The probability of finding the electron at a certain distance from the nucleus | p. 308 |
The functions R[subscript n,l] (r) | p. 310 |
Plots of R[subscript n,l] (r) | p. 311 |
The mean values of r, r[superscript 2], Coulomb energy, centrifugal energy, and radial kinetic energy | p. 312 |
The angular dependence of the wave function | p. 317 |
Some nomenclature | p. 319 |
The s-states | p. 319 |
The np orbitals | p. 320 |
The nd orbitals | p. 323 |
Hydrogen atom: absorption and emission spectroscopy | p. 325 |
The transition dipole | p. 327 |
The selection rules | p. 328 |
The radial integrals | p. 330 |
The spin of the electron and its role in spectroscopy | p. 331 |
Introduction | p. 331 |
The spin operators | p. 334 |
Spin eigenstates and eigenvalues | p. 335 |
The scalar product | p. 337 |
The emission spectrum of a hydrogen atom in a magnetic field: the normal Zeeman effect | p. 339 |
The experiment | p. 340 |
A modern (but oversimplified) version of the Lorentz model | p. 342 |
The energy of the hydrogen atom in a magnetic field | p. 343 |
The emission frequencies | p. 345 |
The spectrum | p. 347 |
The role of spin in light emission by a hydrogen atom: the anomalous Zeeman effect | p. 348 |
The interaction between spin and a magnetic field | p. 348 |
The energies of the electron in the hydrogen atom: the contribution of spin | p. 348 |
Comments and warnings | p. 350 |
The electronic structure of molecules: The H[subscript 2] molecule | p. 353 |
Introduction | p. 353 |
The Born-Oppenheimer approximation | p. 355 |
The electronic energies E[subscript n] (R) are the potential energies for the nuclear motion | p. 358 |
How to use the variational principle | p. 363 |
Application to the harmonic oscillator | p. 363 |
An application of the variational principle that uses a basis set | p. 366 |
The many-body wave function as a product of orbitals | p. 369 |
The curse of multi-dimensionality | p. 369 |
The wave function as a product of orbitals | p. 370 |
How to choose good orbitals | p. 372 |
The electron wave function must be antisymmetric | p. 372 |
Indistinguishable particles | p. 372 |
The antisymmetrization of a product of orbitals | p. 375 |
How to generalize to more than two electrons | p. 377 |
The Pauli principle | p. 379 |
Which electrons should be antisymmetrized | p. 380 |
The molecular orbitals in a minimal basis set: [sigma subscript u] and [sigma subscript g] | p. 383 |
The MO-LCAO method | p. 383 |
The minimal basis set | p. 384 |
Determine the molecular orbitals by using symmetry | p. 384 |
The molecular orbitals are normalized | p. 385 |
The symmetry of [sigma subscript g] and [sigma subscript u] | p. 387 |
The antisymmetrized products used in the configuration interaction wave functions must be eigenfunctions of S[superscript 2] and S[subscript z] | p. 387 |
The strategy for constructing the functions [Phi subscript i](1, 2) | p. 389 |
The spin states | p. 389 |
The singlet state [vertical bar] 0, 0> | p. 390 |
The triplet states [vertical bar] 1, m[subscript s]> | p. 391 |
Pairing up the spin and the orbital functions to create antisymmetric configurations | p. 391 |
The states [Phi subscript 1], [Phi subscript 2], and [Phi subscript 6] | p. 391 |
The states [Phi subscript 3], [Phi subscript 4], and [Phi subscript 5] | p. 392 |
The notations [superscript 1 Sigma subscript g+], [superscript 1 Sigma subscript g-], [superscript 3 Sigma subscript u,-1], [superscript 3 Sigma subscript u,0], [superscript 3 Sigma subscript u,1], [superscript 1 Sigma subscript u,0] | p. 392 |
The configurations in terms of atomic orbitals: physical interpretation | p. 393 |
The integrals required by the configuration interaction method | p. 394 |
The overlap matrix is diagonal | p. 395 |
Only the off-diagonal matrix elements <[Phi subscript 1 vertical bar]H[vertical bar Phi subscript 2]> and <[Phi subscript 2 vertical bar]H[vertical bar Phi subscript 1]> differ from zero | p. 395 |
The Hamiltonian matrix | p. 396 |
The Hamiltonian in atomic units | p. 396 |
Atomic units | p. 397 |
The matrix elements in terms of atomic orbitals | p. 397 |
Expression for the matrix elements | p. 398 |
The overlap integral S(R) | p. 399 |
The integral J(R) | p. 399 |
The integral K(R) | p. 401 |
The integral J'(R) | p. 401 |
The integral K'(R) | p. 402 |
The integral L(R) | p. 404 |
The ground and excited state energies given by perturbation theory | p. 405 |
Behavior of H[subscript 11] (R) at large R | p. 407 |
The configuration interaction method | p. 409 |
The variational eigenvalue problem: a summary | p. 409 |
The eigenvalues and the eigen vectors of matrix H | p. 410 |
The coupling between configurations | p. 411 |
When perturbation theory is accurate | p. 412 |
The configuration interaction energies | p. 412 |
The configuration interaction wave function of the ground state | p. 414 |
Summary | p. 416 |
Nuclear magnetic resonance and electron spin resonance | p. 421 |
Introduction | p. 421 |
More information about spin operators and spin states | p. 424 |
The NMR spectrum of a system with one independent spin | p. 428 |
The energy of the spin states for non-interacting spins | p. 428 |
The energy levels | p. 429 |
The rate of energy absorption | p. 430 |
NMR notation and units | p. 430 |
The order of magnitude of various quantities | p. 431 |
Hot bands | p. 432 |
The chemical shift | p. 434 |
The magnetic field acting on a nucleus depends on environment | p. 434 |
The NMR spectrum of a system of two non-interacting nuclei having spin 1/2 | p. 436 |
The Hamiltonian and the states of a system of two non-interacting spin 1/2 particles | p. 436 |
The order of magnitude of these energies | p. 438 |
The selection rules | p. 438 |
The frequencies of the allowed transitions | p. 440 |
The spin-spin interaction | p. 441 |
Spin-spin coupling | p. 441 |
The interaction between nuclear spins | p. 442 |
The spectrum of two distinguishable, interacting nuclei | p. 443 |
The energies of the spin states | p. 443 |
The Hamiltonian | p. 444 |
The states of the interacting spins | p. 444 |
The Galerkin method: how to turn an operator equation into a matrix equation | p. 446 |
The matrix elements H[subscript nm] = <[psi subscript n vertical bar]H[vertical bar psi subscript m]> | p. 447 |
Perturbation theory | p. 449 |
The off-diagonal elements | p. 450 |
The lowest energy E[subscript 1] and eigenvector [vertical bar phi subscript 1]> | p. 451 |
The eigenvalue E[subscript 2] and the spin state [vertical bar phi subscript 2]> | p. 452 |
Why [vertical bar phi subscript 1]> and [vertical bar phi subscript 2]> are so different | p. 453 |
The physical meaning of [vertical bar phi subscript 2]> | p. 453 |
The states [vertical bar phi subscript 3]> and [vertical bar phi subscript 4]> and the energies E[subscript 3] and E[subscript 4] | p. 455 |
The orders of magnitude | p. 456 |
The NMR spectrum of two weakly interacting, indistinguishable nuclei having spin 1/2 | p. 457 |
The states that satisfy the symmetry requirements | p. 457 |
Perturbation theory | p. 459 |
The selection rules | p. 461 |
Appendices | p. 463 |
Values of some physical constants | p. 463 |
Energy conversion factors | p. 464 |
Further Reading | p. 465 |
Index | p. 467 |
Table of Contents provided by Ingram. All Rights Reserved. |
ISBN: 9780815340874
ISBN-10: 0815340877
Audience:
Tertiary; University or College
Format:
Paperback
Language:
English
Number Of Pages: 352
Published: 21st February 2006
Publisher: Taylor & Francis Inc
Country of Publication: US
Dimensions (cm): 22.9 x 17.8
x 2.41
Weight (kg): 1.04
Edition Number: 1