World Library  



Physics Literature Collection


The World Public Library Physics Collection contains 263 conversations regarding the nature of physics.

 
  • Cover Image

Section 1 the Basic Tools of Quantum Mechanics

Physics Literature

Excerpt: Chapter 1. Quantum Mechanics Describes Matter in Terms of Wave functions and Energy Levels. Physical Measurements are Described in Terms of Operators Acting on Wave functions. Operators, Wave functions, and the Schr”dinger Equation The trends in chemical and physical properties of the elements described beautifully in the periodic table and the ability of early spectroscopists to fit atomic line spectra by simple mathematical formulas and to interpret atomic ele...

Read More
  • Cover Image

Section 1 the Basic Tools of Quantum Mechanics

Physics Literature

Excerpt: Chapter 1. Quantum Mechanics Describes Matter in Terms of Wave functions and Energy Levels. Physical Measurements are Described in Terms of Operators Acting on Wave functions. Operators, Wave functions, and the Schr”dinger Equation The trends in chemical and physical properties of the elements described beautifully in the periodic table and the ability of early spectroscopists to fit atomic line spectra by simple mathematical formulas and to interpret atomic ele...

Read More
  • Cover Image

Chapter 10 Electronic Wave Functions Must Also Possess Proper Symm...

Physics Literature

Excerpt: Because the total Hamiltonian of a many-electron atom or molecule forms a mutually commutative set of operators with S2, Sz, and A = (™1/N!)Sp sp P, the exact Eigen functions of H must be Eigen functions of these operators. Being an eigenfunction of A forces the Eigen states to be odd under all Pij. Any acceptable model or trial wave function should be constrained to also be an Eigen function of these symmetry operators. If the atom or molecule has additional sy...

Read More
  • Cover Image

Chapter 11 One Must Be Able to Evaluate the Matrix Elements Among ...

Physics Literature

Excerpt: CSFs are used to express the full n-electron wave function. It has been demonstrated that a given electronic configuration can yield several space- and spin- adapted determinental wave functions; such functions are referred to as configuration state functions (CSFs). These CSF wave functions are not the exact Eigen functions of the many-electron Hamiltonian, H; they are simply functions which possess the space, spin, and permutational symmetry of the exact eigen...

Read More
  • Cover Image

Chapter 12 Along Reaction Paths Configurations Can Be Connected On...

Physics Literature

Excerpt: Concepts of Configuration and State Energies. A. Plots of CSF Energies Give Configuration Correlation Diagrams The energy of a particular electronic state of an atom or molecule has been expressed in terms of Hamiltonian matrix elements, using the SC rules, over the various spin-and spatially adapted determinants or CSFs which enter into the state wave function.

Read More
  • Cover Image

Section 4 Molecular Rotation and Vibration

Physics Literature

Excerpt: Chapter 13 - Treating the full internal nuclear-motion dynamics of a polyatomic molecule is complicated. It is conventional to examine the rotational movement of a hypothetical ?rigid molecule as well as the vibrational motion of a non-rotating molecule, and to then treat the rotation vibration couplings using perturbation theory.

Read More
  • Cover Image

Section 5 Time Dependent Processes

Physics Literature

Excerpt: Chapter 14 - The interaction of a molecular species with electromagnetic fields can cause transitions to occur among the available molecular energy levels (electronic, vibrational, rotational, and nuclear spin). Collisions among molecular species likewise can cause transitions to occur. Time-dependent perturbation theory and the methods of molecular dynamics can be employed to treat such transitions.

Read More
  • Cover Image

Chapter 15 the Tools of Time-Dependent Perturbation Theory Can Be ...

Physics Literature

Excerpt: Rotational Transitions. Within the approximation that the electronic, vibrational, and rotational states of a molecule can be treated as independent, the total molecular wave function of the ?initial? state is a product Fi = yei cvi fri of an electronic function yei, a vibrational function cvi, and a rotational function fri. A similar product expression holds for the ?final? wave function Ff.

Read More
  • Cover Image

Chapter 18 the Single Slater Determinant Wave Function (Properly S...

Physics Literature

Excerpt: A. The Energy Expression The most straightforward way to introduce the concept of optimal molecular orbitals is to consider a trial wave function of the form which was introduced earlier in Chapter 9.II. The expectation value of the Hamiltonian for a wave function of the multiconfigurational form Y = SI CIFI, where FI is a space- and spin-adapted CSF which consists of determinental wave functions |fI1fI2fI3 fIN|, can be written as: E =SI,J = 1, M CICJ < FI | H |...

Read More
  • Cover Image

Chapter 19 Corrections to the Mean-Field Model Are Needed to Descr...

Physics Literature

Excerpt: Much of the development of the previous chapter pertains to the use of a single Slater determinant trial wave function. As presented, it relates to what has been called the unrestricted Hartree-Fock (UHF) theory in which each spin-orbital fi has its own orbital energy ei and LCAO-MO coefficients Cn; there may be different Cn,i for a spin-orbitals than for b spin-orbitals. Such a wave function suffers from the spin contamination difficulty detailed earlier.

Read More
  • Cover Image

Chapter 2 Approximation Methods Can Be Used When Exact Solutions t...

Physics Literature

Excerpt: In applying quantum mechanics to ?real? chemical problems, one is usually faced with a Schr”dinger differential equation for which, to date, no one has found an analytical solution. This is equally true for electronic and nuclear-motion problems. It has therefore proven essential to develop and efficiently implement mathematical methods which can provide approximate solutions to such Eigen value equations. Two methods are widely used in this context- the variati...

Read More
  • Cover Image

Chapter 20 Many Physical Properties of a Molecule Can Be Calculate...

Physics Literature

Excerpt: I. Calculations of Properties Other Than the Energy. There are, of course, properties other than the energy that are of interest to the practicing chemist. Dipole moments, polarizabilities, transition probabilities among states, and vibrational frequencies all come to mind. Other properties that are of importance involve operators whose quantum numbers or symmetry indices label the state of interest. Angular momentum and point group symmetries are examples of th...

Read More
  • Cover Image

Chapter 3 the Application of the Schrdinger Equation to the Motion...

Physics Literature

Excerpt: Many elements of chemists? pictures of molecular structure hinge on the point of view that separates the electronic motions from the vibrational/rotational motions and treats couplings between these (approximately) separated motions as 'perturbations'. It is essential to understand the origins and limitations of this separated-motions picture. To develop a framework in terms of which to understand when such separability is valid, one thinks of an atom or molecul...

Read More
  • Cover Image

Section 2 Simple Molecular Orbital Theory

Physics Literature

Excerpt: In this section, the conceptual framework of molecular orbital theory is developed. Applications are presented and problems are given and solved within qualitative and semiempirical models of electronic structure. A b Initi o approaches to these same matters, whose solutions require the use of digital computers, are treated later in Section 6. Semiempirical methods, most of which also require access to a computer, are treated in this section and in Appendix F.

Read More
  • Cover Image

Section 2 Simple Molecular Orbital Theory

Physics Literature

Excerpt: In this section, the conceptual framework of molecular orbital theory is developed. Applications are presented and problems are given and solved within qualitative and semiempirical models of electronic structure. A b Initi o approaches to these same matters, whose solutions require the use of digital computers, are treated later in Section 6. Semiempirical methods, most of which also require access to a computer, are treated in this section and in Appendix F.

Read More
  • Cover Image

Chapter 6 Along Reaction Paths Orbital's Can Be Connected One-To-O...

Physics Literature

Excerpt: Reduction in Symmetry - As fragments are brought together to form a larger molecule, the symmetry of the nuclear framework (recall the symmetry of the coulombic potential experienced by electrons depends on the locations of the nuclei) changes. However, in some cases, certain symmetry elements persist throughout the path connecting the fragments and the product molecule. These preserved symmetry elements can be used to label the orbitals throughout the 'reaction'.

Read More
  • Cover Image

Chapter 7 the Most Elementary Molecular Orbital Models Contain Sym...

Physics Literature

Excerpt: The LCAO-MO Expansion and the Orbital-Level Schr”dinger Equation In the simplest picture of chemical bonding, the valence molecular orbitals fi are constructed as linear combinations of valence atomic orbitals cm according to the LCAOMO formula: fi = Sm Cim cm. The core electrons are not explicitly included in such a treatment, although their effects are felt through an electrostatic potential V that has the following properties ...

Read More
  • Cover Image

Section 3 Electronic Configurations Term Symbols and States

Physics Literature

Excerpt: One of the goals of quantum chemistry is to allow practicing chemists to use knowledge of the electronic states of fragments (atoms, radicals, ions, or molecules) to predict and understand the behavior (i.e., electronic energy levels, geometries, and reactivities) of larger molecules. In the preceding Section, orbital correlation diagrams were introduced to connect the orbitals of the fragments along a 'reaction path? leading to the orbitals of the products. In ...

Read More
  • Cover Image

Chapter 9 Electronic Wavefuntions Must Be Constructed to Have Perm...

Physics Literature

Excerpt: Electronic Configurations. Atoms, linear molecules, and non-linear molecules have orbitals which can be labeled either according to the symmetry appropriate for that isolated species or for the species in an environment which produces lower symmetry. These orbitals should be viewed as regions of space in which electrons can move, with, of course, at most two electrons (of opposite spin) in each orbital. Specification of a particular occupancy of the set of orbit...

Read More
  • Cover Image

Words to the Reader about How to Use This Textbook

Physics Literature

Excerpt: What This Book Does and Does Not Contain: This text is intended for use by beginning graduate students and advanced upper division undergraduate students in all areas of chemistry. It provides: // (i) An introduction to the fundamentals of quantum mechanics as they apply to chemistry, // (ii) Material that provides brief introductions to the subjects of molecular spectroscopy chemical dynamics, // (iii) An introduction to computational chemistry applied to the t...

Read More
 
9
|
10
|
11
|
12
|
13
Records: 201 - 220 of 295 - Pages: 



Copyright © World Library Foundation. All rights reserved. eBooks from World eBook Library are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.