Everything about Quantum Chemistry totally explained
Quantum chemistry is a branch of
theoretical chemistry, which applies
quantum mechanics and
quantum field theory to address issues and problems in
chemistry. The description of the
electronic behavior of
atoms and
molecules as pertaining to their
reactivity is one of the applications of quantum chemistry. Quantum chemistry lies on the border between
chemistry and
physics, and significant contributions have been made by scientists from both fields. It has a strong and active overlap with the field of
atomic physics and
molecular physics, as well as
physical chemistry.
Quantum chemistry mathematically describes the fundamental behavior of
matter at the
molecular scale. It is, in principle, possible to describe all chemical systems using this theory. In practice, only the simplest chemical systems may realistically be investigated in purely
quantum mechanical terms, and approximations must be made for most practical purposes (for example,
Hartree-Fock,
post Hartree-Fock or
Density functional theory, see
computational chemistry for more details). Hence a detailed understanding of
quantum mechanics isn't necessary for most chemistry, as the important implications of the theory (principally the
orbital approximation) can be understood and applied in simpler terms.
In quantum mechanics (several applications in computational chemistry and quantum chemistry), the
Hamiltonian, or the physical state, of a particle can be expressed as the sum of two operators, one corresponding to
kinetic energy and the other to
potential energy. The
Hamiltonian in the
Schrödinger wave equation used in quantum chemistry doesn't contain terms for the
spin of the electron.
Solutions of the Schrödinger equation for the hydrogen atom gives the form of the wave function for
atomic orbitals, and the relative energy of the various orbitals. The orbital approximation can be used to understand the other atoms for example
helium,
lithium and
carbon.
History
The
history of quantum chemistry essentially began with the 1838 discovery of
cathode rays by
Michael Faraday, the 1859 statement of the
black body radiation problem by
Gustav Kirchhoff, the 1877 suggestion by
Ludwig Boltzmann that the energy states of a physical system could be discrete, and the 1900 quantum hypothesis by
Max Planck that any energy radiating atomic system can theoretically be divided into a number of discrete energy elements
ε such that each of these energy elements is proportional to the
frequency ν with which they each individually radiate
energy, as defined by the following formula:
»
where
h is a numerical value called
Planck’s Constant. Then, in 1905, to explain the
photoelectric effect (1839), for example, that shining light on certain materials can function to eject electrons from the material,
Albert Einstein postulated, based on Planck’s quantum hypothesis, that
light itself consists of individual quantum particles, which later came to be called
photons (1926). In the years to follow, this theoretical basis slowly began to be applied to chemical structure, reactivity, and bonding.
Electronic structure
The first step in solving a quantum chemical problem is usually solving the
Schrödinger equation (or
Dirac equation in
relativistic quantum chemistry) with the
electronic molecular Hamiltonian. This is called determining the
electronic structure of the molecule. It can be said that the electronic structure of a molecule or crystal implies essentially its chemical properties.
Wave model
The foundation of quantum mechanics and quantum chemistry is the
wave model, in which the atom is a small, dense, positively charged
nucleus surrounded by electrons. Unlike the earlier
Bohr model of the atom, however, the wave model describes electrons as "
clouds" moving in
orbitals, and their positions are represented by
probability distributions rather than discrete points. The strength of this model lies in its
predictive power. Specifically, it predicts the pattern of chemically similar elements found in the
periodic table. The wave model is so named because electrons exhibit properties (such as interference) traditionally associated with waves. See
wave-particle duality.
Valence bond
»
Although the mathematical basis of quantum chemistry had been laid by
Schrödinger in
1926, it's generally accepted that the first true calculation in quantum chemistry was that of the German physicists
Walter Heitler and
Fritz London on the hydrogen (H
2) molecule in
1927. Heitler and London's method was extended by the American theoretical physicist
John C. Slater and the American theoretical chemist
Linus Pauling to become the
Valence-Bond (VB) [or
Heitler-London-Slater-Pauling (HLSP)] method. In this method, attention is primarily devoted to the pairwise interactions between atoms, and this method therefore correlates closely with classical chemists' drawings of
bonds.
Molecular orbital
»
An alternative approach was developed in
1929 by
Friedrich Hund and
Robert S. Mulliken, in which
electrons are described by mathematical functions delocalized over an entire
molecule. The
Hund-Mulliken approach or
molecular orbital (MO) method is less intuitive to chemists, but has turned out capable of predicting
spectroscopic properties better than the VB method. This approach is the conceptional basis of the
Hartree-Fock method and further
post Hartree-Fock methods.
Density functional theory
»
The
Thomas-Fermi model was developed independently by
Thomas and
Fermi in
1927. This was the first attempt to describe many-electron systems on the basis of
electronic density instead of
wave functions, although it wasn't very successful in the treatment of entire molecules. The method did provide the basis for what is now known as
density functional theory. Though this method is less developed than post Hartree-Fock methods, its lower computational requirements allow it to tackle larger
polyatomic molecules and even
macromolecules, which has made it the most used method in
computational chemistry at present.
Chemical dynamics
A further step can consist of solving the
Schrödinger equation with the total
molecular Hamiltonian in order to study the motion of molecules. Direct solution of the Schrödinger equation is called
quantum molecular dynamics, within the
semiclassical approximation
semiclassical molecular dynamics, and within the
classical mechanics framework
molecular dynamics (MD). Statistical approaches, using for example
Monte Carlo methods, are also possible.
Adiabatic chemical dynamics
» Main article: Adiabatic formalism or Born-Oppenheimer approximation
In
adiabatic dynamics, interatomic interactions are represented by single
scalar potentials called
potential energy surfaces. This is the
Born-Oppenheimer approximation introduced by
Born and
Oppenheimer in
1927. Pioneering applications of this in chemistry were performed by
Rice and
Ramsperger in 1927 and
Kassel in
1928, and generalized into the
RRKM theory in
1952 by
Marcus who took the
transition state theory developed by
Eyring in
1935 into account. These methods enable simple estimates of unimolecular
reaction rates from a few characteristics of the potential surface.
Non-adiabatic chemical dynamics
»
Non-adiabatic dynamics consists of taking the interaction between several coupled potential energy surface (corresponding to different electronic
quantum states of the molecule). The coupling terms are called
vibronic couplings. The pioneering work in this field was done by
Stueckelberg,
Landau, and
Zener in the
1930s, in their work on what is now known as the
Landau-Zener transition. Their formula allows the transition probability between two
diabatic potential curves in the neighborhood of an
avoided crossing to be calculated.
Quantum chemistry and quantum field theory
The application of
quantum field theory (QFT) to chemical systems and theories has become increasingly common in the modern physical sciences. One of the first and most fundamentally explicit appearances of this is seen in the theory of the
photomagneton. In this system,
plasmas, which are ubiquitous in both physics and chemistry, are studied in order to determine the basic
quantization of the underlying
bosonic field. However, quantum field theory is of interest in many fields of chemistry, including:
nuclear chemistry,
astrochemistry,
sonochemistry, and
quantum hydrodynamics. Field theoretic methods have also been critical in developing the ab initio Effective Hamiltonian theory of semi-empirical pi-electron methods.
Further Information
Get more info on 'Quantum Chemistry'.
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