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Quantum chemistry is a branch of chemistry whose primary focus is the application of quantum mechanics in physical models and experiments of chemical systems. It involves heavy interplay of experimental and theoretical methods.
Experimental quantum chemists rely heavily on spectroscopy, through which information regarding the quantization of energy on a molecular scale can be obtained. Common methods are infra-red (IR) spectroscopy and nuclear magnetic resonance (NMR) spectroscopy.
Quantum chemistry
Quantum chemistry is a branch of chemistry whose primary focus is the application of quantum mechanics in physical models and experiments of chemical systems. It involves heavy interplay of experimental and theoretical methods.
Experimental quantum chemists rely heavily on spectroscopy, through which information regarding the quantization of energy on a molecular scale can be obtained. Common methods are infra-red (IR) spectroscopy and nuclear magnetic resonance (NMR) spectroscopy.
Theoretical quantum chemistry, the workings of which also tend to fall under the category of computational chemistry, seeks to calculate the predictions of quantum theory as atoms and molecules can only have discrete energies; as this task, when applied to polyatomic species, invokes the many-body problem, these calculations are performed using computers rather than by analytical "pen and paper" methods, pen recorder or computerized data station with a VDU.
In these ways, quantum chemists investigate chemical phenomena.
In reactions, quantum chemistry studies the ground state of individual atoms and molecules, the excited states, and the transition states that occur during chemical reactions.
On the calculations: quantum chemical studies use also semi-empirical and other methods based on quantum mechanical principles, and deal with time dependent problems. Many quantum chemical studies assume the nuclei are at rest (Born-Oppenheimer approximation). Many calculations involve iterative methods that include self-consistent field methods. Major goals of quantum chemistry include increasing the accuracy of the results for small molecular systems, and increasing the size of large molecules that can be processed, which is limited by scaling considerations - the computation time increases as a power of the number of atoms.
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 such that each of these energy elements is proportional to the frequency with which they each individually radiate energy and a numerical value called Planck's Constant.
Then, in 1905, to explain the photoelectric effect (1839), i.e., 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. Probably the greatest contribution to the field was made by Linus Pauling.
Electronic structure
Computational chemistry. 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. An exact solution for the Schrödinger equation can only be obtained for the hydrogen atom. Since all other atomic, or molecular systems, involve the motions of three or more "particles", their Schrödinger equations cannot be solved exactly and so approximate solutions must be sought.
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 theory
Although the mathematical basis of quantum chemistry had been laid by Schrödinger in 1926, it is generally accepted that the first true calculation in quantum chemistry was that of the German physicists Walter Heitler and Fritz London on the hydrogen (H2) 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 theory
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 was not 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 significantly lower computational requirements (scaling typically no worse than with respect to basis functions) allow it to tackle larger polyatomic molecules and even macromolecules. This computational affordability and often comparable accuracy to MP2 and CCSD (post-Hartree-Fock methods) has made it one of the most popular methods 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 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
Vibronic coupling
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.
Relativistic quantum chemistry invokes quantum chemical and relativistic mechanical arguments to explain elemental properties and structure, especially for the heavier elements of the periodic table. A prominent example of such an explanation would be the fact that the color of gold is explained via such relativistic effects.
The term "relativistic effects" was developed in light of the history of quantum mechanics. Initially quantum mechanics was developed without considering the theory of relativity. By convention, "relativistic effects" are those discrepancies between values calculated by models considering and not considering relativity. Relativistic effects are important for the heavier elements with highatomic numbers. In the most common layout of the periodic table, these elements are shown in the lower area. Examples are the lanthanides and actinides.
Relativistic effects in chemistry can be considered to be perturbations, or small corrections, to the non-relativistic theory of chemistry, which is developed from the solutions of the Schrödinger equation. These corrections affect the electrons differently depending on the electron speed relative to the speed of light. Relativistic effects are more prominent in heavy elements because only in these elements electrons do attain relativistic speeds.
Beginning in 1935 Bertha Swirles describes a relativistic treatment of a many-electron system, in spite of Paul Dirac's 1929 assertion that the only imperfections remaining in quantum mechanics «give rise to difficulties only when high-speed particles are involved, and are therefore of no importance in the consideration of atomic and molecular structure and ordinary chemical reactions in which quantum mechanics is, indeed, usually sufficiently accurate if one neglects relativity variation of mass and velocity and assumes only Coulomb forces between the various electrons and atomic nuclei».
Theoretical chemists by and large agreed with Dirac's sentiment until the 1970s, when relativistic effects began to become realized in heavy elements. The Schrödinger equation had been developed without considering relativity in Schrödinger's famous 1926 paper. Relativistic corrections were made to the Schrödinger equation (see Klein-Gordon equation) in order to explain the fine structure of atomic spectra, but this development and others did not immediately trickle into the chemical community. Since atomic spectral lines were largely in the realm of physics and not in that of chemistry, most chemists were unfamiliar with relativistic quantum mechanics, and their attention was on lighter elements typical for the organic chemistry focus of the time.
Dirac's opinion on the role relativistic quantum mechanics would play for chemical systems is wrong for two reasons: the first being that electrons in s and p atomic orbitals travel at a significant fraction of the speed of light and the second being that there are indirect consequences of relativistic effects which are especially evident for d and f atomic orbitals.
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