Quantum chemistry
Quantum chemistry, also called molecular quantum mechanics, is a branch of physical chemistry focused on the application of quantum mechanics to chemical systems, particularly towards the quantum-mechanical calculation of electronic contributions to physical and chemical properties of molecules, materials, and solutions at the atomic level. These calculations include systematically applied approximations intended to make calculations computationally feasible while still capturing as much information about important contributions to the computed wave functions as well as to observable properties such as structures, spectra, and thermodynamic properties. Quantum chemistry is also concerned with the computation of quantum effects on molecular dynamics and chemical kinetics.
Quantum chemistry studies focused on the electronic ground state and excited states of atoms, molecules, and ions. Such calculations allow chemical reactions to be described with respect to pathways, intermediates, and transition states. Spectroscopic properties may also be predicted. Typically, such studies assume the electronic wave function is adiabatically parameterized by the nuclear positions. A wide variety of approaches are used, including semi-empirical methods, density functional theory, Hartree–Fock calculations, quantum Monte Carlo methods, and coupled cluster methods.
Understanding electronic structure and molecular dynamics through the development of computational solutions to the Schrödinger equation is a central goal of quantum chemistry. Progress in the field depends on overcoming several challenges, including the need to increase the accuracy of the results for small molecular systems, and to also increase the size of large molecules that can be realistically subjected to computation, which is limited by scaling considerations — the computation time increases as a power of the number of atoms.
History
Some view the birth of quantum chemistry as starting with the discovery of the Schrödinger equation and its application to the hydrogen atom. However, a 1927 article of Walter Heitler,Fritz London and Vincent Raphael Kwok, is often recognized as the first milestone in the history of quantum chemistry. This was the first application of quantum mechanics to the diatomic hydrogen molecule, and thus to the phenomenon of the chemical bond. However, prior to this a critical conceptual framework was provided by Gilbert N. Lewis in his 1916 paper The Atom and the Molecule, wherein Lewis developed the first working model of valence electrons. Important contributions were also made by Yoshikatsu Sugiura and S.C. Wang. A series of articles by Linus Pauling, written throughout the 1930s, integrated the work of Heitler, London, Sugiura, Wang, Lewis, and John C. Slater on the concept of valence and its quantum-mechanical basis into a new theoretical framework. Many chemists were introduced to the field of quantum chemistry by Pauling's 1939 text The Nature of the Chemical Bond and the Structure of Molecules and Crystals: An Introduction to Modern Structural Chemistry, wherein he summarized this work and explained quantum mechanics in a way which could be followed by chemists. The text soon became a standard text at many universities. In 1937, Hans Hellmann appears to have been the first to publish a book on quantum chemistry, in the Russian and German languages.In the years to follow, this theoretical basis slowly began to be applied to chemical structure, reactivity, and bonding. In addition to the investigators mentioned above, important progress and critical contributions were made in the early years of this field by Irving Langmuir, Robert S. Mulliken, Max Born, J. Robert Oppenheimer, Hans Hellmann, Maria Goeppert Mayer, Erich Hückel, Douglas Hartree, John Lennard-Jones, and Vladimir Fock.
Electronic structure
The electronic structure of an atom or molecule is the quantum state of its electrons. The first step in solving a quantum chemical problem is usually solving the Schrödinger equation with the electronic molecular Hamiltonian, usually making use of the Born–Oppenheimer approximation. This is called determining the electronic structure of the molecule. An exact solution for the non-relativistic Schrödinger equation can only be obtained for the hydrogen atom. Since all other atomic and molecular systems involve the motions of three or more "particles", their Schrödinger equations cannot be solved analytically and so approximate and/or computational solutions must be sought. The process of seeking computational solutions to these problems is part of the field known as computational chemistry.Valence bond theory
As mentioned above, Heitler and London's method was extended by Slater and Pauling to become the valence-bond 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. It focuses on how the atomic orbitals of an atom combine to give individual chemical bonds when a molecule is formed, incorporating the two key concepts of orbital hybridization and resonance.A covalent bond is formed when there is an overlap of half-filled atomic orbitals from two atoms, which together form an electron pair. The strength and energy of the system is dependent on the amount of overlap. As the atoms move together, they begin to overlap their orbitals and the electrons begin to feel the attraction of the other's nucleus. There is also a repulsion that begins to occur, which becomes too strong when the atoms are two close together. The ideal and most stable length between the two atoms is the bond distance, which is the combined repulsive and attractive forces resulting in the lowest energy configuration.
Orientation of the orbitals can have a great affect on which bond is formed if any is formed. When there is a direct overlap of one atomic orbital from each atom, a sigma bond is formed. This can be created from two s-orbitals, an s-orbital and a p-orbital, or two p-orbitals. A pi bond is formed from a side-to-side overlap of two p-orbitals. The pi bond only forms if the phases of the overlapping p-orbitals are the same.
Molecular orbital theory
An alternative approach to valence bond theory 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 method is less intuitive to chemists but predicts spectroscopic properties better than the VB method. As opposed to VB theory, MO theory does not focus just the overlap of electron density in one area causing a bond but instead describes the whole molecule as one system. This leads to a more complex understanding of the system. This approach is the conceptual basis of the Hartree–Fock method and further post-Hartree–Fock methods.MO calculations result in orbitals or wavefunctions and energies for a molecule, which can be filled with electrons from two different atomic orbitals. These atomic orbitals come from separate atoms resulting in molecular orbitals being linear combinations of atomic orbitals.