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Theoretical chemistry seeks to provide explanations to chemical and physical observations. Should the properties derived from the quantum theory give a good account of the above mentioned phenomena, we derive consequences using the same theory. Should the derived consequences fall too far from the experimental evidence, we go to a different theory. G. Lewis proposed that chemical properties originated from the electrons of the atom's valence shell, ever since the theoretical chemistry has dealt with modelling of the outer electrons of interacting atoms or molecules in a reaction. Theoretical chemistry includes the fundamental laws of physics Coulomb's law, Kinetic energy, Potential energy, the Virial Theorem, Planck's Law, Pauli exclusion principle and many others to explain but also predict chemical observed phenomena. The term quantum chemistry which comes from Bohr's quantized model of electron in the atom, applies to both the time independent Schrödinger and the time dependent Dirac formulations.
In general one has to distinguish, theoretical approach (theory level such as Hartree-Fock (HF), Coupled cluster, Relativistic, etc.) from mathematical formalism, plane wave, spherical harmonics, Bloch wave periodic potential. Methods that solve iteratively the energies (Eigenvalues) of stationary state waves in a potential include Restricted Hartree-Fock (RHF), Multi-configurational self-consistent field (CASSCF or MCSCF) but the theory pertains to Schroedinger. Related areas in theoretical chemistry include the mathematical characterization of bulk materials (e.g. the study of electronic band structure in solid state physics) using the theory of Electronic band structure in a Periodic Crystal Lattice. Different theoretical approaches are Molecular mechanics and Topology. The study of the applicability of well established mathematical theories to chemistry is crucial to metals (i.e. topology in the study of small bodies explains the elaborate electronic structures of clusters). This later area of theoretical chemistry originates from the so-called mathematical chemistry. Time Dependent Quantum Molecular Dynamics, is a modern approach to the interaction of light with molecules that vibrate and drive reactions in a desired direction.
Time independent or non-relativistic quantum chemistry is the most widely used formalism of quantum mechanics to solve electronic problems in chemistry. This part of theoretical chemistry may be broadly divided into electronic structure, dynamics, and statistical mechanics. The relativistic quantum chemistry Dirac equation on the other hand explains electron phenomena in heavy atoms with complex electronic interactions, i.e. spin-orbit coupling and relativistic corrections observed for heavy elements such as Re, Os, Ir, Pt, Au, Hg and Pb. Both relativistic quantum chemistry and non-relativistic quantum chemistry are used to solve the problem of predicting chemical reactivity which depends on electrons.
Some chemical theoreticians Car-Parrinello apply molecular dynamics to provide a thorough bridge between the electronic phenomena and the displacement phenomena, this includes properties within organized systems. Currently, many experimental chemists are using Hybrid Gradient Corrected Density Functionals (e.g. B3LYP) to explain the magnetic properties of metals with unpaired electrons; however, a rigorous theoretical examination of this, shows a misuse of the DFT approach, as the electronic spin appears only in Dirac time dependent equations. One way to avoid a full 4e Dirac calculation, is to use TD-DFT method which includes several electronic states for the "same ground geometry". This approach leads to overemphasize on the orbital part wave function to deduce the electronic spin properties, without considering the spin equations, or that the geometry of excited and ground state differ.
Theoretical attempts on chemical problems go back to before 1926, but until the formulation of the Schrödinger equation by the Austrian physicist Erwin Schrödinger in that year, the techniques available were rather crude and approximated. Currently, much more sophisticated theoretical approaches, based on Quantum Field Theory and Non-equilibrium Green's Function Theory are very popular. Green's Function theory provides a much closer explanation of electronic transitions than the Hartree-Fock formalism.
In order to explain an observable one has to choose the "appropriate level of theory". For example, some theoretical methods (DFT) may not be appropriate to solve magnetic coupling or electron transitions properties. Instead, there are serious reports like Multireference configuration interaction (MRCI), which accurately and thoroughly explain the observed phenomena by means of the fundamental interactions. Major components include quantum chemistry, the application of quantum mechanics to the understanding of valence, molecular dynamics, statistical thermodynamics and theories of electrolyte solutions, reaction networks, polymerization, catalysis, molecular magnetism and spectroscopy.
Branches of theoretical chemistry 
- Quantum chemistry
- The application of quantum mechanics or fundamental interactions to chemical and physico-chemical problems. Spectroscopic and magnetic properties are between the most frequently modelled.
- Computational chemistry
- The application of computer codes to chemistry, involving approximation schemes such as Hartree–Fock, post-Hartree–Fock, density functional theory, semiempirical methods (such as PM3) or force field methods. Molecular shape is the most frequently predicted property. Computers can also predict vibrational spectra and vibronic coupling, but also acquire and Fourier transform Infra-red Data into frequency information. The comparison with predicted vibrations supports the predicted shape.
- Molecular modelling
- Methods for modelling molecular structures without necessarily referring to quantum mechanics. Examples are molecular docking, protein-protein docking, drug design, combinatorial chemistry. The fitting of shape and electric potential are the driving factor in this graphical approach.
- Molecular dynamics
- Application of classical mechanics for simulating the movement of the nuclei of an assembly of atoms and molecules. The rearrangement of molecules within an ensemble is controlled by Van der Waals forces and promoted by temperature.
- Molecular mechanics
- Modelling of the intra- and inter-molecular interaction potential energy surfaces via a sum of interaction forces. Classic mechanics Hooke's law for stretching, bending and torsions are used to predict the shape of known and new molecules.
- Mathematical chemistry
- Discussion and prediction of the molecular structure using mathematical methods without necessarily referring to quantum mechanics. Topology is a branch of mathematics that allows to predict properties of flexible finite size bodies like clusters.
- Theoretical chemical kinetics
- Theoretical study of the dynamical systems associated to reactive chemicals, the activated complex and their corresponding differential equations.
- Cheminformatics (also known as chemoinformatics)
- The use of computer and informational techniques, applied to crop information to solve problems in the field of chemistry.
Historically, the major field of application of theoretical chemistry has been in the following fields of research:
- Atomic physics: The discipline dealing with electrons and atomic nuclei.
- Molecular physics: The discipline of the electrons surrounding the molecular nuclei and of movement of the nuclei. This term usually refers to the study of molecules made of a few atoms in the gas phase. But some consider that molecular physics is also the study of bulk properties of chemicals in terms of molecules.
- Physical chemistry and chemical physics: Chemistry investigated via physical methods like laser techniques, scanning tunneling microscope, etc. The formal distinction between both fields is that physical chemistry is a branch of chemistry while chemical physics is a branch of physics. In practice this distinction is quite vague.
- Many-body theory: The discipline studying the effects which appear in systems with large number of constituents. It is based on quantum physics – mostly second quantization formalism – and quantum electrodynamics.
Hence, the theoretical chemistry discipline is sometimes seen[by whom?] as a branch of those fields of research. Nevertheless, more recently, with the rise of the density functional theory and other methods like molecular mechanics, the range of application has been extended to chemical systems which are relevant to other fields of chemistry and physics like biochemistry, condensed matter physics, nanotechnology or molecular biology.
- Attila Szabo and Neil S. Ostlund, Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory, Dover Publications; New Ed edition (1996) ISBN 0-486-69186-1, ISBN 978-0-486-69186-2
- Robert G. Parr and Weitao Yang, Density-Functional Theory of Atoms and Molecules, Oxford Science Publications; first published in 1989; ISBN 0-19-504279-4, ISBN 0-19-509276-7
- D.J. Tannor, V. Kazakov and V. Orlov, Control of Photochemical Branching: Novel Procedures for Finding Optimal Pulses and Global Upper Bounds, in Time Dependent Quantum Molecular Dynamics, J. Broeckhove and L. Lathouwers, eds., 347-360 (Plenum, 1992)
|“||The deepest part of Theoretical Chemistry must end up in Quantum Mechanics.||”|
|“||Facts are the air of scientists. Without them you can never fly.||”|