Pariser–Parr–Pople method
Encyclopedia
In molecular physics
, the Pariser–Parr–Pople method applies semi-empirical quantum mechanical methods to the quantitative prediction of electronic structures and spectra, in molecule
s of interest in the field of organic chemistry
. Previous methods existed, such as the Hückel method
which lead to the Hückel's rule
, but were limited in their scope, application and complexity, as is the Extended Huckel method
.
This approach was developed in the 1950s by Rudolph Pariser
with Robert Parr
and co-developed by John Pople
. It is essentially a more efficient method of finding reasonable approximations of molecular orbital
s, useful in predicting physical and chemical nature of the molecule under study since molecular orbital characteristics have implications with regards to both the basic structure
and reactivity of a molecule. This method used the zero-differential overlap
(ZDO) approximation to reduce the problem to reasonable size and complexity but still required modern solid state
computer
s (as opposed to punched card
or vacuum tube
systems) before becoming fully useful for molecules larger than benzene
.
Originally, Pariser's goal of using this method was to predict the characteristics of complex organic dyes, but this was never realized. The method has wide applicability in precise prediction of electronic transitions, particularly lower singlet
transitions, and found wide application in theoretical and applied quantum chemistry
. The two basic papers on this subject were among the top five chemistry and physics citations reported in ISI, Current Contents 1977 for the period of 1961–1977 with a total of 2450 references.
In contrast to the Hartree–Fock-based semiempirical
method counterparts (i.e.: MOPAC
), the pi-electron theories have a very strong ab initio
basis. The PPP formulation is actually an approximate pi-electron effective operator, and the empirical parameters, in fact, include effective electron correlation effects. A rigorous, ab initio theory of the PPP method is provided by diagrammatic, multi-reference, high order perturbation theory (Freed, Brandow, Lindgren, etc.). (The exact formulation is non-trivial, and requires some field theory) Large scale ab initio calculations (Martin and Birge, Martin and Freed, Sheppard and Freed, etc.) have confirmed many of the approximations of the PPP model and explain why the PPP-like models work so well with such a simple formulation.
Molecular physics
Molecular physics is the study of the physical properties of molecules, the chemical bonds between atoms as well as the molecular dynamics. Its most important experimental techniques are the various types of spectroscopy...
, the Pariser–Parr–Pople method applies semi-empirical quantum mechanical methods to the quantitative prediction of electronic structures and spectra, in molecule
Molecule
A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...
s of interest in the field of organic chemistry
Organic chemistry
Organic chemistry is a subdiscipline within chemistry involving the scientific study of the structure, properties, composition, reactions, and preparation of carbon-based compounds, hydrocarbons, and their derivatives...
. Previous methods existed, such as the Hückel method
Hückel method
The Hückel method or Hückel molecular orbital method proposed by Erich Hückel in 1930, is a very simple linear combination of atomic orbitals molecular orbitals method for the determination of energies of molecular orbitals of pi electrons in conjugated hydrocarbon systems, such as ethene,...
which lead to the Hückel's rule
Hückel's rule
In organic chemistry, Hückel's rule estimates whether a planar ring molecule will have aromatic properties. The quantum mechanical basis for its formulation was first worked out by physical chemist Erich Hückel in 1931...
, but were limited in their scope, application and complexity, as is the Extended Huckel method
Extended Huckel method
The extended Hückel method is a semiempirical quantum chemistry method, developed by Roald Hoffmann since 1963. It is based on the Hückel method but, while the original Hückel method only considers pi orbitals, the extended method also includes the sigma orbitals.The extended Hückel method can be...
.
This approach was developed in the 1950s by Rudolph Pariser
Rudolph Pariser
Rudolph Pariser is a physical and polymer chemist. He was born in Harbin, China to merchant parents. He attended the Von Hindenburg Schule in Harbin, an American Missionary School in Beijing and American School in Tokyo...
with Robert Parr
Robert Parr
Robert Ghormley Parr is a theoretical chemist. He is a chemistry professor at the University of North Carolina at Chapel Hill.-Career:...
and co-developed by John Pople
John Pople
Sir John Anthony Pople, KBE, FRS, was a Nobel-Prize winning theoretical chemist. Born in Burnham-on-Sea, Somerset, England, he attended Bristol Grammar School. He won a scholarship to Trinity College, Cambridge in 1943. He received his B. A. in 1946. Between 1945 and 1947 he worked at the Bristol...
. It is essentially a more efficient method of finding reasonable approximations of molecular orbital
Molecular orbital
In chemistry, a molecular orbital is a mathematical function describing the wave-like behavior of an electron in a molecule. This function can be used to calculate chemical and physical properties such as the probability of finding an electron in any specific region. The term "orbital" was first...
s, useful in predicting physical and chemical nature of the molecule under study since molecular orbital characteristics have implications with regards to both the basic structure
Chemical structure
A chemical structure includes molecular geometry, electronic structure and crystal structure of molecules. Molecular geometry refers to the spatial arrangement of atoms in a molecule and the chemical bonds that hold the atoms together. Molecular geometry can range from the very simple, such as...
and reactivity of a molecule. This method used the zero-differential overlap
Zero-differential overlap
Zero differential overlap is an approximation that is used to ignore certain integrals, usually two-electron repulsion integrals, in semi-empirical quantum chemistry methods quantum chemistry molecular orbital methods....
(ZDO) approximation to reduce the problem to reasonable size and complexity but still required modern solid state
Solid state (electronics)
Solid-state electronics are those circuits or devices built entirely from solid materials and in which the electrons, or other charge carriers, are confined entirely within the solid material...
computer
Computer
A computer is a programmable machine designed to sequentially and automatically carry out a sequence of arithmetic or logical operations. The particular sequence of operations can be changed readily, allowing the computer to solve more than one kind of problem...
s (as opposed to punched card
Punched card
A punched card, punch card, IBM card, or Hollerith card is a piece of stiff paper that contains digital information represented by the presence or absence of holes in predefined positions...
or vacuum tube
Vacuum tube
In electronics, a vacuum tube, electron tube , or thermionic valve , reduced to simply "tube" or "valve" in everyday parlance, is a device that relies on the flow of electric current through a vacuum...
systems) before becoming fully useful for molecules larger than benzene
Benzene
Benzene is an organic chemical compound. It is composed of 6 carbon atoms in a ring, with 1 hydrogen atom attached to each carbon atom, with the molecular formula C6H6....
.
Originally, Pariser's goal of using this method was to predict the characteristics of complex organic dyes, but this was never realized. The method has wide applicability in precise prediction of electronic transitions, particularly lower singlet
Singlet
A pair of spin-1/2 particles can be combined to form one of three states of total spin 1 called the triplet, or a state of spin 0 which is called the singlet. In theoretical physics, a singlet usually refers to a one-dimensional representation...
transitions, and found wide application in theoretical and applied quantum chemistry
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...
. The two basic papers on this subject were among the top five chemistry and physics citations reported in ISI, Current Contents 1977 for the period of 1961–1977 with a total of 2450 references.
In contrast to the Hartree–Fock-based semiempirical
Semi-empirical quantum chemistry methods
Semi-empirical quantum chemistry methods are based on the Hartree-Fock formalism, but make many approximations and obtain some parameters from empirical data. They are very important in computational chemistry for treating large molecules where the full Hartree-Fock method without the...
method counterparts (i.e.: MOPAC
MOPAC
In computational chemistry, MOPAC is a popular computer program designed to implement semi-empirical quantum chemistry algorithms, such as MINDO, MNDO, AM1, PM3, PM5, and . It was largely written in the group of Michael Dewar at University of Texas, Austin...
), the pi-electron theories have a very strong ab initio
Ab initio
ab initio is a Latin term used in English, meaning from the beginning.ab initio may also refer to:* Ab Initio , a leading ETL Tool Software Company in the field of Data Warehousing.* ab initio quantum chemistry methods...
basis. The PPP formulation is actually an approximate pi-electron effective operator, and the empirical parameters, in fact, include effective electron correlation effects. A rigorous, ab initio theory of the PPP method is provided by diagrammatic, multi-reference, high order perturbation theory (Freed, Brandow, Lindgren, etc.). (The exact formulation is non-trivial, and requires some field theory) Large scale ab initio calculations (Martin and Birge, Martin and Freed, Sheppard and Freed, etc.) have confirmed many of the approximations of the PPP model and explain why the PPP-like models work so well with such a simple formulation.