PM3, or Parameterized Model number 3, is a semi-empirical

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 for the quantum

Quantum mechanics

Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

 calculation of molecular electronic structure in computational chemistry

Computational chemistry

Computational chemistry is a branch of chemistry that uses principles of computer science to assist in solving chemical problems. It uses the results of theoretical chemistry, incorporated into efficient computer programs, to calculate the structures and properties of molecules and solids...

. It is based on the Neglect of Differential Diatomic Overlap

NDDO

NDDO stands for neglect of diatomic differential overlap. The formalism was first introduced by John Pople and it is now the basis of most successful semiempirical methods. While INDO added all one-centre two electron integrals to the CNDO/2 formalism, NDDO adds all two centre integrals for...

 integral approximation.

The PM3 method uses the same formalism and equations as the AM1 method. The only differences are: 1) PM3 uses two Gaussian functions for the core repulsion function, instead of the variable number used by AM1 (which uses between one and four Gaussians per element); 2) the numerical values of the parameters are different. The other differences lie in the philosophy and methodology used during the parameterization: whereas AM1 takes some of the parameter values from spectroscopical measurements, PM3 treats them as optimizable values.

The method was developed by J. J. P. Stewart and first published in 1989. It is implemented in the 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...

 program (of which the older versions are public domain), along with the related RM1, AM1, MNDO

MNDO

MNDO, or Modified Neglect of Differential Overlap is a semi-empirical method for the quantum calculation of molecular electronic structure in computational chemistry. It is based on the Neglect of Differential Diatomic Overlap integral approximation. Similarly, this method replaced the earlier...

 and MINDO

MINDO

MINDO, or Modified Intermediate Neglect of Differential Overlap is a semi-empirical method for the quantum calculation of molecular electronic structure in computational chemistry. It is based on the Intermediate Neglect of Differential Overlap method of John Pople. It was developed by the group...

 methods, and in several other programs such as GAUSSIAN

GAUSSIAN

Gaussian is a computational chemistry software program initially released in 1970 by John Pople and his research group at Carnegie-Mellon University as Gaussian 70. It has been continuously updated since then...

, CP2K

CP2K

CP2K is a freely available program, written in Fortran 95, to perform atomistic and molecular simulations of solid state, liquid, molecular and biological systems...

, GAMESS (US)

GAMESS (US)

GAMESS is a computational chemistry software program that stands for General Atomic and Molecular Electronic Structure System. The original code started on October 1, 1977 as a National Resources for Computations in Chemistry project. In 1981, the code base split into GAMESS and GAMESS variants,...

, GAMESS (UK)

GAMESS (UK)

GAMESS is a computational chemistry software program that stands for General Atomic and Molecular Electronic Structure System. The original code split in 1981 into GAMESS and GAMESS variants, which now differ significantly...

, PC GAMESS

PC GAMESS

PC GAMESS/Firefly is an ab initio computational chemistry program for Intel-compatible x86, x86-64 processors based on GAMESS sources. However, it has mostly been rewritten , especially in platform-specific parts , mathematic functions , and quantum chemical methods PC GAMESS/Firefly is an ab...

, Chem3D, AMPAC

AMPAC

AMPAC is a general-purpose semiempirical quantum chemistry program. It is marketed by Semichem, Inc. and was developed originally by Michael Dewar and his group....

, ArgusLab, BOSS, and SPARTAN

Spartan (software)

SPARTAN is a molecular modeling and computational chemistry application from . It contains code for molecular mechanics, semi-empirical methods, ab initio models, density functional models, post-Hartree-Fock models, and thermochemical recipes including T1....

.

The original PM3 publication included parameters for the following elements: H

Hydrogen

Hydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly...

, C

Carbon

Carbon is the chemical element with symbol C and atomic number 6. As a member of group 14 on the periodic table, it is nonmetallic and tetravalent—making four electrons available to form covalent chemical bonds...

, N

Nitrogen

Nitrogen is a chemical element that has the symbol N, atomic number of 7 and atomic mass 14.00674 u. Elemental nitrogen is a colorless, odorless, tasteless, and mostly inert diatomic gas at standard conditions, constituting 78.08% by volume of Earth's atmosphere...

, O

Oxygen

Oxygen is the element with atomic number 8 and represented by the symbol O. Its name derives from the Greek roots ὀξύς and -γενής , because at the time of naming, it was mistakenly thought that all acids required oxygen in their composition...

, F

Fluorine

Fluorine is the chemical element with atomic number 9, represented by the symbol F. It is the lightest element of the halogen column of the periodic table and has a single stable isotope, fluorine-19. At standard pressure and temperature, fluorine is a pale yellow gas composed of diatomic...

, Al, Si

Silicon

Silicon is a chemical element with the symbol Si and atomic number 14. A tetravalent metalloid, it is less reactive than its chemical analog carbon, the nonmetal directly above it in the periodic table, but more reactive than germanium, the metalloid directly below it in the table...

, P

Phosphorus

Phosphorus is the chemical element that has the symbol P and atomic number 15. A multivalent nonmetal of the nitrogen group, phosphorus as a mineral is almost always present in its maximally oxidized state, as inorganic phosphate rocks...

, S

Sulfur

Sulfur or sulphur is the chemical element with atomic number 16. In the periodic table it is represented by the symbol S. It is an abundant, multivalent non-metal. Under normal conditions, sulfur atoms form cyclic octatomic molecules with chemical formula S8. Elemental sulfur is a bright yellow...

, Cl

Chlorine

Chlorine is the chemical element with atomic number 17 and symbol Cl. It is the second lightest halogen, found in the periodic table in group 17. The element forms diatomic molecules under standard conditions, called dichlorine...

, Br

Bromine

Bromine ") is a chemical element with the symbol Br, an atomic number of 35, and an atomic mass of 79.904. It is in the halogen element group. The element was isolated independently by two chemists, Carl Jacob Löwig and Antoine Jerome Balard, in 1825–1826...

, and I

Iodine

Iodine is a chemical element with the symbol I and atomic number 53. The name is pronounced , , or . The name is from the , meaning violet or purple, due to the color of elemental iodine vapor....

.

The PM3 implementation in the SPARTAN

Spartan (software)

SPARTAN is a molecular modeling and computational chemistry application from . It contains code for molecular mechanics, semi-empirical methods, ab initio models, density functional models, post-Hartree-Fock models, and thermochemical recipes including T1....

 program includes PM3tm with additional extensions for transition metals supporting calculations on Ca

Calcium

Calcium is the chemical element with the symbol Ca and atomic number 20. It has an atomic mass of 40.078 amu. Calcium is a soft gray alkaline earth metal, and is the fifth-most-abundant element by mass in the Earth's crust...

, Ti

Titanium

Titanium is a chemical element with the symbol Ti and atomic number 22. It has a low density and is a strong, lustrous, corrosion-resistant transition metal with a silver color....

, V

Vanadium

Vanadium is a chemical element with the symbol V and atomic number 23. It is a hard, silvery gray, ductile and malleable transition metal. The formation of an oxide layer stabilizes the metal against oxidation. The element is found only in chemically combined form in nature...

, Cr

Chromium

Chromium is a chemical element which has the symbol Cr and atomic number 24. It is the first element in Group 6. It is a steely-gray, lustrous, hard metal that takes a high polish and has a high melting point. It is also odorless, tasteless, and malleable...

, Mn

Manganese

Manganese is a chemical element, designated by the symbol Mn. It has the atomic number 25. It is found as a free element in nature , and in many minerals...

, Fe

Iron

Iron is a chemical element with the symbol Fe and atomic number 26. It is a metal in the first transition series. It is the most common element forming the planet Earth as a whole, forming much of Earth's outer and inner core. It is the fourth most common element in the Earth's crust...

, Co

Cobalt

Cobalt is a chemical element with symbol Co and atomic number 27. It is found naturally only in chemically combined form. The free element, produced by reductive smelting, is a hard, lustrous, silver-gray metal....

, Ni

Nickel

Nickel is a chemical element with the chemical symbol Ni and atomic number 28. It is a silvery-white lustrous metal with a slight golden tinge. Nickel belongs to the transition metals and is hard and ductile...

, Cu

Copper

Copper is a chemical element with the symbol Cu and atomic number 29. It is a ductile metal with very high thermal and electrical conductivity. Pure copper is soft and malleable; an exposed surface has a reddish-orange tarnish...

, Zn

Zinc

Zinc , or spelter , is a metallic chemical element; it has the symbol Zn and atomic number 30. It is the first element in group 12 of the periodic table. Zinc is, in some respects, chemically similar to magnesium, because its ion is of similar size and its only common oxidation state is +2...

, Zr

Zirconium

Zirconium is a chemical element with the symbol Zr and atomic number 40. The name of zirconium is taken from the mineral zircon. Its atomic mass is 91.224. It is a lustrous, grey-white, strong transition metal that resembles titanium...

, Mo

Molybdenum

Molybdenum , is a Group 6 chemical element with the symbol Mo and atomic number 42. The name is from Neo-Latin Molybdaenum, from Ancient Greek , meaning lead, itself proposed as a loanword from Anatolian Luvian and Lydian languages, since its ores were confused with lead ores...

, Tc, Ru

Ruthenium

Ruthenium is a chemical element with symbol Ru and atomic number 44. It is a rare transition metal belonging to the platinum group of the periodic table. Like the other metals of the platinum group, ruthenium is inert to most chemicals. The Russian scientist Karl Ernst Claus discovered the element...

, Rh

Rhodium

Rhodium is a chemical element that is a rare, silvery-white, hard and chemically inert transition metal and a member of the platinum group. It has the chemical symbol Rh and atomic number 45. It is composed of only one isotope, 103Rh. Naturally occurring rhodium is found as the free metal, alloyed...

, Pd, Hf

Hafnium

Hafnium is a chemical element with the symbol Hf and atomic number 72. A lustrous, silvery gray, tetravalent transition metal, hafnium chemically resembles zirconium and is found in zirconium minerals. Its existence was predicted by Dmitri Mendeleev in 1869. Hafnium was the penultimate stable...

, Ta

Tantalum

Tantalum is a chemical element with the symbol Ta and atomic number 73. Previously known as tantalium, the name comes from Tantalus, a character in Greek mythology. Tantalum is a rare, hard, blue-gray, lustrous transition metal that is highly corrosion resistant. It is part of the refractory...

, W

Tungsten

Tungsten , also known as wolfram , is a chemical element with the chemical symbol W and atomic number 74.A hard, rare metal under standard conditions when uncombined, tungsten is found naturally on Earth only in chemical compounds. It was identified as a new element in 1781, and first isolated as...

, Re

Rhenium

Rhenium is a chemical element with the symbol Re and atomic number 75. It is a silvery-white, heavy, third-row transition metal in group 7 of the periodic table. With an average concentration of 1 part per billion , rhenium is one of the rarest elements in the Earth's crust. The free element has...

, Os

Osmium

Osmium is a chemical element with the symbol Os and atomic number 76. Osmium is a hard, brittle, blue-gray or blue-blacktransition metal in the platinum family, and is the densest natural element. Osmium is twice as dense as lead. The density of osmium is , slightly greater than that of iridium,...

, Ir

Iridium

Iridium is the chemical element with atomic number 77, and is represented by the symbol Ir. A very hard, brittle, silvery-white transition metal of the platinum family, iridium is the second-densest element and is the most corrosion-resistant metal, even at temperatures as high as 2000 °C...

, Pt

Platinum

Platinum is a chemical element with the chemical symbol Pt and an atomic number of 78. Its name is derived from the Spanish term platina del Pinto, which is literally translated into "little silver of the Pinto River." It is a dense, malleable, ductile, precious, gray-white transition metal...

, and Gd

Gadolinium

Gadolinium is a chemical element with the symbol Gd and atomic number 64. It is a silvery-white, malleable and ductile rare-earth metal. It is found in nature only in combined form. Gadolinium was first detected spectroscopically in 1880 by de Marignac who separated its oxide and is credited with...

. Many other elements, mostly metals, have been parameterized in subsequent work.

A model for the PM3 calculation of lanthanide complexes, called Sparkle/PM3, was also introduced.