Semi-empirical quantum chemistry methods
Encyclopedia
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 approximations is too expensive. The use of empirical parameters appears to allow some inclusion of electron correlation effects into the methods.
Within the framework of Hartree-Fock calculations, some pieces of information (such as two-electron integrals) are sometimes approximated or completely omitted. In order to correct for this loss, semi-empirical methods are parametrized, that is their results are fitted by a set of parameters, normally in such a way as to produce results that best agree with experimental data, but sometimes to agree with ab initio
results.
Semi-empirical methods follow what are often called empirical methods where the two-electron part of the Hamiltonian
is not explicitly included. For π-electron systems, this was the Hückel method
proposed by Erich Hückel
. For all valence electron systems, the Extended Hückel method
was proposed by Roald Hoffmann
.
Semi-empirical calculations are much faster than their ab initio counterparts. Their results, however, can be very wrong if the molecule being computed is not similar enough to the molecules in the database used to parametrize the method.
Semi-empirical calculations have been most successful in the description of organic chemistry, where only a few elements are used extensively and molecules are of moderate size. However, semi-empirical methods were also applied to solids and nanostructures but with different parameterization.
As with empirical methods, we can distinguish methods that are:
or those:
the latter being by far the largest group of methods.
The table below shows some software packages that carry out semi-empirical methods, indicating the other methods that they include where applicable.
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...
methods are based on the Hartree-Fock
Hartree-Fock
In computational physics and chemistry, the Hartree–Fock method is an approximate method for the determination of the ground-state wave function and ground-state energy of a quantum many-body system....
formalism, but make many approximations and obtain some parameters from empirical data. They are very important 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...
for treating large molecules where the full Hartree-Fock method without the approximations is too expensive. The use of empirical parameters appears to allow some inclusion of electron correlation effects into the methods.
Within the framework of Hartree-Fock calculations, some pieces of information (such as two-electron integrals) are sometimes approximated or completely omitted. In order to correct for this loss, semi-empirical methods are parametrized, that is their results are fitted by a set of parameters, normally in such a way as to produce results that best agree with experimental data, but sometimes to agree with ab initio
Ab initio quantum chemistry methods
Ab initio quantum chemistry methods are computational chemistry methods based on quantum chemistry. The term ab initiowas first used in quantum chemistry by Robert Parr and coworkers, including David Craig in a semiempirical study on the excited states of benzene.The background is described by Parr...
results.
Semi-empirical methods follow what are often called empirical methods where the two-electron part of the Hamiltonian
Hamiltonian (quantum mechanics)
In quantum mechanics, the Hamiltonian H, also Ȟ or Ĥ, is the operator corresponding to the total energy of the system. Its spectrum is the set of possible outcomes when one measures the total energy of a system...
is not explicitly included. For π-electron systems, this was 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,...
proposed by Erich Hückel
Erich Hückel
Erich Armand Arthur Joseph Hückel was a German physicist and physical chemist. He is known for two major contributions:*The Debye–Hückel theory of electrolytic solutions...
. For all valence electron systems, the Extended Hückel 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...
was proposed by Roald Hoffmann
Roald Hoffmann
Roald Hoffmann is an American theoretical chemist who won the 1981 Nobel Prize in Chemistry. He currently teaches at Cornell University in Ithaca, New York.-Escape from the Holocaust:...
.
Semi-empirical calculations are much faster than their ab initio counterparts. Their results, however, can be very wrong if the molecule being computed is not similar enough to the molecules in the database used to parametrize the method.
Semi-empirical calculations have been most successful in the description of organic chemistry, where only a few elements are used extensively and molecules are of moderate size. However, semi-empirical methods were also applied to solids and nanostructures but with different parameterization.
As with empirical methods, we can distinguish methods that are:
- restricted to π-electrons. These method exist for the calculation of electronically excited states of polyenes, both cyclic and linear. These methods, such as the Pariser-Parr-Pople method (PPP), can provide good estimates of the π-electronic excited states, when parameterized well. Indeed, for many years, the PPP method outperformed ab initio excited state calculations.
or those:
- restricted to all valence electrons. These methods can be grouped into several groups:
- Methods such as CNDO/2CNDO/2CNDO is the abbreviation for Complete Neglect of Differential Overlap. Although CNDO is based on quantum chemistry, it is more specifically one of the first semi-empirical quantum chemistry methods. It uses two approximations:...
, INDOINDOINDO stands for Intermediate Neglect of Differential Overlap. It is a semi-empirical quantum chemistry method that is a development of the complete neglect of differential overlap method introduced by John Pople...
and NDDONDDONDDO 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...
that were introduced by John PopleJohn PopleSir 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...
. The implementations aimed to fit, not experiment, but ab initio minimum basis set results. These methods are now rarely used but the methodology is often the basis of later methods.
- Methods that are in the MOPACMOPACIn 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...
, AMPACAMPACAMPAC is a general-purpose semiempirical quantum chemistry program. It is marketed by Semichem, Inc. and was developed originally by Michael Dewar and his group....
, and/or SPARTANSpartan (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....
computer programs originally from the group of Michael Dewar. These are MINDOMINDOMINDO, 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...
, MNDOMNDOMNDO, 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...
, AM1, PM3PM3 (chemistry)PM3, or Parameterized Model number 3, 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....
, RM1 , PM6 and SAM1SAM1SAM1, or "Semiempirical ab initio Model 1", is a semiempirical quantum chemistry method for computing molecular properties. It is an implementation the general Neglect of Differential Diatomic Overlap integral approximation, and is efficient and accurate. Related methods are AM1, PM3 and the older...
. Here the objective is to use parameters to fit experimental heats of formation, dipole moments, ionization potentials, and geometries.
- Methods whose primary aim is to predict the geometries of coordination compounds, such as Sparkle/AM1, available for lanthanide complexes.
- Methods whose primary aim is to calculate excited states and hence predict electronic spectra. These include ZINDOZINDOZINDO is a semi-empirical quantum chemistry method used in computational chemistry. It is a development of the INDO method. It stands for Zerner's Intermediate Neglect of Differential Overlap, as it was developed by Michael Zerner...
and SINDOSINDOSINDO, or actually SINDO1, is one of many semi-empirical quantum chemistry methods. It stands for symmetric orthogonalised INDO and was developed by K. Jug and coworkers. Like MINDO, it is a development of the INDO method. The main development is the inclusion of d orbitals for atoms of the...
.
the latter being by far the largest group of methods.
The table below shows some software packages that carry out semi-empirical methods, indicating the other methods that they include where applicable.
| Package | Molecular Mechanics Molecular mechanics Molecular mechanics uses Newtonian mechanics to model molecular systems. The potential energy of all systems in molecular mechanics is calculated using force fields... |
Hartree-Fock Hartree-Fock In computational physics and chemistry, the Hartree–Fock method is an approximate method for the determination of the ground-state wave function and ground-state energy of a quantum many-body system.... |
Post-Hartree-Fock methods | Density Functional Theory Density functional theory Density functional theory is a quantum mechanical modelling method used in physics and chemistry to investigate the electronic structure of many-body systems, in particular atoms, molecules, and the condensed phases. With this theory, the properties of a many-electron system can be determined by... |
| 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.... |
N | N | N | N |
| 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... |
Y | Y | N | Y |
| 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... |
N | Y | Y | Y |
| 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,... |
N | Y | Y | Y |
| 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... |
Y | Y | Y | Y |
| MOLCAS MOLCAS MOLCAS is an ab initio computational chemistry program, developed at Lund University in collaboration with others. Focus in the program is placed on methods for calculating general electronic structures in molecular systems in both ground and excited states. MOLCAS is, in particular, designed to... |
Y | Y | Y | Y |
| 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... |
N | N | N | N |
| 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... |
Y | Y | Y | Y |
| PQS PQS (chemical) PQS is a general purpose quantum chemistry program. Its roots go back to the first ab initio gradient program developed in Professor Peter Pulay's group but now it is developed and distributed commercially by Parallel Quantum Solutions. There is a reduction in cost for academic users and a site... |
Y | Y | Y | Y |
| 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.... |
Y | Y | Y | Y |
| SPARTAN Student 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.... |
Y | Y | Y | Y |
| VASP Vienna Ab-initio Simulation Package The Vienna Ab-initio Simulation Package, better known as VASP, is a package for performing ab initio quantum mechanical molecular dynamics using either Vanderbilt pseudopotentials, or the Projector Augmented Wave Method, and a plane wave basis set... |
N | Y | Y | Y |