Size consistency
Encyclopedia
In quantum chemistry
, size consistency (or strict separability) is a property that guarantees the consistency
of the energy behavior when interaction between the involved molecular system is nullified (for example, by distance).
Let A and B be two non-interacting systems. If a given theory for the evaluation of the energy is size consistent, then the energy of the supersystem A-B is equal to the sum of the energy of A plus the energy of B taken by themselves (
). This property is of particular importance to obtain correctly behaving dissociation curves. Others have more recently argued that the entire potential energy surface should be well-defined.
Of the common quantum mechanical methods Hartree-Fock
, coupled cluster
, many-body perturbation theory
(to any order), and full configuration interaction
(CI) are size consistent. A major drawback of truncated CI is that it is not size-consistent and that the quality of the description decreases with increasing size of the system. The error in CISD calculations can be corrected with e.g. quadratic configuration interaction
. Sometimes numerical errors can cause a method that is formally size-consistent to behave
in a non-size-consistent manner.
Size-extensivity, on the other hand, is a more mathematically formal characteristic which refers to the correct (linear) scaling of a method with the number of electrons.
Core-extensivity is yet another related property, which extends to requirement to the proper treatment of excited states.
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...
, size consistency (or strict separability) is a property that guarantees the consistency
Consistency
Consistency can refer to:* Consistency , the psychological need to be consistent with prior acts and statements* "Consistency", an 1887 speech by Mark Twain...
of the energy behavior when interaction between the involved molecular system is nullified (for example, by distance).
Let A and B be two non-interacting systems. If a given theory for the evaluation of the energy is size consistent, then the energy of the supersystem A-B is equal to the sum of the energy of A plus the energy of B taken by themselves (
). This property is of particular importance to obtain correctly behaving dissociation curves. Others have more recently argued that the entire potential energy surface should be well-defined.Of the common quantum mechanical methods 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....
, coupled cluster
Coupled cluster
Coupled cluster is a numerical technique used for describing many-body systems. Its most common use is as one of several quantum chemical post-Hartree–Fock ab initio quantum chemistry methods in the field of computational chemistry...
, many-body perturbation theory
Perturbation theory (quantum mechanics)
In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. The idea is to start with a simple system for which a mathematical solution is known, and add an...
(to any order), and full configuration interaction
Configuration interaction
Configuration interaction is a post-Hartree–Fock linear variational method for solving the nonrelativistic Schrödinger equation within the Born–Oppenheimer approximation for a quantum chemical multi-electron system. Mathematically, configuration simply describes the linear combination...
(CI) are size consistent. A major drawback of truncated CI is that it is not size-consistent and that the quality of the description decreases with increasing size of the system. The error in CISD calculations can be corrected with e.g. quadratic configuration interaction
Quadratic configuration interaction
Quadratic configuration interaction is an extension of Configuration interaction that corrects for size-consistency errors in the all singles and double excitation CI methods ....
. Sometimes numerical errors can cause a method that is formally size-consistent to behave
in a non-size-consistent manner.
Size-extensivity, on the other hand, is a more mathematically formal characteristic which refers to the correct (linear) scaling of a method with the number of electrons.
Core-extensivity is yet another related property, which extends to requirement to the proper treatment of excited states.