In quantum chemistry, size consistency and size extensivity are concepts relating to how the behaviour of quantum chemistry calculations changes with size. Size consistency (or strict separability) is a property that guarantees the consistency of the energy behaviour when interaction between the involved molecular system is nullified (for example, by distance). Size-extensivity, introduced by Bartlett, is a more mathematically formal characteristic which refers to the correct (linear) scaling of a method with the number of electrons.[1]
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, separated by a sufficiently large distance so there is essentially no shared electron density, is equal to the sum of the energy of A plus the energy of B taken by themselves . This property of size consistency 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.[2]
Size consistency and size extensivity are sometimes used interchangeably in the literature, However, there are very important distinctions to be made between them.[3] Hartree–Fock, coupled cluster, many-body perturbation theory (to any order), and full configuration interaction (FCI) are size extensive but not always size consistent. For example, the Restricted Hartree–Fock model is not able to correctly describe the dissociation curves of H2 and therefore all post HF methods that employ HF as a starting point will fail in that matter (so-called single-reference methods). Sometimes numerical errors can cause a method that is formally size-consistent to behave in a non-size-consistent manner.[4]
Core-extensivity is yet another related property, which extends the requirement to the proper treatment of excited states.[5]
^Bartlett, R. J. (1981). "Many-Body Perturbation Theory and Coupled Cluster Theory for Electron Correlation in Molecules". Annual Review of Physical Chemistry. 32: 359. Bibcode:1981ARPC...32..359B. doi:10.1146/annurev.pc.32.100181.002043.
^Taylor, P. R. (1994). "Coupled-cluster Methods in Quantum Chemistry". In Roos, Björn O. (ed.). Lecture Notes in Quantum Chemistry: European Summer School. Lecture Notes in Chemistry. Vol. 64. Berlin: Springer-Verlag. pp. 125–202. doi:10.1007/978-3-642-57890-8_3. ISBN 978-3-642-57890-8.
^"Size-Extensivity and Size-Consistency". Uam.es. 1995-01-20. Archived from the original on 2017-06-06. Retrieved 2014-02-01.
^Van Dam, Huub; Van Lenthe, Joop; Pulay, Peter (1998). "The size consistency of multi-reference Møller-Plesset perturbation theory". Molecular Physics. 93 (3): 431. Bibcode:1998MolPh..93..431V. doi:10.1080/002689798169122.
^Mukhopadhyay, S; Chaudhuri, Rajat; Mukhopadhyay, Debasis; Mukherjee, Debashis (1990). "A comparative study of core-extensive and core—valence-extensive coupled-cluster theories for energy differences: Excitation energies". Chemical Physics Letters. 173 (2–3): 181. Bibcode:1990CPL...173..181M. doi:10.1016/0009-2614(90)80074-N.
and 28 Related for: Size consistency and size extensivity information
chemistry, sizeconsistencyandsizeextensivity are concepts relating to how the behaviour of quantum chemistry calculations changes with size. Size consistency...
both sizeconsistencyandsizeextensivity of CISD energies. Therefore, Davidson correction is frequently referred to in literature as size-consistency correction...
adenopathy is a disease of the lymph nodes, in which they are abnormal in size or consistency. Lymphadenopathy of an inflammatory type (the most common type) is...
production, are texture, structure, bulk density, porosity, consistency, temperature, colour and resistivity. Soil texture is determined by the relative proportion...
from liquid silicone rubber (LSR), but some seem to be made from high-consistency rubber (HCR). While LSR is indeed liquid, HCR is a putty-like material...
guarantees the sizeextensivity of the solution. Sizeconsistency in CC theory, also unlike other theories, does not depend on the sizeconsistency of the reference...
fibre, and diluted to as uniform and constant as possible consistency. The pH is controlled and various fillers, such as whitening agents, sizeand wet strength...
consistency to function mentally in the real world. A person who experiences internal inconsistency tends to become psychologically uncomfortable and...
automotive and truck scrap tires. During the recycling process, steel and tire cord (fluff) are removed, leaving tire rubber with a granular consistency. Continued...
invasive ductal carcinoma NOS, and invasive carcinoma NST all refer to the same type of breast cancer. For consistencyand to serve an international audience...
74,000 years old. The specimens are not fossilized and have been described as having "the consistency of wet blotting paper". Once exposed, the bones had...
Disputes regarding the internal consistencyand textual integrity of the Bible have a long history. Classic texts that discuss questions of inconsistency...
consistent. Most methods being used in practice attain higher order. Consistency is a necessary condition for convergence[citation needed], but not sufficient;...
transparency, still and motion picture films previously available in many formats, including 35 mm and sheet sizes to 11 × 14 inch size. Ektachrome has a...
range in sizeand behavior from the three largest species alive, the Mekong giant catfish from Southeast Asia, the wels catfish of Eurasia, and the piraíba...
about the possible sizes of infinite sets. It states: "There is no set whose cardinality is strictly between that of the integers and the real numbers."...
contractility, consistency, and their capacity to bleed. The optimal timing of performing wound debridement and closure is debated and dependent on the...
paint is the traditional medium for impasto painting, due to its thick consistencyand slow drying time. Acrylic paint can also be used for impasto by adding...
regularly winter in the Aleutian island chain and do so broadly and with a fair amount of consistency in much of southern Canada, from British Columbia to Labrador...
Solonen, T.; Byholm, P.; Huhta, E.; Tøttrup Nielsen, J. and Tornberg, R. 2012. "Spatial consistency in susceptibility of prey species to predation by two...
design consistencyand shifting resources towards quality control. For the 1966 model year, to better compete with the Cadillac Coupe de Ville and the Imperial...
of plants being grown and why, and the consistency of water and nutrient delivery. Hydroponics is often favored by farmers and growers of edible crops...
SECURITY), etc. "Online" and "offline" are synonymous with "mounted" and "not mounted". While storage devices usually have their size expressed in powers of...
choice that was made to maintain consistency with earlier films. Horner said "we knew Velociraptor should have feathers and be more colorful, but we couldn't...
trapped behind the bullet, slightly greater (consistency in) muzzle velocities, and increased accuracy and ease of maintenance.[better source needed] The...
sand to reduce shrinkage. The clay is first ground and mixed with water to the desired consistency. The clay is then pressed into steel moulds with a...
terrestrial mammals: about 36%, compared to 4% in cow milk. This gives it a consistency similar to cottage cheese, which prevents it from dissolving in the water...
instance reduces the surface tension between water and solids) it allows bubbles of a desired size to form. These are created during concrete mixing (while...