Basis set superposition error

In quantum chemistry, calculations using finite basis sets are susceptible to basis set superposition error (BSSE). As the atoms of interacting molecules (or of different parts of the same molecule - intramolecular BSSE){{cite journal |journal=J. Chem. Phys. |doi=10.1063/1.2997349 |title=Enthalpy difference between conformations of normal alkanes: Intramolecular basis set superposition error (BSSE) in the case of n-butane and n-hexane |year=2008 |volume = 129 |pages = 164101 |first=Roman M. |last=Balabin|authorlink=Roman Balabin |pmid=19045241 |issue=16|bibcode = 2008JChPh.129p4101B }}{{cite book | last = Hobza | first = Pavel | author2 = Müller-Dethlefs, Klaus | title = Non-covalent Interactions: Theory and Experiment | publisher = Royal Society of Chemistry | year = 2010 | location = Cambridge, England | pages = 13 | isbn = 978-1-84755-853-4 | url = http://www.rsc.org/ebooks/archive/free/BK9781847558534/BK9781847558534-00001.pdf | access-date = 2010-05-21 | archive-url = https://web.archive.org/web/20110606123609/http://www.rsc.org/ebooks/archive/free/BK9781847558534/BK9781847558534-00001.pdf | archive-date = 2011-06-06 | url-status = dead }} approach one another, their basis functions overlap. Each monomer "borrows" functions from other nearby components, effectively increasing its basis set and improving the calculation of derived properties such as energy.{{cite journal |last1=Liedl |first1=Klaus R. |title=Dangers of counterpoise corrected hypersurfaces. Advantages of basis set superposition improvement |journal=The Journal of Chemical Physics |year=1998 |volume=108 |issue=8 |pages=3199–3204 |doi=10.1063/1.475715|bibcode=1998JChPh.108.3199L |doi-access=free }} If the total energy is minimised as a function of the system geometry, the short-range energies from the mixed basis sets must be compared with the long-range energies from the unmixed sets, and this mismatch introduces an error.

Other than using infinite basis sets, two methods exist to eliminate the BSSE. In the chemical Hamiltonian approach (CHA),{{cite journal |doi=10.1063/1.476931 |first=I. |last=Mayer |author2=Valiron, P. |title=Second order Møller–Plesset perturbation theory without basis set superposition error |journal=J. Chem. Phys. |year=1998 |volume=109 |issue=9 |pages=3360–3373 |bibcode = 1998JChPh.109.3360M |doi-access=free }}{{cite web |author=Bende, Attila |title=THE CHEMICAL HAMILTONIAN APPROACH (CHA) |url=http://www.itim-cj.ro/~bende/Cha.html |url-status=dead |archive-url=https://web.archive.org/web/20120306161925/http://www.itim-cj.ro/~bende/Cha.html |archive-date=6 March 2012 |accessdate=14 May 2010}} basis set mixing is prevented a priori, by replacing the conventional Hamiltonian with one in which all the projector-containing terms that would allow mixing have been removed. In the counterpoise method (CP),{{cite journal |doi=10.1021/cr00031a007 |first=Frans B. |last=Van Duijneveldt |author2=van Duijneveldt-van de Rijdt, Jeanne G. C. M.|author3= van Lenthe, Joop H. |title=State of the art in counterpoise theory |journal=Chem. Rev. |year=1994 |volume=94 |issue=7 |pages=1873–1885 }}{{cite web

|url = http://qcl.theochem.tu-muenchen.de/qcl/help/counterpoise_e.html

|title = Counterpoise Correction

|author = Rösch, N.

|year = 2003

|location = Technical University of Munich, Quantum Chemistry Laboratory

|accessdate = 14 May 2010

|archive-date = 18 April 2015

|archive-url = https://web.archive.org/web/20150418002539/http://qcl.theochem.tu-muenchen.de/qcl/help/counterpoise_e.html

|url-status = dead

}}{{cite web

| url = http://stark.udg.es/~perico/bbopt.html

| title = Counterpoise Corrected Potential Energy Surfaces

| author = Sedano, Pedro Salvador

| year = 2000

| location = University of Girona

| accessdate = 14 May 2010

}} the BSSE is calculated by re-performing all the calculations using the mixed basis sets, and the error is then subtracted a posteriori from the uncorrected energy. (The mixed basis sets are realised by introducing "ghost orbitals", basis set functions which have no electrons or protons. It however has been shown that there is an inherent danger in using counterpoise corrected energy surfaces, due to the inconsistent effect of the correction in different areas of the energy surface.) Though conceptually very different, the two methods tend to give similar results.{{cite journal |doi=10.1002/(SICI)1096-987X(19980430)19:6<575::AID-JCC1>3.0.CO;2-O |first=Béla |last=Paizs |author2=Suhai, Sándor |title=Comparative study of BSSE correction methods at DFT and MP2 levels of theory |year=1998 |journal=J. Comput. Chem. |volume=19 |issue=6 |pages=575–584 }} It also has been shown that the error is often larger when using the CP method since the central atoms in the system have much greater freedom to mix with all of the available functions compared to the outer atoms. Whereas in the CHA model, those orbitals have no greater intrinsic freedom and therefore the correction treats all fragments equally.{{cite journal |doi=10.1021/ct400990u |first=Lukasz |last=Mentel |author2=Baerends, Evert Jan |title=Can the Counterpoise Correction for Basis Set Superposition Effect Be Justified? |year=2013 |journal=J. Comput. Chem. |volume=10 |issue=1 |pages=252–267 |pmid=26579908 }} The errors inherent in either BSSE correction disappear more rapidly than the total value of BSSE in larger basis sets.{{cite journal |doi=10.1002/qua.10827|first=I. |last=Mayer |title=Interrelations between the a priori and a posteriori BSSE correction schemes. |year=2004 |journal=Int. J. Quantum Chem. |volume=100 |issue=4 |pages=559–566 }}

See also

References

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Category:Quantum chemistry

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