In
quantum chemistry
Quantum chemistry, also called molecular quantum mechanics, is a branch of physical chemistry focused on the application of quantum mechanics to chemical systems, particularly towards the quantum-mechanical calculation of electronic contributions ...
, calculations using finite
basis sets
Basis may refer to:
Finance and accounting
*Adjusted basis, the net cost of an asset after adjusting for various tax-related items
*Basis point, 0.01%, often used in the context of interest rates
*Basis trading, a trading strategy consisting of ...
are susceptible to basis set superposition error (BSSE). As the atoms of interacting molecules (or of different parts of the same molecule - intramolecular BSSE)
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
In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat a ...
.
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), basis set mixing is prevented ''a priori'', by replacing the conventional
Hamiltonian
Hamiltonian may refer to:
* Hamiltonian mechanics, a function that represents the total energy of a system
* Hamiltonian (quantum mechanics), an operator corresponding to the total energy of that system
** Dyall Hamiltonian, a modified Hamiltonian ...
with one in which all the
projector
A projector or image projector is an optical device that projects an image (or moving images) onto a surface, commonly a projection screen. Most projectors create an image by shining a light through a small transparent lens, but some newer types ...
-containing terms that would allow mixing have been removed. In the ''counterpoise method'' (CP), 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. 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. The errors inherent in either BSSE correction disappear more rapidly than the total value of BSSE in larger basis sets.
See also
*
Basis set (chemistry)
In theoretical and computational chemistry, a basis set is a set of functions (called basis functions) that is used to represent the electronic wave function in the Hartree–Fock method or density-functional theory in order to turn the partial ...
*
Quantum chemistry
Quantum chemistry, also called molecular quantum mechanics, is a branch of physical chemistry focused on the application of quantum mechanics to chemical systems, particularly towards the quantum-mechanical calculation of electronic contributions ...
*
Quantum chemistry computer programs
Quantum chemistry computer programs are used in computational chemistry to implement the methods of quantum chemistry. Most include the Hartree–Fock (HF) and some post-Hartree–Fock methods. They may also include density functional theory (DFT ...
References
Quantum chemistry
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