Basis set superposition error
Encyclopedia
In quantum chemistry
, calculations of molecular properties are susceptible to basis set superposition error (BSSE) if they use finite basis sets
. As the atoms of interacting molecules (or of different parts of the same molecule) 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
. 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
with one in which all the projector-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.) Though conceptually very different, the two methods tend to give similar results.
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...
, calculations of molecular properties are susceptible to basis set superposition error (BSSE) if they use finite basis sets
Basis set (chemistry)
A basis set in chemistry is a set of functions used to create the molecular orbitals, which are expanded as a linear combination of such functions with the weights or coefficients to be determined. Usually these functions are atomic orbitals, in that they are centered on atoms. Otherwise, the...
. As the atoms of interacting molecules (or of different parts of the same molecule) 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
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...
. 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 (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...
with one in which all the projector-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.) Though conceptually very different, the two methods tend to give similar results.
See also
- Basis set (chemistry)Basis set (chemistry)A basis set in chemistry is a set of functions used to create the molecular orbitals, which are expanded as a linear combination of such functions with the weights or coefficients to be determined. Usually these functions are atomic orbitals, in that they are centered on atoms. Otherwise, the...
- Quantum chemistryQuantum chemistryQuantum chemistry is a branch of chemistry whose primary focus is the application of quantum mechanics in physical models and experiments of chemical systems...
- Quantum chemistry computer programsQuantum chemistry computer programsQuantum chemistry computer programs are used in computational chemistry to implement the methods of quantum chemistry. Most include the Hartree–Fock and some post-Hartree–Fock methods. They may also include density functional theory , molecular mechanics or semi-empirical quantum...