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raman
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1: Why are the elements of a basis set taken to be orthogonal? But in real sense atomic orbitals do overlap.
JPRitchie said:The number of basis functions involved in heavy atom electronic structure calculations are small compared to those needed for proteins. The smallest known protein has about 45 residues, and a couple of hundred atoms. This results in thousands of basis functions.
Now if you add a transition metal or two, then you've really got a lot. Not only do you have to compute a lot of integrals, but you have to form and diagonalize the Fock matrix or something like it.
Post-HF treatments are needed, in any case, for reliable results, and that's really out there for these systems.
-Jim Ritchie
Orthogonality in basis sets refers to the property of basis functions (such as atomic orbitals) being perpendicular or independent of each other. This means that the overlap between different basis functions is zero, allowing for accurate and efficient calculations in quantum chemistry.
Orthogonality is important in basis sets because it ensures that the basis functions are not affecting each other's contributions to the overall wavefunction. This allows for better separation and understanding of the different contributions in a quantum system.
Orthogonality is achieved in basis sets by carefully choosing the shape and size of the basis functions. This is typically done by using orthogonal polynomials, such as the spherical harmonics, which have the desired orthogonality properties.
Yes, basis functions can still have some overlap even if they are considered orthogonal. This is because the mathematical definition of orthogonality only requires a zero overlap to be considered orthogonal, but in practice, there may still be some small overlap due to the finite precision of calculations.
Orthogonality plays a crucial role in the accuracy of calculations in quantum chemistry. By ensuring that the basis functions are independent of each other, orthogonality reduces the amount of computational effort needed to accurately describe a system. This leads to more efficient and reliable results in quantum chemical calculations.