from our computations, by “experiment” (checking calculations against reality),
good results. Basis functions are mathematical functions (usually Gaussian) that
work; atomic orbitals are functions, circumscribed by theory, that arise from
solution of the Schr€odinger equation.
References
- Levine IN (2000) Quantum chemistry, 5th edn. Prentice Hall, Upper Saddle River, NJ, chapter 6
- Levine IN (2000) Quantum chemistry,5th edn. Prentice Hall, Upper Saddle River, NJ, chapter 10
- Levine IN (2000) Quantum chemistry, 5th edn. Prentice Hall, Upper Saddle River, NJ, p 310
- Levine IN (2000) Quantum chemistry, 5th edn. Prentice Hall, Upper Saddle River, NJ,
section 15.4
Chapter 5, Harder Questions, Answers
Q7
One desirable feature of a basis set is that it should be “balanced”. How might a
basis set be unbalanced?
Recall from the answer to Q6 that a basis set is a collection of mathematical
functions that “work”. By an unbalanced basis set [1] one usually means a mixed set in
which a big basis has been placed on some atoms and a small basis on others. The
atom with a small basis steals basis functions from the other atoms, leading to
exaggerated basis set superposition error (BSSE) (Section 5.4.3) and a corresponding
error in energy. This pilfering of basis functions is aided by moving the function-
deficient atom closer to the function-rich one during geometry optimization, leading
to an error in geometry.
Reference
- Young D (2001) Computational chemistry. A practical guide for applying techniques to real
world problems. Wiley, New York, section 28.3
Chapter 5, Harder Questions, Answers
Q8
In a HF [Hartree–Fock] calculation, you can always get a lower energy (a “better”
energy, in the sense that it is closer to the true energy) for a molecule by using a
bigger basis set, as long as the HF limit has not been reached. Yet a bigger basis set
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