References
- Bethe HA, Salpeter E (1957) Quantum mechanics of one-and two-electron atoms. Academic,
New York. (a) pp 58, 182, 185. (b) pp 182, 186. (c) p 102 - (a) Bowman JL (2008) Science 319:40. (b) Garand E, Zhou J, Manolopoulos DE, Alexander
MH, Neumark DM (2008) Science 319:72 (Erratum: Science, 2008, 320:612). (c) Chapter 2,
section 2.3. - Dewar MJS (1992) A semiempirical life. American Chemical Society, Washington DC, p 129
Chapter 5, Harder Questions, Answers
Q2
Can the Schr€odinger equation be solvedexactlyfor a species with two protons and
one electron? Why or why not?
This is the the simplest possible molecule, the hydrogen molecule ion, H 2 +,a
known entity [1]. Strictly speaking, this presents a three-body problem – two
protons and an electron – which cannot be solved exactly [2]. To a good approxi-
mation, however, the protons can be taken as stationary compared to the electron
(the Born–Oppenheimer principle) andthissystem can be solved exactly [3].
References
- Thomson JJ (1907) Philos Mag VI 561
- But see Lopez X, Ugalde JM, Echevarrı ́a L, Luden ̃a EV (2006) Phys Rev A 74:042504
- (a) Levine IN (2000) Quantum chemistry, 5th edn. Prentice Hall, Upper Saddle River, NJ,
section 13.4. (b) Lowe JP (1977) Quantum chemistry. Academic, New York, section 7–5
Chapter 5, Harder Questions, Answers
Q3
The input for anab initiocalculation (or a semiempirical calculation of the type
discussed in Chapter 6, or a DFT calculation – Chapter 7) on a molecule is usually
just the Cartesian coordinates of the atoms (plus the charge and multiplicity). So
how does the program know where the bonds are, i.e. what the structural formula of
the molecule is?
What is a bond? At one level, the answer is simple: it is a connector between two
atoms (we are talking about covalent bonds, not ionic “bonds”, which are a mere
622 Answers