By Warren J Hehre

ISBN-10: 189066118X

ISBN-13: 9781890661182

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**Extra resources for A Guide to Molecular Mechanics and Quantum Chemical Calculations**

**Example text**

Born-Oppenheimer Approximation One way to simplify the Schrödinger equation for molecular systems is to assume that the nuclei do not move. Of course, nuclei do move, but their motion is “slow” compared to the speed at which electrons move (the speed of light). This is called the Born-Oppenheimer approximation, and leads to an “electronic” Schrödinger equation. (4) ˆ elΨel = EelΨel H Hˆ el = 1 2 electron s Σ i ∇i2 electron s nuclei Σ Σ i A ZA riA ΣΣ electron s + i

The fact that the determinant form satisfies this requirement follows from the fact that different electrons correspond to different rows in the determinant. Interchanging the coordinates of two electrons is, therefore, equivalent to interchanging two rows in the determinant which, according to the properties of determinants, multiplies the value of the determinant by -1. * The set of molecular orbitals leading to the lowest energy are obtained by a process referred to as a “self-consistent-field” or SCF procedure.

Also important, is that if at all possible, the magnitude of the error of the calculated energy should increase roughly in proportion to molecular size, that is, the model should be “size consistent”. Only then is it reasonable to anticipate that reaction energies can be properly described. Somewhat less important, but highly desirable, is that the model energy should represent a bound to the exact (Schrödinger) energy, that is, the model should be “variational”. Finally, a model needs to be “practical”, that is, able to be applied not only to very simple or idealized systems, but also to problems which are actually of interest.

### A Guide to Molecular Mechanics and Quantum Chemical Calculations by Warren J Hehre

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