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Chapter 9: Problem 19

Use the AM1 and PM3 semiempirical methods to compute the equilibrium bond lengths and enthalpies of formation of (a) ethanol, (b) 1,4 -dichlorobenzene.

Short Answer

Expert verified
Results will vary depending on the program used and its specific implementation of the AM1 and PM3 methods. It's important to not only consider the raw numerical output, but also the differences in these values between methods, to understand their relative strengths and weaknesses.

Step by step solution

01

Setup the Molecule for Calculation

Use a molecular editor to draw the molecules of ethanol and 1,4-dichlorobenzene. Save the molecular structures in a file format that the calculation program supports.
02

Run the AM1 Calculation

Load the molecular structure files into the semiempirical calculation program you are using. Choose the AM1 method and start the calculation. Once the calculation is complete, the program should provide information including the equilibrium bond lengths and enthalpies of formation.
03

Run the PM3 Calculation

Repeat step 2, but choose the PM3 method this time. Again, note the equilibrium bond lengths and enthalpies of formation for each compound.
04

Interpret Results

Compare the results from the AM1 and PM3 methods. Calculate the difference in predicted equilibrium bond lengths and enthalpies of formation modes to see which model offers a better prediction.

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Most popular questions from this chapter

Consider the two-clectron integrals over the basis functions defined in eqn 9.17 . If the basis functions are taken to be real, a number of the integrals are equivalent; for example, \((a b | c d)=(a d | c b)\). Find the other integrals that are equal to \((a b | c d)\)

Consider two Slater determinants \(\Phi_{1}\) and \(\Phi_{2}\) that differ by only one spinorbital; that is, $$\begin{array}{l} \Phi_{1}=\left\|\cdots \varphi_{m} \varphi_{i} \cdots\right\| \\ \Phi_{2}=\left\|\cdots \varphi_{p} \varphi_{i} \cdots\right\| \end{array}$$ Derive the following Condon-Slater rule: $$\begin{aligned} \left\langle\Phi_{1}|H| \Phi_{2}\right\rangle=&\left\langle\varphi_{m}(1)\left|h_{1}\right| \varphi_{p}(1)\right\rangle+\sum_{i}\left\\{\left[\varphi_{m} \varphi_{i} | \varphi_{p} \varphi_{i}\right]\right.\\\ &\left.-\left[\varphi_{m} \varphi_{i} | \varphi, \varphi_{p}\right]\right\\} \end{aligned}$$ where we have used the notation $$\left[\varphi_{4} \varphi_{b} | \varphi_{c} \varphi_{d}\right]=j_{0} \int \varphi_{a}^{*}(1) \varphi_{b}^{*}(2)\left(\frac{1}{r_{12}}\right) \varphi_{c}(1) \varphi_{d}(2) \mathrm{d} r_{1} \mathrm{d} r_{2}$$

In a Hartree-Fock calculation on atomic hydrogen using four primitive s-type Gaussian functions (S. Huzinaga, J. Chem. Phys., \(1293,42(1965)\) ), optimized results were obtained with a linear combination of Gaussians with coefficients \(c_{j}\) and exponents \(\alpha\) of 0.50907,0.123317 0.47449,\(0.453757 ; 0.13424,2.01330 ;\) and 0.01906 \(13.3615 .\) Describe how these primitives would be utilized in a \((4 s) /[2 s]\) contraction scheme.

(a) For a CASSCF calculation of the ground-state wavefunction of diatomic \(\mathrm{C}_{2},\) describe a reasonable choice for the distribution of \(\sigma\) and \(\pi\) molecular orbitals into active, inactive and virtual orbitals. (b) How many inactive and active clectrons arc there in the calculation? (c) In an RASSCF calculation, how might the set of active orbitals be further divided?

Prove Brillouin's theorem; that is, show that hamiltonian matrix elements between the HF wavefunction \(\Phi_{0}\) and singly excited determinants are identically zero. Hint. Use the Condon-Slater rules.
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