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Computational Chemistry pp 565–612Cite as

Some “Special” Topics: (Section 8.1) Solvation, (Section 8.2) Singlet Diradicals, (Section 8.3) A Note on Heavy Atoms and Transition Metals

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Abstract

For some purposes solution-phase computations are necessary, e.g. for understanding certain reactions, and for the prediction of pK a in solution. For introducing the effects of solvation there are two methodologies (and hybrids of these two): microsolvation or explicit solvation, and continuum solvation.

Some molecular species are not calculated properly by straightforward model chemistries: these include singlet diradicals and some excited state species. For these the standard method is the complete active space approach, CAS (CASSCF, complete active space SCF). This is a limited version of configuration interaction, in which electrons are promoted from and to a carefully chosen set of molecular orbitals.

For systems with heavy atoms we often employ pseudopotential basis sets (frequently relativistic), which reduce the computational burden of large numbers of electrons. Transition metals present problems beyond those of main-group heavy atoms: not only can relativistic effects be significant, but electron d- or f-levels, variably perturbed by ligands, make possible several electronic states. Also, nearly degenerate s and d levels can cause convergence problems. DFT calculations, with pseudopotentials, are the standard approach for computation on such compounds.

Chapters 1–7: (a) addressed molecules as isolated entities, without reference to their surroundings (except for the water dimer); (b) concentrated on calculations by relatively “automatic” model chemistries ; and (c) used mainly organic molecules as illustrations. This chapter to some extent redresses these constraints.

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Notes

  1. 1.

    A. Klamt, personal communication, 2010 March 13.

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Authors and Affiliations

  1. Trent University, Peterborough, ON, Canada

    Errol G. Lewars

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  1. Errol G. Lewars
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Appendices

Solvation

8.1.1 Easier Questions

  1. 1.

    Using microsolvation, roughly how many water molecules might be needed to provide one layer around CH3F ( suggestion: examine space-filling hand-held or computer-generated models)?

  2. 2.

    What physical properties of solvents have been used to parameterize them for continuum calculations?

  3. 3.

    Give an example of a reaction for which just one explicit solvent molecule might be adequate in simulating a reaction mechanism.

  4. 4.

    For continuum solvation, give an example of a molecule for which a good approximation might be (a) a spherical cavity, (b) an ellipsoidal cavity.

  5. 5.

    Why are continuum solvation methods more widely used than microsolvation methods?

8.1.2 Harder Questions

  1. 1.

    In microsolvation, should the solvent molecules be subjected to geometry optimization?

  2. 2.

    Consider the possibility of microsolvation computations with spherical, polarizable “pseudomolecules”. What might be the advantages and disadvantages of this simplified geometry?

  3. 3.

    In microsolvation, why might just one solvent layer be inadequate?

  4. 4.

    Why is parameterizing a continuum solvent model with the conventional dielectric constant possibly physically unrealistic?

  5. 5.

    Consider the possibility of parameterizing a continuum solvent model with the dipole moment.

Singlet Diradicals

8.2.1 Easier Questions

  1. 1.

    A monoradical is a doublet and a diradical can be a singlet or a triplet. How many spin states are possible for a triradical?

  2. 2.

    What does the Pauli exclusion principle suggest about the relative energies of singlet and triplet diradicals?

  3. 3.

    What is the simplest singlet diradical hydrocarbon species?

  4. 4.

    Which MOs would be appropriate for CASSCF calculations on

    1. 1.

      the ring-opening of cyclobutene to 1,3-butadiene?

    2. 2.

      the Diels-Alder reaction?

  5. 5.

    How many CI configurations are used in

    • a CASSCF(2,2) calculation?

    • a CASSCF(2,3) calculation?

8.2.2 Harder Questions

  1. 1.

    Is CASSCF size-consistent?

  2. 2.

    In one-determinant HF (i.e. SCF) theory, each MO has a unique energy (eigenvalue), but this is not so for the active MOs of a CASSCF calculation. Why?

  3. 3.

    In doubtful cases, the orbitals really needed for a CASSCF calculation can sometimes be ascertained by examining the occupation numbers of the active MOs. Look up this term for a CASSCF orbital.

  4. 4.

    Why does an occupation number (see question 3 above) close to 0 or 2 (more than ca. 1.98 and less than ca. 0.02) indicate that an orbital does not belong in the active space?

  5. 5.

    It has been said that there is no rigorous way to separate static and dynamic electron correlation. Discuss.

Heavy Atoms and Transition Metals

8.3.1 Easier Questions

  1. 1.

    Suggest a simple physical property of an atom for which a comparison of experiment with a calculated value might be used a test of whether the atom should be regarded as being “heavy” (hint: consider the energy of the valence electrons).

  2. 2.

    Suggest a simple property of a compound of element X for which a comparison of experiment with a calculated value might be used a test of whether element X should be regarded as being “heavy”.

  3. 3.

    Dirac, the discoverer of the relativistic one-electron equation, thought that relativity would be unimportant in chemistry (P. A. M. Dirac, “Quantum Mechanics of Many-Electron Systems”, Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1929, 123(792), 714). Why was he mistaken?

  4. 4.

    Of the first 100 elements, how many are transition metals?

  5. 5.

    Use the simple semiclassical Bohr equation for the velocity v of an electron in an atom (Chap. 4, Eq. (4.12) to calculate a value of v for \( Z=100 \) and energy level \( n=1 \):

    $$ v=\frac{Z{e}^2}{2{\varepsilon}_0nh} $$
    (4.12)
    $$ e=1.602\times {10}^{-19}\mathrm{C},\;{\varepsilon}_0=8.854\times {10}^{-12\;}{\mathrm{C}}^2{\mathrm{N}}^{-1}{\mathrm{m}}^{-2},\;h=6.626\times {10}^{-34}\;\mathrm{J}.\mathrm{s} $$

    What fraction of the speed of light \( c=3.0\times {10}^8\kern0.24em {\mathrm{ms}}^{-1} \)) is this value of v?

    Using the “Einstein factor” \( \surd \left(1-{v}^2/{c}^2\right) \), calculate the mass increase factor that this corresponds to.

8.3.2 Harder Questions

  1. 1.

    Is the result of the calculation in question 5 above trustworthy? Why or why not?

  2. 2.

    Should relativistic effects be stronger for d or for f electrons?

  3. 3.

    Why are the transition elements all metals?

  4. 4.

    The simple crystal field analysis of the effect of ligands on transition metal d-electron energies accords well with the “deeper” molecular orbital analysis (see e.g [106]). In what way(s), however, is the crystal field method unrealistic?

  5. 5.

    Suggest reasons why parameterizing molecular mechanics and PM3-type programs for transition metals presents special problems compared with parameterizing for standard organic compounds.

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Lewars, E.G. (2016). Some “Special” Topics: (Section 8.1) Solvation, (Section 8.2) Singlet Diradicals, (Section 8.3) A Note on Heavy Atoms and Transition Metals. In: Computational Chemistry. Springer, Cham. https://doi.org/10.1007/978-3-319-30916-3_8

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