Background theory

Guidelines for Aquatic Toxicity

As we explained last week, this experiment was inspired by a recent article published in the journal Green Chemistry (Voutchkova, et al., 2011). Adelina Voutchkova and Paul Anastas (one of the fathers of green chemistry) worked together to define parameters that correlate with whether or not a molecule would be toxic to aquatic organisms. Many different chemical and physical properties of over 500 compounds were studied and compared to existing data on toxicity for three species: the fathead minnow, Japanese medaka, and Daphnia magna. One property that correlated with toxicity was the octanol-water partition coefficient, which you explored last week. The other significant property was the HOMO-LUMO gap, ΔE, for the molecules. Molecules with a HOMO-LUMO gap < 9eV tend to be reactive with biological molecules.

Computational Modeling

Models are used in chemistry all the time. A model is simply a way to depict or describe a real system or process but in a more convenient or tractable manner. Take, for example, Lewis dot structures. Obviously, Lewis dot structures don’t represent reality but they are a convenient way to depict bonding between atoms and lone pairs of electrons that may exist in a molecule. However, there may be situations where a different model is needed. What if you want to describe the angle between atoms in a molecule? In that case, Lewis dot structures won’t provide you with an adequate model. Instead, you might turn to the VSEPR (valence shell electron pair repulsion) model. The model you choose often depends on your specific needs.

Predicting logP Values

In this experiment, you will look up predicted logP values. There are several different computational models used for calculating logP. Many of the programs sum up the contributions of fragments of the molecules to predict the overall logP. Most models are based on data available from thousands of compounds for which the experimental data has been measured and reported in the literature. Alternately, logP can be experimentally measured in methods similar to what you used in last week’s experiment. A known amount of a solute is added to a mixture of octanol and water. The concentration of solute in each layer is measured and logP calculated.

Predicted logP values are often used instead of experimental values when searching through large volumes of compounds to predict toxicity. Having experimentally determined logP values last week, you can form your own opinion on the reliability and convenience of both predicted and experimental logP measurements.

Methods for Predicting and Calculating ΔE

In your general chemistry textbook, the author describes the predicted energies of molecular orbitals as a linear combination of atomic orbitals into molecular orbitals (LCAO-MO). What this model attempts to predict and explain is how the distribution of electrons changes as atoms get together to form bonds. In this theory, when two atomic orbitals have the proper energy and symmetry to overlap two molecular orbitals are formed. One molecular orbital is the result of a net positive interference between two atomic orbitals. This orbital is called a bonding orbital and is lower in energy than the two atomic orbitals. The second molecular orbital that forms is a result of destructive interference. It is higher in energy than the original atomic orbitals and is called an anti-bonding orbital. An example from the hydrogen molecule H₂ is shown below. The drawings of the orbitals are an attempt at showing the 3D space that describes where the electron is most likely to found relative to the nuclei. Orbitals are related to the probability of finding an electron in a given volume.

There are many times in chemistry where one wishes to be able to compute properties of a molecule of interest (e.g. the HOMO-LUMO band gap), either to compare to an experiment, or as part of a process to design new materials without having to build each and every possible molecule. In this case, it is possible to run an experiment in silico, i.e. run a computer simulation (see Quantum Mechanics Addendum for more details). Generally, when one wishes to know something about the energetics or spectroscopic properties of a molecule quantum chemical computational techniques are the methods of choice.

Theory of Computational Chemistry

The theoretical foundation for computational chemistry is the time-independent Schrodinger wave equation. However, as you may have heard in lecture by now, exact solutions exist for only a small number of systems: rigid rotor, harmonic oscillator, particle in a box, and the hydrogenic ions (H, He⁺, Li²⁺…). Approximations must be used to solve Schrodinger’s equation for larger systems. Two of the most common methods are Hartree-Fock and Density Function Theory. Hartree-Fock (HF) theory is a wavefunction-based approach that relies on the mean-field approximation. HF theory neglects electron correlation by assuming that, instead of the electrons feeling the individual electric fields generated by each of the other electrons in the atom or molecule, they instead feel the average (mean) electric field generated by all of the other electrons except themselves. Then the electrons are basically uncorrelated and the problem is again one that can be solved exactly to find each of the single electron molecular orbitals.

HF theory successfully describes 99% of the exact electronic energy of the molecule. The last 1% of the exact energy that the HF method doesn’t account for is referred to as the correlation energy, and while it is small relative to the total energy of the system, is not negligible. The correlation energy is on the order of about 1 eV per pair of electrons; this energy is of the same order of magnitude as the energy of a chemical bond. The neglected electron correlations are also very important for the evaluation of intermolecular forces such as van der Waals forces between molecules. In particular it could be noted that these kinds of non-covalent interactions are relevant to biological systems (e.g. in protein structure or interactions of various molecules with proteins, etc.).

One popular method, which attempts to characterize the correlation energy and thus recovers the last 1% of the exact energy, is density functional theory (DFT). Instead of using the (more complicated) many electron wave function, DFT instead relies upon the electron density, ρ(r), the number of electrons in an infinitesimal volume, r. The ground state energy of the system is therefore a function of electron density, which itself is a function of r. This means that the ground state energy, E[ρ(r)], is a functional of the electron density, i.e. a mathematical object which maps a function (in this case the electron density) to a number (in this case the ground state energy).

Some of the terms that are needed to describe the ground state energy (such as kinetic energy and exchange and correlation functionals) are in general unknown (and probably unknowable) functionals of the electron density. There is great research interest in developing better and better approximations to these unknown density functionals, including in the research group of Berkeley’s own Professor Martin Head-Gordon. B3LYP density functional is an example of a popular hybrid functional, which contains elements of several classes of functionals and some portion of Hartree-Fock exchange.

The shape and energy of a molecular orbital can be calculated with varying degrees of accuracy depending on both the level of theory and the basis set. A basis set is a mathematical representation of the molecular orbitals within a molecule. More specifically, it is a collection of single electron wavefunctions from which atomic and molecular orbitals can be formed by superposition. The basis set can be interpreted as restricting each electron to a particular region of space. Larger basis sets impose fewer constraints on electrons and more accurately approximate exact molecular orbitals (Figure 2), but require more computational time.

Molecular properties such as the energies of transitions between different energy levels can be measured via spectrometer as well as studied in silico. Depending on the types of energy levels involved these can transitions can be probed with UV and visible light (e.g. for transitions between electronic energy levels), infrared (e.g. for bond vibrations), or even microwave radiation (e.g. for rotations of small molecules). In cases where high resolution in energy is desired, lasers, which contain only a few frequencies of light, can be used to excite the molecules. This can be used to resolve transition energies when very many transitions occur in a very small energy range. By using ultrafast lasers, which can turn on and then off again on the order of femtoseconds, the dynamics of molecular processes, such as bond breaking, can be studied.

For a visualization of what computational modeling can accomplish please see this short video form the Professor Jan H. Jensen from the University of Copenhagen. Note that this video shows both electronic structure theory (what you are using in this experiment) and molecular dynamics simulations.

Voutchkova Aquatic Toxicity Guidelines

In the molecules studied by Voutchkova and Anastas, those with a logK_OW above two tended to be toxic to aquatic species. So a chemist synthesizing new molecules can try to target a logK_OW < 2 and ΔE > 9 eV for the safety of aquatic life (Figure 1).

In this experiment module you will test the Voutchoka model with atrazine. Last week you measured the octanol-water partition coefficient for atrazine. This week you will use WebMO/Q-Chem to compute the HOMO-LUMO band gap (ΔE).

The Voutchkova model correlations were found using toxicity data from a variety of organisms, including green algae. The ecotoxicity assay you setup last week using green algae (P. subcapitata) will allow you to determine the aquatic toxicity of your environmental toxicant. The field of ecotoxicology is very broad – this experiment is designed to give you an introduction into how many of these environmental toxicity assays are accomplished.