The Roles of Theoretical and Computational Chemistry in the Chemistry Curriculum and in Research

1. The Roles of Theoretical and Computational Chemistry in the Chemistry Curriculum and in Research Jack Simons Chemistry Department University of Utah Salt Lake City, Utah http://simons.hec.utah.edu/TheoryPage

2. I often am asked (by neighbors, people I meet on a ski lift, or by colleagues in non-science departments) “What is a theoretical chemist? Are you not a real chemist?” Let’s first ask What does theory mean? From Wikipedia : In science, a theory is a mathematical or logical explanation, or a testable model of the manner of interaction of a set of natural phenomena, capable of predicting future occurrences or observations of the same kind, and capable of being tested through experiment or otherwise falsified through empirical observation.

3. In common language, the word theory is often used to signify a conjecture, an opinion, or a speculation. This usage of theory leads to the common statement "It's not a fact, it's only a theory.” It also gives rise to societal frictions surrounding the theory of evolution and intelligent design- it is difficult to test a hypothesis of what happened in the past unless the hypothesis also predicts what will occur in the future, which is when the testing can occur. In chemistry, a theory is a mathematical or logical explanation, or a modelconnecting laboratory observations to the behavior of the underlying atoms, molecules, or materials. It must be capable of predicting future observations, and capable of being tested through experiment. It is theoretical chemists who create these means for connecting laboratory observations to molecular behavior. Let’s look at some examples of theoretical concepts that arise in the classes we teach at the undergraduate level as well as how theory is used in chemistry research.

4. In the classroom, theoretical chemistry became somewhat controversial during the 1970s-1990s. It was common to hear things like: “Chemistry is an experimental science” “There is too much theory in the undergraduate curriculum” Let’s look at the tables of contents of some widely used undergraduate texts to see what their authors think.

5. Cotton and Wilkinson’s textbook on inorganic chemistry (1962). It looks to me like they think theoretical concepts are essential to understanding inorganic chemistry.

6. Morrison and Boyd’s textbook on organic chemistry. Notice that there are theoretical concepts and laboratory data discussed in close proximity- that is because they are related.

7. Sometimes people think theory is unnecessary, confusing, or even nonsense, and should not be taught. J. F. Ogilvie, J. Chem. Ed. 67, 280 (1990) wrote this about electronic structure theory in classes. I replied with this observation. J. Simons, There are no such things as orbitals- act two, J. Chem. Ed. 68, 131 (1991)

8. OK, maybe orbitals are just constructs of theoretical models of how electrons move in atoms and molecules, but are molecular bond lengths any more “real”? Spacings between lines in rotationally resolved spectra are data. Equations such as h2J(J+1)/(82R2) are used to evaluate R. Line spacings determine vibrationally averaged R-2. But, how does (<v|R-2|v>)-1/2 relate to this R?

9. X-ray diffraction patterns can be used to determine (n = 2d sin) spacings between atoms and thus to obtain a molecular structure. But X-rays scatter from inner-shell electrons, so measure distances between these shells. NMR couplings depend on distances between nuclei as R-6.

10. So, distance parameters extracted (using theory) from rotational spectra, from X-ray diffraction, and from NMR couplings all relate to different properties of the molecule, and none of them offers a direct determination of the Re. My position is that the raw data from experiment may be “real”, but the quantities extracted from them (1) are extracted using theory and (2) are thus no less or more “real” than the theory used to extract them. Let’s look at a couple of other examples.

11. Spacingsbetween lines (v  v+1 energy gaps) in vibrational spectra can be used to determine bond dissociation energies. The equation= e - 2exe (v+1)is used to fit the observed line frequencies. But, notice one must extrapolate to = 0 to obtain D0. D0

12. Chemists often plot the natural logarithm of a rate constant vs. 1/T to obtain an activation energy E*. The equation ln(k) = ln(A) -E*/RT is used to obtain E*. But it is transition-state theory that connects E* to properties of the reacting molecule at the transition state.

13. Thus, the experimental data are “real”, but the quantities obtained using theory to interpret/fit the data are less “real”. Bond lengths and angles, vibrational frequencies, potential energy curves, molecular orbitals, transition states are all “unreal”. They are constructs of various theories used to relate laboratory measurements to atomic, molecular, or materials- level behaviors.

14. Because these theories inevitably involve approximations (i.e., in solving the quantum mechanics equations), their constructs will have intrinsic uncertainties/limitations. Sometimes, the theoretical models are so well established that we obtain very good “agreement” between theory and experiment. For example, analysis of rotational absorption spectra of rigid diatomic molecules yields moments of intertia I = m <r2> in very good agreement with vibrationally averaged bond lengths determined in ab initio calculations. On the other hand, for a “floppy” molecule such as the Ar…HCl van der Waals complex, it is a much more challenging task to relate the experimental rotational spectrum to the three-dimensional potential surface computed using ab initio methods.

15. So, where would chemists be without the theories? They would have no means of connecting lab data to molecular behavior. I think there are two primary reasons that some chemists believe there is too much emphasis on theory in education (and perhaps in research): 1. Chemical theory usually involves quantum mechanics; this is because electrons, atoms, and molecules don’t move according to Newton’s equations. Sorry, but this is just the way it is! Many chemists are not comfortable with quantum mechanics, so they try to minimize its presence. 2. Some people think theoretical chemists are attempting to replace experimental studies by using theory to simulate laboratory measurement. This is not true! So, it is important to clarify how simulation is meant to assist experiment, not to replace it.

16. Thus far, we have seen how theory provides the equations or concepts that connect laboratory data to molecular-level properties. Theoretical chemists also simulate molecular behavior by using quantum (the Schrödinger equation) or classical (Newtonian equations) mechanics to predict this behavior. In the early days of theoretical chemistry, this was not possible because solving these equations was just too time consuming. The advent of modern (and inexpensive) computers has changed this situation qualitatively.

17. Let’s look at a couple of examples of how theoretical chemists simulate molecular behavior. The first involves work done in Mark Johnson’s lab on the IR spectra of water cluster anions (H2O)n-.They needed theory simulation that agreed with their spectra (so they could trust the theory) (1) so they could determine which peaks corresponded to vibrations to O-H bonds involved (or not) in hydrogen bonding and (2) so they could determine which cluster structure’s vibrations “agreed” with their IR data- this is how they know what structure they have in their sample.

18. Let’s look at a couple of examples of how theoretical chemists simulate molecular behavior. Fig. 2. (Bottom) Argon predissociation spectra of (H2O)4– · Ar5 in the bending region (A) and (D2O)4– · Ar10 in the OD stretching region (B). (Middle) Calculated harmonic spectra of (H2O)4– in the bending region (C) and (D2O)4– in the stretching region (D) for the cyclic structure shown, with A and D indicating acceptor and donor H-bonds, respectively. (Top) Analogous calculated spectra for the linear structure shown. Orbital holding the excess electron in (H2O)4-. N. I. Hammer, J-W. Shin, J. M. Headrick, E. G. Diken, J. R. Roscioli, G. H. Weddle, and M. A. Johnson, Science 306, 675 (2004).

19. The second example derives from work of Heather Allen’s experimental group who probe concentrations of cations and anions near the surface and within the interior of small water droplets (aerosols). The simulations by Pavel Jungwirth and Liem Dang and co-workers suggest which ions tend to have higher or lower surface concentrations than interior concentrations. Also, by analyzing the contributions from various ion-water and water-water interaction potentials, the simulations allow one to determine (if one trusts the simulations) what causes some ions to prefer the surface regions.

20. Molecular dynamics calculations show that in salt solutions and bases the positively charged ions, such as alkali cations, are repelled from the interface, whereas the anions, such as halides or hydroxide, exhibit a varying surface propensity, correlated primarily with the ion polarizability and size.[1.2 M conc., in all cases.] Important knowledge for atmospheric and interfacial chemistry. M. Mucha, T. Frigato, L. M. Levering, H. C. Allen, D. J. Tobias, L. X. Dang, and P. Jungwirth, J. Phys. Chem. B 109, 7617 (2005).

21. The third example relates to work that Ken Jordan’s group has been doing trying to understand how an excess electron binds to various water clusters. Through simulations, he was able to show (1) that a given size cluster often has many structures with low energy and (2) that structures having one or more water molecules whose O-H bonds extend outward (labeled AA) tend to bind the excess electron proximal to the AA water molecule. Combining these simulation results and Mark Johnson’s IR data on such clusters, the Jordan and Johnson groups have been able to shed much light on the geometries and electron-binding mechanisms of water clusters.

22. Professor Jordan’sgroup has shown that electrons can bind on surfaces or interiors of water clusters and, when surface bound, there often is one water molecule that adopts the AA motif. T. Sommerfeld and K. D. Jordan, J. Am. Chem. Soc., 128, 5828 (2006).

23. What are my take-home lessons? Theoretical chemistry is on the same team as experimental chemistry. Experiments generate the data and theory offers the connection between the data and molecular behavior. Theory and simulations are important ingredients in chemistry education and research. Simulations (when carried out using underlying theories we have reason to trust) allow us to see what the molecules are doing that gives rise to the experimental observations. Theory/simulation does not attempt to replace experiments. Because theory is spoken in the languages of mathematics and quantum mechanics, we need to make sure our students learn these valuable languages rather than “avoiding” them.

24. For further insight and to find information about many theoretical chemists’ research, I suggest you look at this web site. http://simons.hec.utah.edu/TheoryPage