Excursions in Chemical Dynamics
As early as 1929, Dirac was sufficiently confident in the new quantum theory to assert that the physical laws underlying all chemistry were known; what remained, then, was to find tractable approximations within which to apply them. The most famous of these approximations, due to Born and Oppenheimer, partitions chemistry as formulated quantum mechanically into separate electronic and nuclear problems. While treatments of electronic structure within this framework are now routine among chemists, nuclei are still often treated classically. It is impossible, however, to be certain as to whether nuclear quantum effects will contribute to the physics of any given system. The present work addresses these effects at varying levels of approximation and in the context both of concrete systems (aqueous solutions and isolated molecules) and general methodology.
After a brief introduction in Chapter 1, we proceed in Chapter 2 to discuss recent X-ray photoelectron spectra on aqueous hydroxide solutions, which were seen to exhibit the off-site Auger decay process known as intercoulombic decay (ICD). Arguments were made regarding the necessary conditions for ICD to occur --- specifically, that it would take place selectively along a hydrogen bond donated by the hydroxide ion. This mechanistic claim ties in with an ongoing controversy over the solvation structure of hydroxide and would constitute decisive evidence for the hypercoordinated model (which allows transient hydrogen bond donation by hydroxide) over the proton-hole model (which does not).
We have performed X-ray absorption calculations using the eXcited electron and Core Hole (XCH) method that indicate that hydrogen-bond donation is not a prerequisite for ICD in this system. Additional calculations suggest that X-ray absorption techniques are also unlikely to be able to distinguish between the two solvation models. In reaching these conclusions, we stress that there are general theoretical criteria for the occurrence of ICD and suggest that they may be used predictively. We further propose that our criteria can be combined with the XCH method to aid in the rational design of a new type of chemo-/radio-therapy protocol for cancer treatment. In particular, we are preparing a proof-of-principle experiment on a model biological solution of bismuth, citrate, and urea.
In Chapter 3, we address nuclear motion explicitly. Several models of the X-ray absorption spectrum of nitrogen gas (N2) are studied in the context of the standard Born-Oppenheimer approximation and XCH. Systematic improvements are made to an initially classical model that includes nuclear motion exactly, beginning with the substitution of the quantum mechanical nuclear density in the bond length R for its classical counterpart, followed by the addition of zero-point energy and other level-shifting effects, and finally the inclusion of explicit rovibrational quantization of both the ground and excited states. The quantization is determined exactly using the Colbert-Miller discrete variable representation (DVR), with further details provided in a pair of appendices.
It is shown that the spectrum can be predicted semiquantitatively within this simple framework and that it compares respectably well with the prediction obtained using more accurate potentials. With respect to nuclear dynamics, the key lesson is that quantization of nuclear motion is absolutely essential if one wishes to capture fine structure in the spectrum; simpler approaches will, at best, properly reproduce a sharp absorption edge.
In Chapter 4, we examine a method for the approximate inclusion of true dynamical effects associated with moment-to-moment nuclear motion. In particular, we study ring polymer molecular dynamics (RPMD), which (though developed recently) has already proven to be a useful theory for the calculation of a wide variety of properties of chemical systems. It is founded, however, on a heuristic extension of the rigorously-derived method of path integral molecular dynamics (PIMD). We attempt to derive the method by way of judicious approximations to exact expressions for the correlation function and, that failing, by "reverse engineering." These attempts do not succeed, in general, but may eventually provide a means of obtaining the method in the case of a harmonic oscillator, for which it is exact. At the very least, the expressions obtained offer further evidence that RPMD is a reasonable extension of rigorous methods.