25 November 2010 Cover Art For The Journal Of Physical Chemistry A – "Computation Of Deuterium Isotope Perturbation Of 13C NMR Chemical Shifts of Alkanes: A Local Mode Zero Point Level Approach"

A bit of a sneak preview and a chance to get a second use out of an instructive pair of potentials. This new cover for an upcoming article by Kin Yang and Bruce Hudson expands upon the previous Deuterium-for-Hydrogen substitution study summarized on the blog page (and in a publication of the same name) Vicinal Deuterium Perturbations on Hydrogen NMR Chemical Shifts in Cyclohexanes. In brief, exchanging a hydrogen for a deuterium alters 13C NMR spectra because the deuterium, being twice the mass, has a narrower nuclear probability distribution. If the C-H/D stretching potential were harmonic (symmetric on both the elongation and contraction sides), this would produce no effect. As this stretching potential is anharmonic (as shown below and the background of the above image), the actual average positions of the D and H differ slightly (but enough!), with the C-D bond being, on average, slightly shorter than C-H (something that a quantum chemical calculation will not tell you without treating the nuclei as quantum mechanical objects). Different average bond length, different affect on a bound 13C.

A bit more explanation can be found at www.somewhereville.com/?p=124.

The studies continue, limited largely by the number of simple hydrocarbons with high-quality NMR spectra (and selective deuteration).

The Vibrational Spectrum Of Parabanic Acid By Inelastic Neutron Scattering Spectroscopy And Simulation By Solid-State DFT

Available as an ASAP in The Journal of Physical Chemistry A. As a general rule in computational chemistry, the smaller the molecule, the harder it is to get right. As a brief summary, parabanic acid has several interesting properties of significance to computational chemists as both a model for other systems containing similar sub-structures and as a complicated little molecule in its own right.

1. The solid-state spectrum requires solid-state modeling. This should be of no surprise (see the figure below for the difference in solid-state (top) and isolated-molecule (bottom)). This task was undertaken with both DMol3 and Crystal06, with DMol3 calculations responsible for the majority of the analysis of this system (as has always been the case in the neutron studies reported on this site).

2. The agreement in the hydrogen-bonded N-H…O vibrations is, starting from the crystal structure, in poor agreement with experiment. You'll note the region between 750 and 900 cm-1 is a little too high (and for clarification, the simulated spectrum is in red below). According to the kitchen sink that Matt threw at the structure, the problem is not the same anharmonicity one would acknowledge by Dr. Walnut's "catalytic handwaving" approach to spectrum assignment (Dr. Walnut does not engage in this behavior, rather endeavors to find it in others where it should not be).

3. The local geometry of the hydrogen-bonding network in this molecular solid leads to notable changes in parabanic acid structure that, in turn, leads to the different behavior of the N-H…O vibrational motions. There is one potentially inflammatory comment in the Conclusions section that results from this identification. The parabanic acid molecule is, at its sub-structure, a set of three constrained peptide linkages that under go subtle but vibrationally-observable changes to their geometry because of crystal packing and intermolecular hydrogen bond formation. This means that the isolated molecule and solid-state forms are different and that peptide groups are influenced by neighboring interactions.

So, why should one care? Suppose one is parameterizing a biomolecular force field (CHARMM, AMBER, GROMOS, etc.) using bond lengths, bond angles, etc., for the amino acid geometry and vibrational data for some aspect of the force constant analysis. The structural data for these force fields often originates with solid-state studies (diffraction results). This means, to those very concerned with structural accuracy, that a geometry we know to be influenced by solid-state interactions is being used as the basis for molecular dynamics calculations that will NOT be used in their solid-state forms. Coupled with the different spectral properties due to intermolecular interactions, the description being used as the basis for the biomolecular force field likely being used in solution (solvent box approaches) is based on data in a phase where the structure and dynamics are altered from their less conformationally-restricted counterpart (in this case, solid-state).

A subtle point, but that's where applied theoreticians do some of their best work.

Matthew R. Hudson, Damian G. Allis, and Bruce S. Hudson

Department of Chemistry, 1-014 Center for Science and Technology, Syracuse University, Syracuse, New York 13244-4100

Abstract: The incoherent inelastic neutron scattering spectrum of parabanic acid was measured and simulated using solid-state density functional theory (DFT). This molecule was previously the subject of low-temperature X-ray and neutron diffraction studies. While the simulated spectra from several density functionals account for relative intensities and factor group splitting regardless of functional choice, the hydrogen-bending vibrational energies for the out-of-plane modes are poorly described by all methods. The disagreement between calculated and observed out-of-plane hydrogen bending mode energies is examined along with geometry optimization differences of bond lengths, bond angles, and hydrogen-bonding interactions for different functionals. Neutron diffraction suggests nearly symmetric hydrogen atom positions in the crystalline solid for both heavy-atom and N-H bond distances but different hydrogen-bonding angles. The spectroscopic results suggest a significant factor group splitting for the out-of-plane bending motions associated with the hydrogen atoms (N-H) for both the symmetric and asymmetric bending modes, as is also supported by DFT simulations. The differences between the quality of the crystallographic and spectroscopic simulations by isolated-molecule DFT, cluster-based DFT (that account for only the hydrogen-bonding interactions around a single molecule), and solid-state DFT are considered in detail, with parabanic acid serving as an excellent case study due to its small size and the availability of high-quality structure data. These calculations show that hydrogen bonding results in a change in the bond distances and bond angles of parabanic acid from the free molecule values.


Examination of Phencyclidine Hydrochloride via Cryogenic Terahertz Spectroscopy, Solid-State Density Functional Theory, and X-Ray Diffraction

"I'm high on life… and PCP." – Mitch Hedberg

In press, in the Journal of Physical Chemistry A. If the current rosters of pending manuscripts and calculations are any indication, this PCP paper will mark the near end of my use of DMol3 for the prediction (and experimental assignment) of terahertz (THz) spectra (that said, it is still an excellent tool for neutron scattering spectroscopy and is part of several upcoming papers).

While the DMol3 vibrational energy (frequency) predictions are generally in good agreement with experiment (among several density functionals, including the BLYP, BOP,VWN-BP, and BP generalized gradient approximation density functionals), the use of the difference-dipole method for the calculation of infrared intensities has shown itself to be of questionable applicability when the systems being simulated are charged (either molecular salts (such as PCP.HCl) or zwitterions (such as the many amino acid crystal structures)). The previously posted ephedrine paper (in ChemPhysChem) is most interesting from a methodological perspective for the phenomenal agreement in both mode energies AND predicted intensities obtained using Crystal06, another solid-state density functional theory program (that has implemented hybrid density functionals, Gaussian-type basis sets, cell parameter optimization and, of course, a more theoretically sound prediction of infrared intensities by way of Born charges). The Crystal06 calculations take, on average, an order of magnitude longer to run than the comparable DMol3 calculations, but the slight additional gain in accuracy for good density functionals, the much greater uniformity of mode energy predictions across multiple density functionals (when multiple density functionals are tested), and the proper calculation of infrared intensities all lead to Crystal06 being the new standard for THz simulations.

After a discussion with a crystallographer about what theoreticians trust and what they don't in a diffraction experiment, the topic of interatomic separation agreement between theory and experiment came up in the PCP.HCl analysis performed here (wasn't Wayne). As the position of hydrogen atoms in an X-ray diffraction experiment are categorically one of those pieces of information solid-state theoreticians do NOT trust when presented with a cif file, I reproduce a snippet from the paper considering this difference below (and, generally, one will not find comparisons of crystallographically-determined hydrogen positions and calculated hydrogen positions in any of the THz or inelastic neutron scattering spectroscopy papers found on this blog).

The average calculated distance between the proton and the Cl ion is 2.0148 Angstroms, an underestimation of nearly 0.13 Angstroms when compared to the experimental data. This deviation is likely strongly tied to the uncertainly in the proton position as determined by the X-ray diffraction experiment and is, therefore, not used as a proper metric of agreement between theory and experiment. The distance from the nitrogen atom to the Cl ion has been determined to be an average of 3.0795 Angstroms, which is within 0.002 Angstroms of the experimentally determined bond length. This proper comparison of heavy atom positions between theory and experiment indicates that this interatomic separation has been very well predicted by the calculations.

Patrick M. Hakey, Matthew R. Hudson, Damian G. Allis, Wayne Ouellette, and Timothy M. Korter

Department of Chemistry, Syracuse University, Syracuse, NY 13244-4100

The terahertz (THz) spectrum of phencyclidine hydrochloride from 7.0 – 100.0 cm-1 has been measured at cryogenic (78 K) temperature. The complete structural analysis and vibrational assignment of the compound have been performed employing solid-state density functional theory utilizing eight generalized gradient approximation density functionals and both solid-state and isolated-molecule methods. The structural results and the simulated spectra display the substantial improvement obtained by using solid-state simulations to accurately assign and interpret solid-state THz spectra. A complete assignment of the spectral features in the measured THz spectrum has been completed at a VWN-BP/DNP level of theory, with the VWN-BP density functional providing the best-fit solid-state simulation of the experimentally observed spectrum. The cryogenic THz spectrum contains eight spectral features that, at the VWN-BP/DNP level, consist of fifteen infrared-active vibrational modes. Of the calculated modes, external crystal vibrations are predicted to account for 42% of the total spectral intensity.