Investigation of Crystalline 2-Pyridone Using Terahertz Spectroscopy and Solid-State Density Functional Theory

Accepted in Chemical Physics Letters. A solid-state density functional theory (DFT) follow-up to the solution-phase 2-pyridone (2PD) study published by Motley and Korter previously. Much of the work-up for this paper was straightforward, run-of-the-mill calculation and correlation (on the theory side, anyway). The most difficult part of the analysis was the identification of the easiest way to present the normal mode analysis of the 2PD crystal cell.

In terahertz (THz) spectroscopy, one observes the lowest-frequency vibrational motions of molecules (if the molecule has low-lying vibrational modes, of course). In the solid-state (such as molecular crystals), one observes both low-lying molecular vibrational motions (if they exist) and the relative motions between molecules in the unit cell. The boilerplate separation of internal (intramolecular) and external (between-molecule) modes is performed (and presented) as follows:

A crystal unit cell containing M molecules with N atoms contains 3N-6M internal modes (those modes associated with intramolecular motions), 6M-3 external modes (those modes associated with relative motions between the M molecules, such as rotations and translations), and three acoustic modes.

Some molecules simply do not absorb in the THz region, so all assignments are for external motions (and one simply identifies molecules sliding along axes or spinning around their centers of mass in their lattice site). Some molecules are very strongly bound to neighboring molecules in their lattice sites, which results in significant changes to the mode energies of low-lying vibrational modes (these are far more complicated systems to perform assignments of and a few of these cases are being prepared for future publications). Some molecules are strongly bound in very localized ways in their crystal cell to neighboring molecules and are very weakly bound to other neighbors in other ways. In 2PD, chains of molecules are strongly bound through hydrogen bonding along the crystal c-axis (see the figure below) and only weakly interacting between chains. In the figure below, the blue and red chains are strongly coupled in-chain (hydrogen-bonding) and only weakly coupled (dispersion and van der Waals forces) between chains.

The assignment of the 2PD solid is simplified by two important facts. First, the two chains (red and blue) are related by symmetry (the unit cell contains two anti-parallel 2PD chains). Second, the chains are very weakly interacting.

What point 1 means is that the chains, if in isolation, would undergo the same vibrational motions at the same energies (as if the chains were simply chiral molecules).

What point 2 means is that these chains are, because they interact very weakly, approaching a limit where there can, in fact, be considered isolated chains so that the unit cell will contain vibrational motions that involve the two chains undergoing the same motion in-phase with respect to reach other (in-phase here meaning that, for instance, both of your lungs are expanding at the same time) and out-of-phase with respect each other (the hypothetical case where the left and right lobes are out-of-sync with one another).

For instance, if both chains are sliding along the crystal c-axis in a vibrational mode, that makes the mode the in-phase acoustic translation in c (because the whole cell is sliding in one direction). If the two chains are sliding in opposite directions with respect to each other, this makes the mode the optical translation in c (the center of mass of the cell stays put while the chains undergo out-of-phase motions).

This simplification for the 2PD assignment (and other solid-state molecular chains) turned out to be the mode assignment based on the treatment of not the in-cell contents of atoms and molecular fragments (if we kept ourselves to only viewing what is happening in the cell, for instance), but instead the relative motions of the chains, which requires ever-so-slightly thinking outside of the box.

Tanieka L. Motley, Damian G. Allis, and Timothy M. Korter*

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

Crystalline 2-pyridone has been investigated using terahertz vibrational spectroscopy in the range of 10 to 90 cm-1 (0.3 to 2.7 THz). Solid-state density functional theory (B3LYP, BP, and PW91 with the 6-311G(d,p) basis set) was used to simulate and assign both observed terahertz spectral features and a previously published far-infrared spectrum up to 400 cm-1. The PW91 functional was found to provide the best combination of crystal structure and vibrational frequency reproduction. Observed spectral features below 150 cm-1 are assigned to intermolecular movements of the 2-pyridone chains within the unit cell. The use of independent intramolecular and intermolecular frequency scalars is proposed.

www.sciencedirect.com/science/journal/00092614
dx.doi.org/10.1016/j.cplett.2008.09.021
en.wikipedia.org/wiki/2-Pyridone
en.wikipedia.org/wiki/Density_functional_theory
en.wikipedia.org/wiki/Terahertz
en.wikipedia.org/wiki/Vibrational_spectroscopy
en.wikipedia.org/wiki/Hydrogen_bonds
en.wikipedia.org/wiki/Van_der_Waals_force
en.wikipedia.org/wiki/Chirality_(chemistry)
en.wikipedia.org/wiki/Phonon

An Investigation of (1R,2S)-(-)-Ephedrine Using Solid-State Density Functional Theory and Cryogenic Terahertz Spectroscopy

Accepted in ChemPhysChem. Two important points. First, as shown in the crystal cell figure below, the low-frequency study of the ephedrine molecular solid is one that is best considered in the context of two infinite chains (red and blue) that are strongly interacting along the chain and very weakly interacting between chains. The key point is the realization that the ephedrine molecular solid is not best considered as four molecules packed into a crystal cell. The original round of mode assignments, based only in crystal cell contents, was a very complicated list of relative motions and nearly irreconcilable collisions of in- and out-of-phase motions. Thinking outside-the-unit-cell and realizing that the mode motions could be described far more easily (and logically) as chains instead of packed molecules made the final assignment and analysis of the terahertz spectrum very straightforward. The lesson is to take a good look at your molecular solid before attempting to describe the motions and consider divide-and-conquer approaches if you see correlations.

The second reason I am specifically pleased with this paper is that it is the first real terahertz study using Crystal06 that employs multiple generalized gradient approximation density functionals (BP, PBE, PW91) and basis sets (6-31G(d,p) and 6-311G(d,p)) and shows that these multiple levels of theory provide very similar results. That has, generally, NOT been the case with the many previous DMol3 studies that required difference-dipole intensity calculations instead of the use of more rigorous Wannier function-based intensities possible within the Crystal06 code.

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

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

Abstract: The terahertz (THz) spectrum of (1R,2S)-(-)-ephedrine from 8.0 to 100.0 cm-1 has been investigated at liquid-nitrogen (78.4 K) temperature. A complete structural analysis has been performed in conjunction with a vibrational assignment of the experimental spectrum using solid-state density functional theory (DFT). In order to obtain the crystallographic lattice constants at a temperature relevant for the DFT simulations, the compound has also been characterized by cryogenic single-crystal X-ray diffraction. Theoretical modeling (solid-state and isolated-molecule) of the compound includes the use of three generalized gradient approximation density functionals (BP, PBE, PW91) and two Gaussian-type basis sets (6-31G(d,p) and 6-311G(d,p)). Assignment of the THz spectrum is performed at a PW91/6-311G(d,p) level of theory, which provides the best solid-state simulation agreement with experiment. The solid-state analysis indicates that the seven experimental spectral features observed at liquid-nitrogen temperature are comprised of 13 IR-active vibrational modes. Of these modes, nine are external crystal vibrations and provide approximately 57% of the predicted spectral intensity.

www3.interscience.wiley.com/journal/72514732/home?CRETRY=1&SRETRY=0
en.wikipedia.org/wiki/Ephedrine
en.wikipedia.org/wiki/Terahertz
www.crystal.unito.it/
en.wikipedia.org/wiki/Density_functional_theory
en.wikipedia.org/wiki/Basis_set_(chemistry)
accelrys.com/products/materials-studio/modules/dmol3.html
en.wikipedia.org/wiki/Wannier_function
chemistry.syr.edu
www.syr.edu

The Cryogenic Terahertz Spectrum Of (+)-Methamphetamine Hydrochloride And Assignment Using Solid-State Density Functional Theory

In press in the Journal of Physical Chemistry.  This paper on the low-frequency vibrational properties of methamphetamine marks a transitional point in the simulation of terahertz (THz) spectra by density functional theory (DFT), as both Crystal06 and Abinit provide the means to calculating infrared intensities in the solid-state by a more rigorous method than the difference-dipole method that has been used in the many previous THz papers with DMol3 (performed externally from the DMol3 program proper).  The original manuscript came back with two important comments from Reviewer 3 (that crazy Reviewer 3.  Is there nothing they’ll think of to critique?).

The best-fit spectral assignment by visual inspection (BOP/DNP level of theory) and by statistical analysis (BP/DNP level of theory) are shown below (the paper, of course, contains significantly more on this point).  With these two spectral simulations in mind, Reviewer 3 presented the following analysis that I think is certainly worth considering generally to anyone new to the computational chemistry game and even by general practitioners who might risk becoming complaisant in their favorite theoretical technique.  There’s a reason we refer to the collection of computational quantum chemical tools as the “approximate methods.”

I have difficulty with what appears to be a generalization of the applicability of using density functional for modeling THz spectra… It is disturbing that the different functionals will generate different numbers of modes within the spectral region, and it is hard to imagine how we should move forward with density functional for calculating spectra of this type.  In fact, it is true that one needs to include the “lattice” to get the spectra right in these regions, but it is not obvious that DFT will provide the level of rigor required to develop a predictive capability. Furthermore, given the “uncertainties regarding the number of modes”, is it possible that the mode assignments are invalid?

In my opinion, the authors point out the need for solid-state DFT, but should point out that in its current incarnation, that DFT is currently inadequate for quantitative comparison with experiment, and that more work needs to be done with the theory to make it quantitative.

The response to the reviewer about these points goes as such:

We agree completely with the reviewer’s criticism on these points of spectral reproduction, but we also believe that there should be a sharp separation between the capabilities of the DFT formalism and the capabilities of the many empirically-derived density functionals that currently make up the complement of “tools” within the DFT formalism.  Unlike the selection of basis set, which we often presume will improve agreement because of the improvement to the description of the electronic wavefunction that comes from additional functions, it is the case (specifically among the survey studies in THz simulations performed by the authors in this and previous publications) among the currently available GGA density functionals that the reproduction of the physical property under consideration is determined by the functional.  We also know that the reproduction of the lowest-energy solid-state vibrational features in molecular solids were NOT part of the initial complement of metrics used in gauging the accuracy of density functionals, so it is clear that we are performing survey calculations using available tools to determine which tools may be most reliably employed for performing THz assignments while not actively engaged in the development of new tools.  In the simulation of vibrational spectra, it is clear that we can never entirely trust the simulations until it is known unambiguously by experimentalists exactly what the motion associated with each vibrational mode is, which brings up the need for polarization experiments, Raman experiments to complement the mode assignments, etc.  Such rigorous detail for this region of the spectrum is very likely not known for a great many molecules of interest by the communities most interested in the benefits of THz spectroscopy.

In the meantime and in the absence of “complete datasets,” we agree with all of the reviewers (to a point either addressed directly or indirectly through questions along the same vein) that the best that a theoretical survey like the one presented here can do is aid in the generation of a functional consensus view, which is something that requires mode-by-mode analyses as mentioned by the reviewer.

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

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

Abstract: The cryogenic terahertz spectrum of (+)-methamphetamine hydrochloride from 10.0 – 100.0 cm-1 is presented, as is the complete structural analysis and vibrational assignment of the compound using solid-state density functional theory. This cryogenic investigation reveals multiple spectral features not previously reported in room-temperature terahertz studies of the title compound. Modeling of the compound employed eight density functionals utilizing both solid-state and isolated-molecule methods. The results clearly indicate the necessity of solid-state simulations for the accurate assignment of solid-state THz spectra. Assignment of the observed spectral features to specific atomic motions is based upon the BP density functional, which provided the best-fit solid-state simulation of the experimental spectrum. The seven experimental spectral features are the result of thirteen infrared-active vibrational modes predicted at a BP/DNP level of theory, with more than 90% of the total spectral intensity associated with external crystal vibrations.

pubs.acs.org/journal/jpcafh
en.wikipedia.org/wiki/Methamphetamine
en.wikipedia.org/wiki/Time_domain_terahertz_spectroscopy
en.wikipedia.org/wiki/Density_functional_theory
www.physics.ohio-state.edu/~aulbur/dft.html
www.crystal.unito.it
www.abinit.org
www.somewhereville.com/?cat=8
accelrys.com/products/materials-studio/modules/dmol3.html
link.aip.org/link/?JCPSA6/110/10664/1
link.aps.org/doi/10.1103/PhysRevA.38.3098
en.wikipedia.org/wiki/Computational_chemistry
chemistry.syr.edu