Finally! A Good Use For The Nano Gallery (Kudos To

An unlabeled version of the fused-diamondoid-carbon-nanotube-van-der-waals-crimp-junction found a home in the NanoSonic Nanotechnology Coloring Book, page 8 (I show it below (with mine shown a little more nano-sized)). I think that’s pretty hip.

Kudos to Tom Moore for pointing it out.

Cover Art For The 7 May 2010 Issue Of The Journal Of Organic Chemistry – Notes On Presentation

The cover art for the 7 May 2010 issue of the Journal of Organic Chemistry accompanies the article by (2nd semester organic chemistry professor, co-author, and 2010 American Chemical Society James Flack Norris Award in Physical Organic Chemistry recipient) John E. Baldwin and Alexey P. Kostikov entitled “On the Stereochemical Characteristic of the Thermal Reactions of Vinylcyclobutane.”

This Perspective outlines the stereochemical and mechanistic complexities inherent in the thermal reactions converting vinylcyclobutane to cyclohexene, butadiene, and ethylene. The structural isomerization and the fragmentation processes seem, at first sight, to be obvious and simple. When considered more carefully and investigated with the aid of deuterium-labeled stereochemically well-defined vinylcyclobutane derivatives there emerges a complex kinetic situation traced by 56 structure-to-structure transformations and 12 independent kinetic parameters. Experimental determinations of stereochemical details of stereomutations and [1,3] carbon sigmatropic shifts are now being pursued and will in time contribute to gaining relevant evidence casting light on the reaction dynamics involved as flexible short-lived diradical intermediates trace the paths leading from one d2-labeled vinylcyclobutane starting material to a mixture of 16 structures.

Continue reading “Cover Art For The 7 May 2010 Issue Of The Journal Of Organic Chemistry – Notes On Presentation”

Terahertz Spectroscopic Investigation Of S-(+)-Ketamine Hydrochloride And Vibrational Assignment By Density Functional Theory, “Function Follows Functional Follows Formalism”

Accepted in the Journal of Physical Chemistry A, with my fingers crossed for pulling off the rare double-header in an upcoming print edition of the journal (having missed it by three intermediate articles with the Cs2B12H12 and HMX papers back in 2006 (you’d keep track, too). A fortuitous overlap of scheduled defense dates between P. Hakey, Ph.D. and M. Hudson, A.B.D.). A brief summary of interesting points from this study is provided below, including what I think is a useful point about how to most easily interpret AND represent solid-state vibrational spectra for publications.

1. AS USUAL, YOU CANNOT USE GAS-PHASE CALCULATIONS TO ASSIGN SOLID-STATE TERAHERTZ SPECTRA. It will take a phenomenal piece of data and one helluvan interpretation to convince me otherwise. As a more subtle point (for those attempting an even worse job of vibrational mode assignment), if the molecule exists in its protonated form in the solid-state, do not use the neutral form for your gas-phase calculation (this is a point that came up as part of an MDMA re-assignment published (and posted here) previously).

2. It is very difficult to find what I would consider to be “complete data sets” for molecules and solids being studied by spectroscopic and computational methods. For many molecular solids, the influences of thermal motion are not important to providing a proper vibrational analysis by solid-state density functional theory methods. Heating a crystal may make spectral lines broader, but phase changes and unusual spectral features do not often result when heating a sample from cryogenic (say, liquid nitrogen) to room temperature. Yes, there are thousands of cases where this is not true, but several fold more cases where it is. We are fortunate to live in a temperature regime where characterization is reasonably straightforward and yet we can modify a system to observe its subtle changes under standard laboratory conditions. The THz spectrum of S-(+)-Ketamine Hydrochloride gets a bit cleaner upon cooling, which makes the assignment easier. As the ultimate goal is to be able to characterize these systems in a person’s pocket instead of their liquid nitrogen thermos, the limited observed change to the spectrum upon cooling is important to note.

3. Crystal06 vs. DMol3 – This paper contains what is hoped to be a level, pragmatic discussion about the strengths and weaknesses of computational tools available to terahertz spectroscopists for use in their efforts to assign spectra. This type of discussion is, as a computational chemist using tools and not developing tools, a touchy subject to present on not because of the finger-pointing of limitations with software, but because the Crystal06 team and Accelrys (through Delley’s initial DMol3 code) clearly are doing things that the vast majority of their users (myself included) could in no way do by themselves. The analysis for the theory-minded terahertz spectroscopist is presented comparing two metrics – speed and functionality (specifically, infra-red intensity prediction). What is observed as the baseline is that both DMol3 and Crystal06 make available density functionals and basis sets that, when used at high levels of theory and rigorous convergence criteria, produce simulated terahertz spectra with vibrational mode energies that are in good (if not very good) agreement with each other. For the terahertz spectroscopist, Crystal06 provides as output (although this is system size- and basis set size-dependent) rigorous infrared intensity predictions for vibrational modes, inseparable from mode energy as “the most important” pieces of information for mode assignments. While DMol3 does not produce infrared intensities (the many previous terahertz papers I’ve worked on employed difference-dipole calculations that are, at best, a guesstimate), DMol3 produces very good mode energy predictions in 1/6th to (I’ve seen it happen) 1/10th the time of a comparable Crystal06 calculation. This is the reason DMol3 has been the go-to program for all of the neutron scattering spectroscopy papers cited on this blog (where intensity is determined by normal mode eigenvectors, which are provided by both (and any self-respecting quantum chemical code) programs).

Now, it should be noted that this difference in functionality has NOTHING to do with formalism. Both codes are excellent for what they are intended to do. To the general assignment-minded spectroscopist (the target audience of the Discussion in the paper), any major problem with Crystal06 likely originates with the time to run calculations (and, quite frankly, the time it takes to run a calculation is the worst possible reason for not running a calculation if you need that data. Don’t blame the theory, blame the deadline). In my past exchanges with George Fitzgerald of Accelrys, the issue of DMol3 infrared intensities came up as a feature request that would greatly improve the (this) user experience and Dr. Fitzgerald is very interested (of course) in making a great code that much better. Neither code will be disappearing from my toolbox anytime soon.

4. The Periodicity Of The Molecular Solid Doesn’t Care What The Space Group Is – One of the more significant problems facing the assignment-minded spectroscopist is the physical description of molecular motion in a vibrational mode. In the simplest motions involving the most weakly interacting molecules, translational and rotational motions are often quite easy to pick out and state as such. When the molecules are very weakly interacting, often the intramolecular vibrational modes are easy to identify as well, as they are largely unchanged from their gas-phase descriptions. In ionic solids or strongly hydrogen-bonded systems, it is often much harder to separate out individual molecular motions from “group modes” involving the in- and out-of-phase motions of multiple molecules. In the unit cells of molecular solids, it can be the case that these group modes appear, by inspection, to be extremely complicated, sometimes too involved to easily describe in the confines of a table in a journal article.

S-(+)-Ketamine Hydrochloride is one such example where a great simplification in vibrational mode description comes from thinking, well, “outside the box.” The image below shows two cells and the surrounding molecules of S-(+)-Ketamine Hydrochloride. As it is difficult to see why the mode descriptions are complex from just an image, assume that I am right in this statement of complexity. Part of this complexity comes from the fact that the two molecules in the unit cell are not strongly interacting, instead packed together by van der Waals and dispersion forces more than anything else. The key to a greatly simplified assignment comes from the realization that the most polar fragments of these molecules are aligned on the edges of the unit cell.

An alternate view of molecular vibrational motion comes from considering not the contents of the defined unit cell but the hydrogen-bonding and ionic bonding arrangement that exists between pairs of molecules between unit cells. The colorized image below shows two distinct chains (red and blue) that, when the predicted vibrational modes are animated, become trivial to characterize as the relative motions of a hydrogen/ionic-bonded chain. Rotational motions appear as spinning motions of the chains, translational motions as either chain sliding motions or chain breathing modes. It appears as a larger macromolecule undergoing very “molecular” vibrations. In optical vibrational spectroscopy, selection rules and the unit cell arrangement do not produce in- and out-of-phase motions of the red and blue chains, as only one “chain” exists in the periodicity of the unit cell. In neutron scattering spectroscopy, these relative motions between red and blue would appear in the phonon region. This same discussion was had, in part, in a previous post on the solid-state terahertz assignment of ephedrine (with a nicer picture).

So, look at the cell contents, then see if there’s more structure than crystal packing would indicate. It greatly simplifies the assignment (which, in turn. greatly simplifies the reader’s digestion of the vibrational motions).

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

Department of Chemistry, Syracuse University, Syracuse, New York 13244-4100

Abstract: The terahertz (THz) spectrum of (S)-(+)-ketamine hydrochloride has been investigated from 10 to 100 cm-1 (0.3-3.0 THz) at both liquid-nitrogen (78 K) and room (294 K) temperatures. Complete solid-state density functional theory structural analyses and normal-mode analyses are performed using a single hybrid density functional (B3LYP) and three generalized gradient approximation density functionals (BLYP, PBE, PW91). An assignment of the eight features present in the well-resolved cryogenic spectrum is provided based upon solid-state predictions at a PW91/6-31G(d,p) level of theory. The simulations predict that a total of 13 infrared- active vibrational modes contribute to the THz spectrum with 26.4% of the spectral intensity originating from external lattice vibrations.

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.

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.

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.

The Inelastic Neutron Scattering Spectrum Of Nicotinic Acid And Its Assignment By Solid-State Density Functional Theory

Accepted in Chemical Physics Letters.  What began as a reasonably straightforward inelastic neutron scattering (INS) assignment was expanded upon reviewer request to include an analysis of the potential for in-cell nicotinic acid (or niacin, depending on who you ask.   Not to be confused with this Niacin, which would be another post altogether) prototropic tautomerization (technically, one might consider this just proton migration along the chain of the nicotinic acid molecules in the solid-state, which might just be more supported as, providing the punch line early, proton migration does not seem to occur in this system), a point that was mentioned in the paper as a possibility within the crystal cell but not originally examined as part of the spectral assignment.   In the crystal cell picture shown below, tautomerization would result in proton H5 migrating to N’, yielding a chain (if it propagated down the entire one-dimensional chain of nicotinic acid molecules in the solid-state) of zwitterions (molecules with both positive and negative charges on the covalent framework).   Anyone with experience in the solid-state study of amino acids knows that zwitterions are not only stable species in the solid-state, but they can also the dominant species in the solid-state, as ionic interactions and the dipole alignment that results from the alignment of, in this case, zwitterions, can yield greater stability than the neutral species, where only hydrogen bonding and dispersions forces occur in the crystal packing arrangement.

The inelastic neutron scattering assignment by solid-state density functional theory (DFT) strongly supports that, at the 25 K temperature of the neutron experiment, the crystal cell is of the neutral, non-zwitterionic form (as shown below, which labels the possible arrangements of hydrogens in the Z=4 crystal cell).  Furthermore, despite the existence of several potentially stable proton arrangements in the crystal cell (the three additional forms shown below), the nicotinic acid crystal cell seems to prefer the neutral form even through room temperature.  Fortunately, previous studies using other spectroscopic methods seem to agree.  As has been the case for the vast majority of all of the previous INS studies, the solid-state DFT calculations were performed with DMol3 and the INS simulated spectra generated with Dr. A. J. Ramirez-Cuesta’s most excellent aClimax program.

As is often the case when a competent reviewer serves you a critical analysis of your submitted work, the final result is all the better for it.

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

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

Keywords: nicotinic acid, niacin, vitamin B3, inelastic neutron scattering spectroscopy, solid-state density functional theory

Abstract: The 25 K inelastic neutron scattering (INS) spectrum of nicotinic acid has been measured and assigned by solid-state density functional theory (DFT). Vibrational mode energies involving the carboxylic acid proton are found to be significantly altered due to intermolecular hydrogen-bonding. There is good overall agreement between experiment and simulation in all regions of the spectrum, with identified deviations considered in detail by spectral region: phonon (25 – 300 cm-1), molecular (300 – 1600 cm-1), and high-frequency (>2000 cm-1). The relative energies, geometries, and vibrational spectra associated with hypothesized tautomerization in the solid-state have also been investigated.

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.

Importance Of Vibrational Zero-Point Energy Contribution To The Relative Polymorph Energies Of Hydrogen-Bonded Species

In press, in Crystal Growth and Design.  A short paper with an important message.  In principle, solid-state quantum chemical methods provide the tools for both the prediction of crystal polymorphs and the calculation of the relative energies of characterized crystal forms to determine why one version forms preferentially.  That said, modern solid-state quantum chemical methods are dominated by density functional theory which, although work is being performed to address this issue, are fundamentally incapable of accounting for all of the energy terms in the complete lattice energy calculation of solid-state materials because dispersion forces are not accounted for (there are methods around this, be they empirical or by way of solid-state Moeller-Plesset Perturbation Theory, which we may even have the computing power to handle someday…).

In molecular polymorphs, the energies of the crystal cells per molecule may be quite similar to one another because, being molecules with polar and non-polar regions, specific functional groups tend to bind preferentially to other specific functional groups, which all may involve similar interaction energies.  The point is that the lattice energy differences between different polymorphs may be quite small.  In such cases, the vibrational zero-point energy of the crystal cells may be very important contributors to the experimentally determined polymorph energy differences.  Such is found to be the case for the alpha- and gamma- polymorphs of glycine.

Specifically in the glycine example and other polymorphs for which proper thermochemistry is available, we even have a means to estimating what SHOULD be the lattice energy of the crystal without relying on theoretical models (and their inherent limitations).  For glycine, the experimental enthalpies for both crystal forms have been measured.  We have the experimental vibrational spectrum available against which to compare the theoretical work, from which we can determine the zero-point energy for the unit cell (simply 1/2 the sum of the vibrational mode energies).  With that information, we can determine (to a first approximation, there are many other factors to consider that play lesser roles in the final value) the experimental lattice energies.  These values then provide a benchmark for determining the abilities of theoretical models to reproduce this most fundamental of the solid-state quantum chemical properties.

Sharon A. Rivera1,2, Damian G. Allis1,3, Bruce S. Hudson1

1. Department of Chemistry, Syracuse University, Syracuse, NY 13224-4100
2. School of Chemistry, University of New South Wales, Sydney, NSW 2052, Australia
3. Nanorex, Inc., Bloomfield Hills, MI 48302-4100

Abstract: The relative stability of polymorphic crystal forms is a challenging conceptual problem of considerable technical interest.  Current estimates of relative polymorph energies concentrate on lattice energy.  In this work the contribution of differences in zero-point energy and vibrational enthalpy to the enthalpy difference for polymorphs is investigated.  The specific case investigated is that of alpha- and gamma-glycine, for which the experimental enthalpy difference is known.  Periodic lattice DFT computations are used to provide the vibrational spectrum at the Gamma-point.  It is confirmed that these methods provide reasonable descriptions of the inelastic neutron scattering spectra of these two crystals.  It is found that the difference in the zero-point energy is about 1.9 kJ/mol and that the vibrational thermal population difference is 0.9 kJ/mol in the opposite sense.  The overall vibrational contributions to the enthalpy difference are much larger than the observed value of ca. 0.3 kJ/mol.  The vibrational contribution must be largely compensated by the lattice energy difference.  The polymorphs of glycine differ in the pattern of their hydrogen bonds, a feature common to many polymorphs of interest.  The consequent difference in the N-H stretching frequencies is a contributor to the zero-point correction but the major effect stems from changes in the bending vibrations.

The Solid-State Terahertz Spectrum of MDMA (Ecstasy) – A Unique Test for Molecular Modeling Assignments

In press, in Chemical Physics Letters (CPL).  Yes, the blog has taken a bit of a turn, from high explosives to illicit drugs.  I expect my google rating to rise sharply with this post.  The protonated form of the 3,4-methylene-dioxymethamphetamine (Ecstasy, but I’ll keep the post legit, so it is herein referred to as MDMA) molecule (herein referred to as MDMA:H+) and MDMA:H+ in its crystal cell with a chloride ion (Cl, the crystal form herein referred to as MDMA:HCl) is shown below in yet another fantastic NanoEngineer-1 rendering (if I do say so myself).

This CPL article is, to some extent, a response to those in the terahertz community who continue to attempt spectral assignments of crystalline and poly-crystalline samples using isolated-molecule quantum chemical calculations.  The MDMA:HCl sample and MDMA molecule, as a pair, are a very interesting case study of theory and experiment for reasons detailed below.  The spectra, shown below from a previous version of the paper (but the same spectra), show quite a bit of detail that will make sense shortly.

Panel A shows the isolated-molecule calculation for the neutral MDMA molecule at a B3LYP/6-31G(d) level of theory (in red).  You will note that this simulated spectrum is in very good agreement with experiment (in black), reproducing all of the major features and showing a number of smaller features that account for shoulders.  This agreement was the basis for the assignment of the MDMA:HCl spectrum reported in: G Wang, J Shen, Y Jia. “Vibrational spectra of ketamine hydrochloride and 3,4-methylenedioxymethamphetamine in terahertz range.” Journal of Applied Physics 102 (2007) 013106/1-06/4.

The new theoretical analysis reported in the CPL article was instigated by this assignment in this previous publication.  Relevant to the measured sample and the previously reported assignment, two points arise that require address.

1. The previous calculation, as reported, was of the neutral MDMA molecule and is reasonably close to the MDMA spectrum shown above (in red.  This calculation was redone for the CPL article for comparative purposes).  As the experimental THz sample was of solid-state MDMA:HCl, the appropriate form of the molecule to run is not the neutral MDMA molecule, but the protonated form, MDMA:H+.  The protonated form has a different vibrational spectrum (shown in green in Panel A) than the isolated molecule form.  At the very least, the isolated-molecule to consider for the MDMA:HCl sample must be the protonated form.  Interestingly, the re-calculation at B3LYP/6-31G(d) reported for the CPL article predicts a fifth vibrational mode at 48.0 cm-1 that was not reported in the previous study.  We do not know if the previous group missed that peak in the write-up, decided that (since it is a low-intensity mode) it was not worth reporting, or if their starting molecular geometry was somehow different so that the other four modes were predicted to be in the same region and this mode was somehow turned off.

2. The solid-state spectrum shown in Panel B at a BP/DNP level of theory does not agree as well as the isolated-molecule MDMA B3LYP/6-31G(d) calculation. That being said, THAT IS NOT THE POINT.  The goal of a simulated spectrum IS NOT to obtain the closest spectral agreement with experiment.  The goal IS to explain the solid-state spectrum with the best theoretical model possible that, hopefully, is as close to the experimental result as possible.  In this case, the solid-state BP/DNP spectrum contains a finite number of vibrational modes that do group according to features in the THz spectrum, making the assignment reasonably straightforward.  Interestingly, the two most intense modes in the solid-state BP/DNP calculations involve the motions of the Cl…H+-N chains, which CANNOT be accounted for in an isolated-molecule calculation of either the neutral MDMA molecule or the protonated MDMA:H+.

In summary, as taken from the CPL paper:

With all of these considerations taken into account in this re-examination of the MDMA.HCl THz spectrum, it is found that this system serves as a fortuitous example of one whose THz spectrum is predicted quite precisely by two very different approaches, but is only described accurately by one that considers the crystal environment and the actual state of the molecule in its solid-state form.

Damian G. Allis1,2, Patrick M. Hakey1, and Timothy M. Korter1

1. Department of Chemistry, Syracuse University, Syracuse NY 13244-4100 USA
2. Nanorex, Inc., P.O. Box 7188, Bloomfield Hills, MI 48302-7188 USA

Abstract: The terahertz (THz, far-infrared) spectrum of 3,4-methylene-dioxymethamphetamine hydrochloride (Ecstasy) is simulated using solid-state density functional theory.  While a previously reported isolated-molecule calculation is noteworthy for the precision of its solid-state THz reproduction, the solid-state calculation predicts that the isolated-molecule modes account for only half of the spectral features in the THz region, with the remaining structure arising from lattice vibrations that cannot be predicted without solid-state molecular modeling.  The molecular origins of the internal mode contributions to the solid-state THz spectrum, as well as the proper consideration of the protonation state of the molecule, are also considered.