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.

www.elsevier.com/locate/cplett
en.wikipedia.org/wiki/Inelastic_neutron_scattering
en.wikipedia.org/wiki/Nicotinic_acid
en.wikipedia.org/wiki/Niacin
www.niacinb3.com
en.wikipedia.org/wiki/Tautomerization
en.wikipedia.org/wiki/Zwitterion
en.wikipedia.org/wiki/Amino_acids
en.wikipedia.org/wiki/Density_functional_theory
chemistry.syr.edu
www.syr.edu
www.isis.rl.ac.uk/MolecularSpectroscopy/aclimax/
accelrys.com/products/materials-studio/modules/dmol3.html

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

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. Rivera^1,2, Damian G. Allis^1,3, 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.

pubs.acs.org/journals/cgdefu/index.html
en.wikipedia.org/wiki/Quantum_chemistry
en.wikipedia.org/wiki/Polymorphism_(materials_science)
en.wikipedia.org/wiki/Density_functional_theory
en.wikipedia.org/wiki/M%C3%B8ller-Plesset_perturbation_theory
en.wikipedia.org/wiki/Functional_group
en.wikipedia.org/wiki/Zero-point_energy
en.wikipedia.org/wiki/Glycine
en.wikipedia.org/wiki/Enthalpy
creativecraftychemist.blogspot.com
hudsonlab.syr.edu
chemistry.syr.edu
www.syr.edu
www.unsw.edu.au
www.nanorex.com

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. Allis^1,2, 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.

www.sciencedirect.com/science/journal/00092614
en.wikipedia.org/wiki/Explosive
en.wikipedia.org/wiki/Recreational_drug_use
www.google.com
en.wikipedia.org/wiki/Methylenedioxymethamphetamine
en.wikipedia.org/wiki/Chloride
www.nanorex.com
en.wikipedia.org/wiki/Terahertz
www.thznetwork.org/wordpress
en.wikipedia.org/wiki/Quantum_chemistry
en.wikipedia.org/wiki/Hybrid_functional
en.wikipedia.org/wiki/Basis_set_%28chemistry%29
scitation.aip.org/journals/doc/JAPIAU-ft/vol_102/iss_1/013106_1.html
jap.aip.org/jap/top.jsp
en.wikipedia.org/wiki/Protonation
en.wikipedia.org/wiki/Density_functional_theory
www.somewhereville.com
chemistry.syr.edu/faculty/korter.html
chemistry.syr.edu
www.syr.edu

In press, in the journal Chemical Physics Letters. The RDX (cyclotrimethylenetrinitramine) solid-state simulation is the third from the original series of terahertz spectra that served as my ICPRFP research focus. This system is of interest (well, to me anyway) for three reasons.

1. This is the largest DMol³ calculation performed to date for a THz simulation (Z = 8). Between optimization, normal mode analysis, and vibrational mode displacements for the difference dipole intensity calculations, 1.5 solid months on a quad-core box.

2. Zeitler and Taday provided a 7 K THz spectrum of the RDX (in black) to complement the original room temperature spectrum (in blue), providing a far more resolved and feature-rich data set for theoretical comparisons.

3. As obvious from the high-resolution data, the RDX solid-state spectrum contains considerable vibrational structure. In fact, this THz spectrum contains more resolved peaks than there are vibrational modes in the isolated-molecule calculation in this region. While it has been demonstrated in several previous publications that solid-state THz spectra cannot be assigned using isolated-molecule calculations, all of the molecules in the previous studies contained enough vibrational structure in the THz region to potentially let the uninformed researcher attempt to get away with an isolated-molecule assignment. This is not the case for RDX, which contains only 6 isolated-molecule vibrational modes below 125 cm^-1.

Damian G. Allis^1,2, J. Axel Zeitler³, Philip F. Taday⁴, and Timothy M. Korter¹

1. Syracuse University, Department of Chemistry, 1-014 CST, 111 College Place, Syracuse, NY 13244-4100 USA
2. Nanorex, Inc., P.O. Box 7188, Bloomfield Hills, MI 48302-7188 USA
3. Department of Chemical Engineering, University of Cambridge, Pembroke Street, Cambridge CB2 3RA, UK
4. TeraView Limited, Platinum Building, St. Johns Innovation Park, Cambridge CB4 0WS, UK

Abstract: The solid-state terahertz (THz) spectrum (2 – 120 cm^-1) of α-form cyclotrimethylenetrinitramine (RDX) has been simulated using solid-state density functional calculations at a BP/DNP level of theory. BP/DNP features are in good agreement with both 298 K and a new 7 K polycrystalline RDX THz spectrum. The 7 K RDX spectrum is noteworthy for several mode shifts and spectral detail that greatly aids mode assignments. Previous RDX isolated-molecule calculations (with 6 calculated modes below 125 cm^-1) are incapable of accurately predicting the numerous features in this region, highlighting the importance of solid-state theoretical methods for solid-state terahertz feature assignments.

Keywords: Cyclotrimethylenetrinitramine, RDX, solid-state density functional theory, terahertz (THz) spectroscopy

www.sciencedirect.com/science/journal/00092614
en.wikipedia.org/wiki/RDX
en.wikipedia.org/wiki/Terahertz
www.icpostdoc.org
people.web.psi.ch/delley/dmol3.html
www.pssrc.org/index.php?id=axel_zeitler
www.teraview.com
www.syr.edu
chemistry.syr.edu
www.syracuse.com
www.nanorex.com
www.cheng.cam.ac.uk
www.cam.ac.uk
www.teraview.com