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.

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

Vicinal Deuterium Perturbations on Hydrogen NMR Chemical Shifts in Cyclohexanes

In press, in the Journal of the American Chemical Society. To answer a student question (on the first day of class, no less) about the geometry/sp3 hybridization of carbon in my 2nd semester organic chemistry class, Prof. Baldwin began by writing the time-independent Shroedinger Equation on the chalkboard.

Needless to say, the wavefunction that was my future collapsed instantaneously.

To summarize considerable computational effort (and ignoring many, many equations you can find in the paper), the shifts in hydrogen (H) peak positions in the 1H NMR spectrum of cyclohexane that result from deuteration (D) can be explained by considering the contribution of the vibrational stretching mode differences of the C-H and C-D bonds. Interestingly, the trend determined from the computational studies is fairly insensitive to the use of electron correlation methods (B3LYP, MPW91, MP2 were all employed with 6-31++G(2d,p), 6-311++G(2d,2p), and Aug-cc-pVTZ basis sets), with Restricted Hartree-Fock (RHF) results very similar and much faster to calculate. The RHF results served as the basis for the analysis in the paper.

The geometry optimization of a molecule will provide you static bond lengths (C-H, C-D, C-C for cyclohexane). In the case of just the optimizations, H and D look identical to the electronic wavefunction (the basis of the Born-Oppenheimer Approximation). If the bond lengths stretched like harmonic oscillators (the approximation we almost always use when performing normal mode analyses in quantum chemical codes), the calculated bond lengths would be the correct (physical) average bond lengths. Of course, no chemical bond is a perfect harmonic oscillator, a fact that explains transition probabilities for overtone and combination bands that are forbidden within the harmonic approximation. For atom pairs that stretch with a significant anharmonic character (such as C-H/D), the actual description of the bond length is a very important factor to consider when trying to extract important trends based on the actual bond length behavior, and is as described in the figure below.

This figure shows the bottom of the potential wells for idealized harmonic and Morse oscillators. The figure, like the paper, only considers the contribution from the vibrational zero-point level (v0). The Heq/Deq position at the bottom of the potential wells is the calculated bond length after geometry optimization. If the stretching potential is harmonic (red), the average position of the H/D atom is always at this position regardless of the system energy (the H atom is sampling as much of the short-side of the potential as it is the long-side, which, you guessed it, averages to the middle).

Now consider the anharmonic oscillators (our Morse functions). The H atom, being lighter, has a higher vibrational zero-point energy (VZPE). Its average position (or mean displacement from the C atom) due to VZPE (Heq + v0) is slightly longer. The deuterium, with twice the mass, has a lower VZPE. As a result of lying lower along the Morse potential, its average VZPE-corrected position (Deq + v0) is closer to the calculated static position than for H. The difference in the contributed length to the average positions is shown in green. This position-based description is really just for show and neglects all of the quantum theory, but it does make the point. You can consider the green to be the effective additional distance within the Morse potential that the two atoms sample compared to the harmonic potential as part of their stretching mode, with the average position differing due to this larger spatial sampling in each oscillation.

So, “real C-D” is shorter than “real C-H”. Accordingly, the 1H NMR peak position of C-H in the presence of C-H bonds (which are further away) is different than in the presence of C-D bonds (which are closer).

This is also the first paper I’ve been on that did not directly involve my making an image (hence the involved image above).

Daniel J. O’Leary1, Damian G. Allis2,3, Bruce S. Hudson2, Shelly James2, Katherine B. Morgera2, and John E. Baldwin2

1. Department of Chemistry, Pomona College, Claremont, California 9171-6338
2. Department of Chemistry, Syracuse University, Syracuse, New York 13244-4100
3. Nanorex, Inc., P.O. Box 7188, Bloomfield Hills, Michigan 48302-7188

Abstract: The substitution of a deuterium for a hydrogen is known to perturb the NMR chemical shift of a neighboring hydrogen atom. The magnitude of such a perturbation may depend on the specifics of bonding and stereochemical relationships within a molecule. For deuterium-labeled cyclohexanes held in a chair conformation at -80oC or lower, all four possible perturbations of H by D as H-C-C-H is changed to D-C-C-H have been determined experimentally, and the variations seen, ranging from 6.9 to 10.4 ppb, have been calculated from theory and computational methods. The predominant physical origins of the NMR chemical shift perturbations in deuterium-labeled cyclohexanes have been identified and quantified. The trends defined by the Δδ perturbation values obtained through spectroscopic experiments and by theory agree satisfactorily. They do not match the variations typically observed in vicinal JH-H coupling constants as a function of dihedral angles.

pubs.acs.org/journals/jacsat/index.html
en.wikipedia.org/wiki/Orbital_hybridisation
chemistry.syr.edu/faculty/baldwin.html
en.wikipedia.org/wiki/Schr%C3%B6dinger_equation
en.wikipedia.org/wiki/NMR
en.wikipedia.org/wiki/Cyclohexane
en.wikipedia.org/wiki/Deuterium
en.wikipedia.org/wiki/Hydrogen
en.wikipedia.org/wiki/Electron_correlation
en.wikipedia.org/wiki/Density_functional_theory
en.wikipedia.org/wiki/Hybrid_functional
en.wikipedia.org/wiki/M%C3%B8ller-Plesset_perturbation_theory
en.wikipedia.org/wiki/Basis_set_(chemistry)
en.wikipedia.org/wiki/Hartree-Fock
en.wikipedia.org/wiki/Born-Oppenheimer_approximation
en.wikipedia.org/wiki/Harmonic_oscillator
en.wikipedia.org/wiki/Overtone
en.wikipedia.org/wiki/Molecular_vibration
en.wikipedia.org/wiki/Morse_potential
en.wikipedia.org/wiki/Zero-point_energy
www.chemistry.pomona.edu/Chemistry/O%27Leary.html
www.chemistry.pomona.edu
www.pomona.edu
chemistry.syr.edu
www.syr.edu
www.nanorex.com