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

Sunday, February 21st, 2010

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.

pubs.acs.org/journal/jpcafh
www.somewhereville.com/?p=29
www.somewhereville.com/?p=26
www.somewhereville.com/?p=126
en.wikipedia.org/wiki/Density_functional_theory
en.wikipedia.org/wiki/Ketamine
www.crystal.unito.it
accelrys.com/products/materials-studio/quantum-and-catalysis-software.html
en.wikipedia.org/wiki/Time_domain_terahertz_spectroscopy
en.wikipedia.org/wiki/Computational_chemistry
accelrys.com
en.wikipedia.org/wiki/Inelastic_neutron_scattering
en.wikipedia.org/wiki/Vibrational_spectroscopy
www.somewhereville.com/?p=680

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

Sunday, February 21st, 2010

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

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

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

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

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

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

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

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

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

pubs.acs.org/doi/abs/10.1021/jp9114095
pubs.acs.org/journal/jpcafh
en.wikipedia.org/wiki/Computational_chemistry
accelrys.com/products/materials-studio/quantum-and-catalysis-software.html
www.crystal.unito.it
en.wikipedia.org/wiki/Anharmonicity
chemistry.syr.edu/faculty/walnut.html
en.wikipedia.org/wiki/Hydrogen_bond
en.wikipedia.org/wiki/Peptide
en.wikipedia.org/wiki/Force_field_%28chemistry%29
www.charmm.org
ambermd.org
gromacs.org
en.wikipedia.org/wiki/Molecular_dynamics

L-Alanine Alaninium Nitrate (LAAN) Shout-Out At spectroscopyNOW.com (And Better Raman Image Here)

Tuesday, December 1st, 2009

It doesn’t happen often.  Simply marking for interested parties that David Bradley wrote a piece about the recent L-Alanine Alaninium Nitrate article published in Physical Chemistry Chemical Physics (Phys. Chem. Chem. Phys., 2009, 11, 9474 – 9483, DOI: 10.1039/b905070a) with a specific focus on the organic ferroelectric behavior of this system as argued from the results of the inelastic neutron scattering (INS) and temperature-dependent Raman spectroscopic studies.  Also, of course, the entire discussion and analysis revolves around the results of the density functional theory (DFT) studies performed on the solid-state system with DMol3.

I find it mildly amusing that a paper that went through several rather exhaustive crystallography-focused review cycles (fighting with crystallography-specific reviewers about the use of the vibrational spectroscopy to provide the more realistic view of this organic salt in the solid-state) makes headlines (well, you know) only for the vibrational spectroscopy.  I certainly won’t point fingers (only browsers), but I’ve yet to see someone say the same of vibrational spectroscopists.

As a brief addition, the Raman spectrum presented on the spectroscopyNOW website does not provide quite the resolution of the original.  In the interest of laying all doubts aside, a larger version of the same image is provided below.

The 293 K and 78 K Raman spectra of LAAN showing temperature-dependent peak changes (black box).

According to the article (his, not ours)…

Even if there turns out to be no ferroelectric transition in LAAN, it could still represent an unusual and intriguing structure in which both a neutral and zwitterionic L-alanine amino acid exist in the same crystal cell together with crystalline nitric acid. Such a material might help to improve the computational structural models, improve our understanding of the spectra of related materials and perhaps offer clues to designing a next-generation material that does have the elusive ferroelectric properties.

The article is available at www.spectroscopynow.com/coi/cda/detail.cda?id=22458&type=Feature&chId=3&page=1.  A local copy of the article (in PDF format) is here: 2009december1_spectroscopynow_organicferroelectrics.pdf

www.spectroscopynow.com/coi/cda/detail.cda?id=567&type=Feature&chId=0&page=1
www.somewhereville.com/?p=775
www.rsc.org/publishing/journals/cp/Index.asp
www.rsc.org/publishing/journals/CP/article.asp?doi=b905070a
en.wikipedia.org/wiki/Ferroelectricity
en.wikipedia.org/wiki/Neutron_scattering
en.wikipedia.org/wiki/Raman_spectroscopy
en.wikipedia.org/wiki/Density_functional_theory
accelrys.com/products/materials-studio/modules/dmol3.html
books.google.com/books?id=eZxreAojmj8C&pg=PA19&lpg=PA19&dq=crystallographers+are+bad+scientists&…&f=false
www.spectroscopynow.com
www.spectroscopynow.com/coi/cda/detail.cda?id=22458&type=Feature&chId=3&page=1
www.somewhereville.com/blogfiles/2009december1_spectroscopynow_organicferroelectrics.pdf

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

Wednesday, September 30th, 2009

“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.

en.wikipedia.org/wiki/Mitch_Hedberg
pubs.acs.org/journal/jpcafh
en.wikipedia.org/wiki/Phencyclidine
accelrys.com/products/materials-studio/modules/dmol3.html
en.wikipedia.org/wiki/Terahertz_radiation
en.wikipedia.org/wiki/Density_functional_theory
en.wikipedia.org/wiki/Density_functional_theory#Approximations_.28Exchange-correlation_functionals.29
en.wikipedia.org/wiki/Zwitterions
en.wikipedia.org/wiki/Amino_acid
www.somewhereville.com/?p=680
www3.interscience.wiley.com/journal/122540399/abstract
www.crystal.unito.it
en.wikipedia.org/wiki/Basis_set_(chemistry)
en.wikipedia.org/wiki/X-ray_scattering_techniques
en.wikipedia.org/wiki/Inelastic_neutron_scattering
chemistry.syr.edu
www.syr.edu

Low-Temperature X-ray Structure Determination and Inelastic Neutron Scattering Spectroscopic Investigation of L-Alanine Alaninium Nitrate, a Homologue of a Ferroelectric Material

Wednesday, July 29th, 2009

Accepted in Physical Chemistry Chemical Physics. Quite possibly the hardest-fought article within the peer review process I’ve found myself on the revision-side of, with an interesting debate between we authors and two crystallography reviewers occurring over three total revisions (and, it should be noted, two of the three original reviewers accepted the article without any revision, so this really was a debate between we authors and the crystallography reviewers).

To briefly summarize (as the content of the controversy is part of ongoing work), the paper includes an inelastic neutron scattering (INS) spectrum at 25 K, a new X-ray diffraction study at 90 K, and 77 K and 293 K Raman spectra. The INS spectrum and 77 K Raman spectrum contain a feature at 450 cm-1 that does not occur at higher temperature and that is not predicted by the solid-state density functional theory simulation with the 90 K structure. The proposed argument is that a proton is either shifted from an alanine -NH3+ group to a nitrate oxygen (which the crystallography reviewers generally refused to accept as a reasonable explanation) or the potential energy surface for this proton between the -NH3+ and nitrate oxygen is changed considerably due to contraction of the unit cell at low temperature (which our 90 K crystal structure does not show and so, if it occurs, must occur at lower temperature).

The disagreement between ourselves and the crystallography reviewers concerns the use of the 90 K structure as a basis for proposing full proton motion from alanine to nitrate. On the one hand, the 90 K structure solves with the protons on the alanine and so, to the extent that one can extrapolate from a single point, there is a notable absence of crystallographic data to confirm that proton motion is occurring. On the other hand, the spectroscopic change (new peak at 450 cm-1) is entirely consistent with the proposed proton motion to the nitrate OR the marked change in the shape of the potential well for the proton motion between the -NH3+ and nitrate oxygen. We expect this mystery to be solved with a very low temperature neutron diffraction study to determine exactly where the proton resides at 25 (or so) K.

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

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

Keywords: L-alanine alaninium nitrate, amino acid salt, nonlinear optical material, vibrational spectroscopy, inelastic neutron scattering spectroscopy, solid-state density functional theory

Abstract: The 2:1 amino acid salt of L-alanine with nitric acid was crystallized and the vibrational spectrum measured at 25 K by incoherent inelastic neutron scattering (INS) spectroscopy. The spectrum was simulated using solid-state density functional theory based on a new 90 K structure determination. A feature observed at approximately 450 cm-1 in the experimental spectrum of L-alanine alaninium nitrate is noticeably absent in the calculation. Further investigation by Raman spectroscopy reveals spectral differences between the spectra at 77 and 293 K. The nature of these spectral changes and the disagreement between the INS spectrum and its simulation are discussed in relation to a possible structural change at low (< 90 K) temperature.

www.rsc.org/publishing/journals/cp/Index.asp
en.wikipedia.org/wiki/Crystallography
en.wikipedia.org/wiki/Inelastic_neutron_scattering
en.wikipedia.org/wiki/Raman_spectroscopy
en.wikipedia.org/wiki/Density_functional_theory
en.wikipedia.org/wiki/Alanine
en.wikipedia.org/wiki/Nitrate
en.wikipedia.org/wiki/Potential_energy_surface
en.wikipedia.org/wiki/Neutron_diffraction

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