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.

The Terahertz Spectrum And Quantum Chemical Assignment Of 2,2,-Bithiophene In Cyclohexane

In press, in the journal Vibrational Spectroscopy. In a bit of a departure from the last several terahertz (THz) papers, this study involves the simulation of the solution-phase THz spectrum of the very, very thoroughly studied 2,2'-bithiophene in solution (cis and trans geometries and lowest-frequency vibrational modes are provided in the figure below), a phase both easier and more difficult than the solid-state density functional theory (DFT) calculations that have been the mainstay of previous studies. Simplicity comes from the molecular symmetry and smaller size of the system under study, with no issues of the temperature dependence of the lattice constants or the intermolecular interaction predictions complicating the spectral assignment of the lowest frequency modes. The difficulty comes from the ability to employ multiple theoretical models to study the system and the need for far higher levels of theory in the gas phase to perform an analysis worthy of experimental comparison.

In this study, the DFT and MP2 quantum chemical calculations were used to consider molecular geometry, cis and trans conformational energy differences, rotational barrier heights, the prediction of normal mode energies, and relative peak intensities.

One topic addressed in solution that is not an issue in the crystals studied to date are the accessibility of relative conformational minima at ambient conditions (kT, room temperature). In the case of 2,2'-bithiophene, the conformational flexibility is around the exocyclic thiophene-thiophene bond. With the description of the potential energy surface (PES) for rotation about the exocyclic bond determined by conformational calculations, the second step is the determination of relative populations of the cis and trans forms as a function of temperature. In this case, weighting of the PES by the Boltzmann distribution function yields the plot shown in the bottom of the figure below, from which the relative cis and trans populations can be determined by integration of the 0 to 90 (cis) and 90 to 180 (trans) regions.

The long-short of this particular study, which I save for the article itself, is that no single theory provides all the best answers, but sufficiently high levels of theory all do settle into the reasonable vicinity of accurate. At least, to the extent that all of the experimental data is in agreement.

Anna M. Fedor1, Damian G. Allis1,2, and Timothy M. Korter1

1. Department of Chemistry, Syracuse University, Syracuse, NY 13244 USA

2. Nanorex, Inc. Bloomfield Hills, MI 48302-7188 USA

Abstract: The room temperature solution-phase terahertz (THz, 7 to 165 cm-1) spectrum of 2,2-bithiophene in cyclohexane is reported. Density functional theory (B3LYP) and ab initio (MP2) methods employing the 6-311++G(2d,2p) and aug-cc-pVDZ basis sets are used to assign the THz vibrational structure and determine the relative populations of the cis and trans conformations, as well as the trans-trans rotational barrier height and the effects of the cyclohexane solvent on the predicted molecular geometries and vibrational frequencies. Significant differences are seen in the performance of the different theoretical methods, with the best performing method dependent upon the molecular property of interest. The best fit model of the experimental THz spectrum is achieved using MP2/aug-cc-pVDZ, which places the relative trans and cis populations at 54% and 46%, respectively.