In press, available from Chemistry – A European Journal. This is a paper a year or so in the making that, had I started it a year from now, would have taken a very different route. Much of the work I’ve done in neutron and terahertz spectroscopy has demonstrated that the inclusion of the crystal environment in quantum chemical treatments of solid-state systems is the key to interpreting the data (makes sense). This paper examines the unusual orientation of the [GeH₃]^- anion in two crown ether complexes with potassium (K⁺) and rubidium (Rb⁺) cations. The crystal cells of these two complexes are far larger than computational resources would handle now (and definitely when the project started), but they’d be easily handled on better equipment (such as an 8-processor box with a terabyte or so of scratch space). The isolated molecule calculations (Dr. Alex Granovsky’s PC-GAMESS version with basis sets from EMSL) demonstrate that the potential energy surfaces corresponding to anion orientations in the vicinity of only the solvated cations is shallow (at best) and that any moderate collection of electrostatic interactions (such as those in the crystal cell) may be enough to stabilize the unexpected anion orientation. It is also of interest to note that the [GeH₃]^- anion prefers to bind to the K/Rb cations by the hydrogens (which we refer to as “inverted”) and NOT the germanium anionic lone pair (the traditional, van’t Hoff arrangement, all of those calculations being performed at B3LYP/6-311G(d,p) and MP2/6-311G(d,p) levels of theory with LANL2DZ ECPs for the K and Rb). This “oddity” was considered previously by the great Paul v. R. Schleyer and coworkers for a similar Na-SiH₃ system some time back (Angew. Chem. 1994, 106, 221-223). This project will hopefully be revisited with solid-state density functional theory to see just how the crystal interactions combine to impose the non-traditional [GeH₃]^- binding orientation.

W. Teng, D. G. Allis and K. Ruhlandt-Senge

Abstract: The preparation of a series of crown ether-ligated alkali metal (M = K, Rb, Cs) germyl derivatives M(crown ether)GeH₃ via hydrolysis of the respective tris(trimethylsilyl)germanides is reported. Depending on the alkali metal and the crown ether diameter, the hydrides display either contact molecules or separated ions in the solid state, providing a unique structural insight into the geometry of the obscure GeH₃^- anion.

Germyl derivatives displaying M-Ge bonds in the solid state are of the general formula M([18]crown-6)(thf)GeH₃ with M = K, 1; M = Rb, 4. Interestingly, the lone pair at germanium is not pointed towards the alkali metal, rather two of the three hydrides are approaching the alkali metal center to display M-H interactions.

Separated ions display alkali metal cations bound to two crown ethers in a sandwich-type arrangement and non-coordinated GeH₃^- anions to afford complexes of the type [M(crown ether)2][GeH₃] with M = K, crown ether = [15]crown-5, 2; M = K, crown ether = [12]crown-4, 3 and M = Cs, crown ether = [18]crown-6, 5.

The highly reactive germyl derivatives were characterized using X-ray crystallography, 1H and 13C NMR, and IR spectroscopy. Density functional theory (DFT) and Second-Order Moeller-Plesset perturbation theory (MP2) calculations were performed to analyze the geometry of the GeH₃^- anion in the contact molecules 1 and 4.

www3.interscience.wiley.com/cgi-bin/jhome/26293?CRETRY=1&SRETRY=0
www3.interscience.wiley.com/cgi-bin/abstract/112234636/ABSTRACT
en.wikipedia.org/wiki/Jacobus_Henricus_van_’t_Hoff
www.emsl.pnl.gov/forms/basisform.html
chemistry.syr.edu/faculty/ruhlandt.html
classic.chem.msu.su/gran/gamess
www.chem.uga.edu/schleyer

At some point in my first or second year as a graduate student, the Spencer Research Group made a trek to Rochester to hear a talk by Senior HP Fellow Stan Williams. After some back-and-forth about the potential of nanotechnology to radically alter the development of computer chips to attain unheard of high speeds, someone in the audience piped up “Why do we need faster computers? How much faster do I need to run Word and Excel?” And this wasn’t a witty uber/1337 poking fun at bloated Windows products. This was a serious, seemingly put-off at the prospects, 60-something-suit-and-tie with, I fear, his elbow firmly on the pulse of the technology budget for his division.

Seven years later, I’m practicing transplant surgery with motherboards too big for their cases. In case this is of use to anyone, I have been, in the last year or so, 8 for 14 on the first order for ASUS K8N-DL motherboards and 12 for 14 in total, meaning 2 sit here useless. These boards are fine once they’re made to work, but the games played with installations and store return policies are far beyond the call of duty given all other time constraints. I am hoping these problems will be remedied with the beginning of a long line of Tyan Thunder K8WE purchases, with which I’m now 2 for 2 (and discovered that now I have to worry about defective MSI video cards).

And, please, never buy computer cases that come with power supplies if you intend on doing anything substantive with them (you should be fine running Excel and Word, of course). Often, you get what you pay for. Sometimes, they don’t even give you that.

www.hpl.hp.com/about/bios/stanwilliams.html
chemistry.syr.edu/faculty/spencer.html
www.msicomputer.com
www.microsoft.com
www.asus.com
www.tyan.com
www.hp.com

A nice summary (in pdf format) by Michael Francis at Accelrys about the use of solid-state density functional theory (DFT) in the assignment of the HMX THz spectrum published in J. Phys. Chem. A earlier this year. Also, I’m on record again extolling the virtues of DMol³, having now used it in a number of inelastic neutron scattering studies, this crazy terahertz business, and for (an upcoming) examining the crystal environment of small polyoxometalates (which I wouldn’t have even considered as early as two years ago given the state of computers way back when). Three more papers on the subject have come out since this case study was presented, all of which are linked and available in the terahertz spectroscopy category of this site.

pubs.acs.org/…/2006/110/i05/html/jp0554285.html
www.accelrys.com/reference/cases/studies/korter.pdf
www.adobe.com/products/acrobat/readstep2.html
www.accelrys.com

In press, available from ChemPhysChem. Wasting no time putting it all on the site. This is the sister paper to the solid-state density functional theory (DFT) paper on HMX from J. Phys. Chem. A (including the complete assignment of modes and motions of the PETN crystal using the DMol³ program) that made pretty good press. As for the determined agreement with experiment in these projects, two points certainly make a line. At the very least, the futility of isolated-molecule calculations for the assignment of crystalline THz spectra is certainly evident in the analysis. There’s quite a bit more work to be had for this project, of course. The good chaps at Teraview, Ltd., the supplier of the spectra, have recently gone cryogenic, which is going to do wonders for the theoretical assignments.

Abstract: The experimental solid-state terahertz (THz) spectrum (3 to 120 cm^-1) of the high explosive pentaerythritol tetranitrate (PETN, C₅H₆N₄O₁₂) has been modeled using solid-state density functional theory (DFT) calculations. Solid-state DFT employing the BP density functional is in best qualitative agreement with the features in the previously reported THz spectrum. The crystal environment of PETN includes numerous intermolecular hydrogen-bonding interactions that contribute to large (up to 80 cm^-1) calculated shifts in molecular normal mode positions in the solid-state. Comparison of the isolated-molecule and solid-state normal mode calculations for a series of density functionals reveals the extent to which the inclusion of crystal packing interactions and the relative motions between molecules are required for correctly reproducing the vibrational structure of solid-state THz spectra. The THz structure below 120 cm^-1 is a combination of both intermolecular (relative rotations and translations) and intramolecular (torsions, large amplitude motions) vibrational motions. Vibrational mode analyses indicate that the first major feature (67.2 cm^-1) in the PETN THz spectrum contains all of the optical rotational and translational cell modes and no internal (molecular) vibrational modes.

www3.interscience.wiley.com/cgi-bin/jhome/72514732
pubs.acs.org/cgi-bin/sample.cgi/jpcafh/…/jp0554285.html
en.wikipedia.org/wiki/PETN
www.accelrys.com/products/mstudio
www.teraview.com

In press, available from the International Journal of High Speed Electronics and Systems. In continuing efforts to pull every bit of useful information out of the solid-state density functional theory calculations run for the terahertz modeling of all the molecular explosives spectra Teraview, Ltd. could get their hands on, this IJHSES paper expands greatly on the SPIE paper posted previously (available here), looking at the dependences on parameter selection in the reproductions of THz spectra for HMX and PETN. Not the assignments of the two spectra (the HMX was performed as posted below, the PETN is as posted above), but the variation in simulation quality as a function of the treatment of the electronic structure (functionals, basis sets, integration grid sizes). I’m in complete agreement with Kieron Burke (well, it’s a fact, not an opinion, so what choice do I have) that “Density functional theory is a completely different, formally rigorous, way of approaching any interacting problem, by mapping it exactly to a much easier-to-solve non-interacting problem.” The problem, to quantum chemists, is the empirical methodology used to develop density functionals. The fact that programs like GAMESS and Gaussian offers 30-or-so density functionals should clue the user in that the agreement between theory and experiment may be as much due to the choice of density functional as the quality of the basis set for the chemical question being addressed. Empirical methods mean never having to say you’re sorry.

With the mandatory spectra figure from the paper, I also post here the timing results for running solid-state HMX and PETN on a single AMD Opteron processor. For what we do to simulate THz spectra, the DMol³ program-option “fine” grid size (0.15 Angstrom grid interval or rmaxp = 12.0 au (6.36 A); up to l = 6 if you’re into the whole [Grid Points] = 0.3351[l]² + 0.5552[l] + 3.9277 thing) is adequate for reproducing THz spectra and making assignments (grid size here referring to the quality of the mesh defined around a molecule used for matrix element evaluation).

Abstract: The analytical applications of terahertz (THz) spectroscopy for the characterization of molecular solids have been limited by the lack of information concerning the assignment of observed spectral features to specific internal (intramolecular) and external (intermolecular) atomic motions. Computational methodologies addressing the assignment of spectral data are the enabling technology for moving THz spectroscopy to the forefront of available detection methods for both imaging and spectroscopic applications. Solid-state density functional theory (DFT) studies have been performed on the high explosives cyclotetramethylenetetranitramine (HMX) and pentaerythritol tetranitrate (PETN) in order to address the dependencies of the predictions of solid-state vibrations in the terahertz (3 to 120 cm^-1) region on the choice of basis set and integration grid size, building on previous work that examined this dependency on the choice of density functional. DFT THz simulations reveal that both the choice of basis set and grid size have important influences on the reproduction of spectral features. The sensitivity to basis set choice is most pronounced in the calculation of vibrational intensities, where it is found that THz absorption intensities are most accurately reproduced when derived from basis set-sensitive Mulliken atomic charges as opposed to basis set-insensitive atomic charges generated by the Hirshfeld partitioning method.

en.wikipedia.org/wiki/Density_functional_theory
www.worldscinet.com/ijhses/ijhses.shtml
en.wikipedia.org/wiki/Terahertz
www.msg.ameslab.gov/GAMESS
en.wikipedia.org/wiki/PETN
en.wikipedia.org/wiki/HMX
dft.rutgers.edu/kieron/
www.teraview.com
www.accelrys.com
www.gaussian.com
www.amd.com