Image caption: An approach combining terahertz spectroscopy, X-ray diffraction, and solid-state density functional theory was utilized to accurately measure the elasticities of poly-l-proline helices by probing their spring-like vibrational motions. In their communication (DOI: 10.1002/anie.201602268), T. M. Korter and co-workers reveal that poly-l-proline is less rigid than commonly expected, and that the all-cis and all-trans helical forms exhibit significantly different Young’s moduli.
If you use these results: Please drop me a line (firstname.lastname@example.org), just to keep track of where this does some good. That said, you should most certainly cite the EMSL and Basis Set references at the bottom of this page.
It’s a fair bet that Sir John Pople would be the world’s most cited researcher by leaps and bounds if people properly cited their use of the basis sets he helped develop.
The full 6-31G, 6-31G(d), and 6-31G(d,p) series (yes, adding 6-31G(d) is a bit of a cheat in this list) from the EMSL Basis Set Exchange is presented here in the interest of giving the general CRYSTALXX (that’s CRYSTAL88, CRYSTAL92, CRYSTAL95, CRYSTAL98, CRYSTAL03, CRYSTAL06, CRYSTAL09, now CRYSTAL14 – providing the names here for those who might be searching by version) user a “standard set” of basis sets that are, for the most part, the same sets one does / could employ in other quantum chemistry codes (with my specific interest being the use and comparison of Gaussian and GAMESS-US in their “molecular” (non-solid-state) implementations). Members of the CRYSTAL developer team provide a number of basis sets for use with the software. While this is good, I will admit that I cannot explain why the developers chose not to include three of the four most famous basis sets in all of (all of) computational chemistry – 3-21G (upcoming), 6-31G(d,p) (presented here), and 6-311G(d,p) (also upcoming).
Published earlier this year in RSC Advances (RSC Adv., 2013, 3, 19081-19096), a follow-up (for my part) to the study The Low-/Room-temperature Forms Of The Lithiated Salt Of 3,6-dihydroxy-2,5-dimethoxy-p-benzoquinone: A Combined Experimental And Dispersion-Corrected Density Functional Study in CrystEngComm last year. The theoretical section for this paper is a tour-de-force of Crystal09 solid-state optimizations, density functional and dispersion-correction dependence, and post-processing using Carlo Gotti’s TOPOND software. In brief, the combination of vibrational spectra, electochemical measurements, and solid-state density functional theory tests are used to predict the structure of the previously unknown lithiated tetramethoxy-p-benzoquinone structure based on the good-to-excellent agreement with two known TMQ crystal structures (the testing of density functionals and dispersion corrections being a very good survey of the pros and cons of the varied methods. If you were pondering an approach to follow to perform the same kind of theoretical analysis, the procedure set up by Gaëtan and Christine in this paper is fully worth your consideration).
In the search for low-polluting electrode materials for batteries, the use of redox-active organic compounds represents a promising alternative to conventional metal-based systems. In this article we report a combined experimental and theoretical study of tetramethoxy-p-benzoquinone (TMQ). In carbonate-based electrolytes, electrochemical behaviour of this compound is characterized by a reversible insertion process located at approximately 2.85 V vs. Li+/Li0. This relatively high potential reactivity, coupled with our effort to develop computational methodologies in the field of organic electrode materials, prompted us to complement these experimental data with theoretical studies performed using density functional theory (DFT). Single crystals of TMQ were synthesized and thoroughly characterized showing that this quinonic species crystallised in the P21/n space group. The experimental crystal structure of TMQ was then used to assess various DFT methods. The structural features and vibrational spectra were thus predicted by using as a whole five common density functionals (PBE, LDA, revPBE, PBEsol, B3PW91) with and without a semi-empirical correction to account for the van der Waals interactions using either Grimme’s (DFT-D2) or Tkatchenko–Scheffler (TS) scheme. The most reliable combination of the DFT functional and the explicit dispersion correction was chosen to study the Li-intercalated molecular crystal (LiTMQ) with the view of indentifying Li insertion sites. A very close agreement with the experiment was found for the average voltage by using the most stable relaxed hypothetical LiTMQ structure. Additionally, a comparison of vibrational spectra gained either for TMQ molecule and its dimer in gas phase or through periodic calculation was undertaken with respect to the experimentally measured infrared spectra. The topological features of the bonds were also investigated in conjunction with estimates of net atomic charges to gain insight into the effect of chemical bonding and intermolecular interaction on Li intercalation. Finally, π-electron delocalization of both quinone and alkali salts of p-semiquinone were determined using the Harmonic Oscillator model of Aromaticity (HOMA) or aromatic fluctuation index (FLU) calculations.
In press, in CrystEngComm (DOI:10.1039/C2CE26523). This is my first full paper completely internet-powered, in that I’ve not physically met any of the other co-authors (also in the internet-powered context, the recent paper on -annulene was written and submitted without sharing a room with Dr. Bruce Hudson, but we’re in the same building, so it doesn’t quite count). Also, one of the few papers for which I had no image generation duties (a rare treat).
The discussion of the very interesting possibilities of molecular redox materials in lithium-ion batteries aside, this paper presents a very thorough example of the power of computational approaches to greatly improve the understanding of solid-state molecular materials by (specifically) 1: overcoming the hydrogen position identification problems inherent in X-ray diffraction methods, 2: reproducing the changes that come with temperature variations in molecular crystals and explaining the origins of those (possibly subtle) changes by way of dispersion-corrected density functional theory, and 3: demonstrating that the nature of intermolecular interactions (specifically hydrogen bonding) can be rigorously cataloged across varied materials using post-optimization tools (in this case, using Carlo Gatti’s excellent TOPOND program).
Caption: Issue cover.
Following our first experimental and computational study of the room temperature (RT) form of the tetrahydrated 3,6-dihydroxy-2,5-dimethoxy-p-benzoquinone (LiM2DHDMQ⋅4H2O) compound, we have researched the occurrence of hydrogen ordering in a new polymorph at lower temperature. The study of polymorphism for the Li2DHDMQ⋅4H2O phase employs both experimental (single crystal X-ray diffraction) and theoretical approaches. While clues for disorder over one bridging water molecule were observed at RT (beta-form),a fully ordered model within a supercell has been evidenced at 100K (alpha-form) and is discussed in conjunction with the features characterizing the first polymorphic form reported previously. Density functional theory (DFT) calculations augmented with an empirical dispersion correction (DFT-D) were applied for the prediction of the structural and chemical bonding properties of the alpha and beta polymorphs of Li2DHDMQ·4H2O. The relative stability of the two polymorphic systems is evidenced. An insight into the interplay of hydrogen bonding, electrostatic and van der Waals (vdW) interactions in affecting the properties of the two polymorphs is gained. This study also shows how information from DFT-D calculations can be used to augment the information from the experimental crystal diffraction pattern and can so play an active role in crystal structure determination, especially by increasing the reliability and accuracy of H-positioning. These more accurate hydrogen coordinates allowed for a quantification of H-bonding strength through a topological analysis of the electron density (Atoms-in-molecules theory).
This post was instigated by Syracuse University Professor of Chemistry and well-known non-blogger Tim Korter concerning efforts to, I believe, generate proper Møller–Plesset Perturbation Theory Of The 4th Order (MP4, and also testing coupled cluster CCSD(T) calculations) intermolecular potentials for improving terms for Grimme dispersion-corrected density functional theory (DFT) calculations with the Gaussian09 package (a program for which many people grumble about various issues but which is, by nearly all metrics, a fantastic set of quantum chemical programs). The examples below, using water only, are just for ease-of-testing, which produce the following results based on the form of the input of the molecular coordinates. For those wondering why, z-matrices are the preferred format for performing SCAN or other automated trajectory calculations (an absolutely useless format, in my opinion, now that we have computers that can handle more than five atoms).
Now enjoying the benefits of dispersion-corrected solid-state density functional theory (and a proper MPICH2 implementation for infrared intensity calculations, although this now a problem for reasons to be addressed in an upcoming post) in Crystal09, three issues in recent calculations caused me to think hard enough about keyword formats and job runs that I have opted to post briefly about what to do in case google and bing are your preferred methods of manual searching.
1. How To Run Only A Single-Point Energy Calculation In Crystal06/Crystal09
This had never come up before and, by the time I needed to find an input file to see what do to, the first google search provided Civalleri’s Total Energy Calculation page that currently has broken links to .zip files. There is quite a bit about the different geometry optimization approaches in the manual, but a search for “single-point” provides no information about what to do for only single-point energy calculations.
Continue reading “Running (Only) A Single-Point Energy Calculation In Crystal06/09, Proper Input Format For Long-Range Dispersion Contributions In Crystal09, And Removing The MPICH2 Content From The Output File In Pcrystal”
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.
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.
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.
“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
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.